From 41ac8289dfe07446107fd4f2aeb4f84ba86e7680 Mon Sep 17 00:00:00 2001 From: Nathan Petersen Date: Mon, 5 Jun 2023 17:00:00 -0500 Subject: [PATCH 01/59] Add initial template of new docs control content per #77 --- .../current-control/continuous-time/cvcr/index.md | 1 + .../current-control/continuous-time/index.md | 12 ++++++++++++ .../current-control/continuous-time/sfpi/index.md | 3 +++ .../continuous-time/single-phase/index.md | 3 +++ .../continuous-time/three-phase/index.md | 3 +++ .../current-control/discrete-time/c2d/index.md | 3 +++ .../discrete-time/direct-digital-cvcr/index.md | 3 +++ .../current-control/discrete-time/index.md | 8 ++++++++ source/applications/current-control/index.md | 11 +++++++++++ .../load-modeling/dq-machine/index.md | 3 +++ .../current-control/load-modeling/index.md | 9 +++++++++ .../load-modeling/mp-winding/index.md | 3 +++ .../current-control/load-modeling/rl-load/index.md | 1 + source/applications/maglev-control/index.md | 3 +++ source/applications/speed-control/index.md | 3 +++ .../control-with-amdc/current-sensor-cal/index.md | 4 ++++ .../control-with-amdc/encoder-fb/index.md | 13 +++++++++++++ source/getting-started/control-with-amdc/index.md | 14 ++++++++++++++ .../integrator-anti-windup/index.md | 9 +++++++++ .../control-with-amdc/inv-pwm-dt-comp/index.md | 6 ++++++ .../control-with-amdc/simulink-code-gen/index.md | 3 +++ source/index.rst | 9 +++++++++ 22 files changed, 127 insertions(+) create mode 100644 source/applications/current-control/continuous-time/cvcr/index.md create mode 100644 source/applications/current-control/continuous-time/index.md create mode 100644 source/applications/current-control/continuous-time/sfpi/index.md create mode 100644 source/applications/current-control/continuous-time/single-phase/index.md create mode 100644 source/applications/current-control/continuous-time/three-phase/index.md create mode 100644 source/applications/current-control/discrete-time/c2d/index.md create mode 100644 source/applications/current-control/discrete-time/direct-digital-cvcr/index.md create mode 100644 source/applications/current-control/discrete-time/index.md create mode 100644 source/applications/current-control/index.md create mode 100644 source/applications/current-control/load-modeling/dq-machine/index.md create mode 100644 source/applications/current-control/load-modeling/index.md create mode 100644 source/applications/current-control/load-modeling/mp-winding/index.md create mode 100644 source/applications/current-control/load-modeling/rl-load/index.md create mode 100644 source/applications/maglev-control/index.md create mode 100644 source/applications/speed-control/index.md create mode 100644 source/getting-started/control-with-amdc/current-sensor-cal/index.md create mode 100644 source/getting-started/control-with-amdc/encoder-fb/index.md create mode 100644 source/getting-started/control-with-amdc/index.md create mode 100644 source/getting-started/control-with-amdc/integrator-anti-windup/index.md create mode 100644 source/getting-started/control-with-amdc/inv-pwm-dt-comp/index.md create mode 100644 source/getting-started/control-with-amdc/simulink-code-gen/index.md diff --git a/source/applications/current-control/continuous-time/cvcr/index.md b/source/applications/current-control/continuous-time/cvcr/index.md new file mode 100644 index 00000000..86a85b8d --- /dev/null +++ b/source/applications/current-control/continuous-time/cvcr/index.md @@ -0,0 +1 @@ +# Complex Vector Current Regulator (CVCR) \ No newline at end of file diff --git a/source/applications/current-control/continuous-time/index.md b/source/applications/current-control/continuous-time/index.md new file mode 100644 index 00000000..e8e3cc94 --- /dev/null +++ b/source/applications/current-control/continuous-time/index.md @@ -0,0 +1,12 @@ +# Continuous-Time Control + +Foo bar + +```{toctree} +:hidden: + +Single-Phase +Three-Phase +sfpi/index +cvcr/index +``` \ No newline at end of file diff --git a/source/applications/current-control/continuous-time/sfpi/index.md b/source/applications/current-control/continuous-time/sfpi/index.md new file mode 100644 index 00000000..819571e8 --- /dev/null +++ b/source/applications/current-control/continuous-time/sfpi/index.md @@ -0,0 +1,3 @@ +# Synchronous Frame PI (SFPI) Current Regulation + +Foo bar \ No newline at end of file diff --git a/source/applications/current-control/continuous-time/single-phase/index.md b/source/applications/current-control/continuous-time/single-phase/index.md new file mode 100644 index 00000000..0e095f17 --- /dev/null +++ b/source/applications/current-control/continuous-time/single-phase/index.md @@ -0,0 +1,3 @@ +# Single-Phase Current Regulation + +Foo bar \ No newline at end of file diff --git a/source/applications/current-control/continuous-time/three-phase/index.md b/source/applications/current-control/continuous-time/three-phase/index.md new file mode 100644 index 00000000..c4447fac --- /dev/null +++ b/source/applications/current-control/continuous-time/three-phase/index.md @@ -0,0 +1,3 @@ +# Three-Phase Current Regulation + +Foo bar \ No newline at end of file diff --git a/source/applications/current-control/discrete-time/c2d/index.md b/source/applications/current-control/discrete-time/c2d/index.md new file mode 100644 index 00000000..be440135 --- /dev/null +++ b/source/applications/current-control/discrete-time/c2d/index.md @@ -0,0 +1,3 @@ +# Continuous-to-Discrete Approximations + +Foo bar \ No newline at end of file diff --git a/source/applications/current-control/discrete-time/direct-digital-cvcr/index.md b/source/applications/current-control/discrete-time/direct-digital-cvcr/index.md new file mode 100644 index 00000000..b934e87e --- /dev/null +++ b/source/applications/current-control/discrete-time/direct-digital-cvcr/index.md @@ -0,0 +1,3 @@ +# Direct Digital CVCR + +Foo bar \ No newline at end of file diff --git a/source/applications/current-control/discrete-time/index.md b/source/applications/current-control/discrete-time/index.md new file mode 100644 index 00000000..111d7f0c --- /dev/null +++ b/source/applications/current-control/discrete-time/index.md @@ -0,0 +1,8 @@ +# Discrete-Time Control + +```{toctree} +:hidden: + +c2d/index +direct-digital-cvcr/index +``` \ No newline at end of file diff --git a/source/applications/current-control/index.md b/source/applications/current-control/index.md new file mode 100644 index 00000000..23251a1c --- /dev/null +++ b/source/applications/current-control/index.md @@ -0,0 +1,11 @@ +# Current Control + +Foo bar + +```{toctree} +:hidden: + +load-modeling/index +continuous-time/index +discrete-time/index +``` \ No newline at end of file diff --git a/source/applications/current-control/load-modeling/dq-machine/index.md b/source/applications/current-control/load-modeling/dq-machine/index.md new file mode 100644 index 00000000..8c7c14a9 --- /dev/null +++ b/source/applications/current-control/load-modeling/dq-machine/index.md @@ -0,0 +1,3 @@ +# DQ Machine Model + +Foo bar diff --git a/source/applications/current-control/load-modeling/index.md b/source/applications/current-control/load-modeling/index.md new file mode 100644 index 00000000..441b005b --- /dev/null +++ b/source/applications/current-control/load-modeling/index.md @@ -0,0 +1,9 @@ +# Load Modeling + +```{toctree} +:hidden: + +rl-load/index +dq-machine/index +mp-winding/index +``` \ No newline at end of file diff --git a/source/applications/current-control/load-modeling/mp-winding/index.md b/source/applications/current-control/load-modeling/mp-winding/index.md new file mode 100644 index 00000000..8e31b609 --- /dev/null +++ b/source/applications/current-control/load-modeling/mp-winding/index.md @@ -0,0 +1,3 @@ +# Multi-Phase Winding + +Introduce generalized Clarke transform and how to apply it to $m$ phase windings, decoupled subspaces, etc. \ No newline at end of file diff --git a/source/applications/current-control/load-modeling/rl-load/index.md b/source/applications/current-control/load-modeling/rl-load/index.md new file mode 100644 index 00000000..4ec7bcbd --- /dev/null +++ b/source/applications/current-control/load-modeling/rl-load/index.md @@ -0,0 +1 @@ +# RL Load Model \ No newline at end of file diff --git a/source/applications/maglev-control/index.md b/source/applications/maglev-control/index.md new file mode 100644 index 00000000..f4adc1b0 --- /dev/null +++ b/source/applications/maglev-control/index.md @@ -0,0 +1,3 @@ +# Maglev Displacement Control + +Basics of levitation systems, mechanical system stability via PID control. \ No newline at end of file diff --git a/source/applications/speed-control/index.md b/source/applications/speed-control/index.md new file mode 100644 index 00000000..7f684070 --- /dev/null +++ b/source/applications/speed-control/index.md @@ -0,0 +1,3 @@ +# Speed Control + +How to get a motor to spin at a desired speed using FOC? \ No newline at end of file diff --git a/source/getting-started/control-with-amdc/current-sensor-cal/index.md b/source/getting-started/control-with-amdc/current-sensor-cal/index.md new file mode 100644 index 00000000..2bfe373d --- /dev/null +++ b/source/getting-started/control-with-amdc/current-sensor-cal/index.md @@ -0,0 +1,4 @@ +# Current Sensor Calibration + +How to calibrate current sensor feedback + diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md new file mode 100644 index 00000000..842e3c27 --- /dev/null +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -0,0 +1,13 @@ +# Encoder Feedback + +## Calibration + +- Converting from raw counts to "theta" +- Direction: +/- depending on phase connections +- Sync machines: dq offset + +## Computing Speed from Position + +- LPF +- State Filter +- Observer \ No newline at end of file diff --git a/source/getting-started/control-with-amdc/index.md b/source/getting-started/control-with-amdc/index.md new file mode 100644 index 00000000..284fb6d8 --- /dev/null +++ b/source/getting-started/control-with-amdc/index.md @@ -0,0 +1,14 @@ +# Control with AMDC + +Foo bar + + +```{toctree} +:hidden: + +current-sensor-cal/index +inv-pwm-dt-comp/index +encoder-fb/index +integrator-anti-windup/index +simulink-code-gen/index +``` \ No newline at end of file diff --git a/source/getting-started/control-with-amdc/integrator-anti-windup/index.md b/source/getting-started/control-with-amdc/integrator-anti-windup/index.md new file mode 100644 index 00000000..f35afa77 --- /dev/null +++ b/source/getting-started/control-with-amdc/integrator-anti-windup/index.md @@ -0,0 +1,9 @@ +# Integrator Anti-Windup + +- How to think about performance of anti-windup +- Different methods + - clamping + - back tracking +- Implementation (continuous/discrete-time) + - Simulink + - Handwritten C code \ No newline at end of file diff --git a/source/getting-started/control-with-amdc/inv-pwm-dt-comp/index.md b/source/getting-started/control-with-amdc/inv-pwm-dt-comp/index.md new file mode 100644 index 00000000..32787da4 --- /dev/null +++ b/source/getting-started/control-with-amdc/inv-pwm-dt-comp/index.md @@ -0,0 +1,6 @@ +# Inverter PWM Dead-Time Compensation + +- Sources of non-linearity + - Dead-time +- How to do +- Example results \ No newline at end of file diff --git a/source/getting-started/control-with-amdc/simulink-code-gen/index.md b/source/getting-started/control-with-amdc/simulink-code-gen/index.md new file mode 100644 index 00000000..5500ece9 --- /dev/null +++ b/source/getting-started/control-with-amdc/simulink-code-gen/index.md @@ -0,0 +1,3 @@ +# Simulink Control Code Generation + +This should basically be a port of the AMDC-Examples autogen docs, examples, etc \ No newline at end of file diff --git a/source/index.rst b/source/index.rst index d203ae6c..f16c1a45 100644 --- a/source/index.rst +++ b/source/index.rst @@ -21,6 +21,15 @@ AMDC Platform Documentation getting-started/onboarding getting-started/tutorials/index getting-started/user-guide/index + getting-started/control-with-amdc/index + +.. toctree:: + :hidden: + :caption: Applications + + applications/current-control/index + applications/speed-control/index + applications/maglev-control/index .. toctree:: :hidden: From 084135bd4c8b58a7d3a164e1feb5413e4d790de1 Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Sat, 20 Jan 2024 15:14:01 +0530 Subject: [PATCH 02/59] initial commit --- source/getting-started/control-with-amdc/encoder-fb/index.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 842e3c27..6fe2179a 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -10,4 +10,6 @@ - LPF - State Filter -- Observer \ No newline at end of file +- Observer + +Anirudh will added content here... \ No newline at end of file From ddbc2b9a75cf041d97805ff5ca775bb655671e46 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Mon, 25 Mar 2024 11:30:52 -0500 Subject: [PATCH 03/59] Update index.md --- .../current-control/load-modeling/rl-load/index.md | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/source/applications/current-control/load-modeling/rl-load/index.md b/source/applications/current-control/load-modeling/rl-load/index.md index 4ec7bcbd..5881c553 100644 --- a/source/applications/current-control/load-modeling/rl-load/index.md +++ b/source/applications/current-control/load-modeling/rl-load/index.md @@ -1 +1,9 @@ -# RL Load Model \ No newline at end of file +# RL Load Model + +Single phase RL load. Content from the lecture series on RL load. This will be a short note. +- Circuit diagram +- Governing differential equation relating V and I +- Transfer function in Laplace domain relating V and I +- Summarize as plant that a controller could use. + + From d2652bf706485cc4a9f7f0cc1a2675a4938b708c Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Thu, 6 Jun 2024 00:21:36 -0500 Subject: [PATCH 04/59] Add content --- source/getting-started/control-with-amdc/encoder-fb/index.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 6fe2179a..62ec9dfc 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -1,5 +1,9 @@ # Encoder Feedback +## Background + +Encoders provide the rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the contrl algorithm. Consequently, few techniques to derive the rotor speed from the measured position is also proposed. For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). + ## Calibration - Converting from raw counts to "theta" From 1f1b8a018a870e40c06da1ba0fe62faa58d3de58 Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Wed, 19 Jun 2024 00:41:43 -0500 Subject: [PATCH 05/59] Update docs --- .../control-with-amdc/encoder-fb/index.md | 67 +++++++++++++++++++ 1 file changed, 67 insertions(+) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 62ec9dfc..82d49e6e 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -6,6 +6,73 @@ Encoders provide the rotor position feedback to the control system in a motor dr ## Calibration +Incremental encoders which are typically used with AMDC have a fixed number of counts per revolution (for example, 1024) and is denoted by `CPR`. The user needs needs to convert the count into usable angular information which maybe used in the code. + +### Converting from raw counts to angle information + +As a first step, the user may use the AMDC `enc` driver function `encoder_get_position()` to get the count of the encoder reading. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft, if it is feasible. This document assumes a positive rotor angular position in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. Care must be taken by the user to ensure that angle is within the bounds of `0` and `2 $\pi$` by appropriately wrapping the variable. + +Example code for when encoder count is increasing with CCW rotation of shaft: +```C +double task_get_theta_m(void) +{ + // Get raw encoder position + uint32_t position; + encoder_get_position(&position); + + // Encoder count per revolution + ENCODER_COUNT_PER_REV = 1024; + + // Angular position to be computed + double theta_m_enc; + + enc_theta_m_offset = 100; + + // Convert to radians + theta_m_enc = (double) PI2 * ( ( (double)position - enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); + + // Wrapping to ensure within bounds + while (theta_m_enc < 0) { + theta_m_enc += PI2; + } + return theta_m_enc; +} +``` + +Example code for when encoder count is decreasing with CCW rotation of shaft: +```C +double task_get_theta_m(void) +{ + // Get raw encoder position + uint32_t position; + encoder_get_position(&position); + + // Encoder count per revolution + ENCODER_COUNT_PER_REV = 1024; + + // Angular position to be computed + double theta_m_enc; + + enc_theta_m_offset = 100; + + // Convert to radians + theta_m_enc = (double) PI2 * ( ( (double)ENCODER_COUNT_PER_REV - (double)1 -(double)position + enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); + + + // Wrapping to ensure within bounds + while (theta_m_enc > PI2) { + theta_m_enc -= PI2; + } + return theta_m_enc; +} +``` + +### Finding the offset + +The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the rotor d-axis is aligned with the phase U of the stator. + +To get the rotor to align with the phase U of stator the user may have some current flow through phase U and out of phase V and phase W. Alternately, the user may also inject some Id current with the AMDC injection function but with the rotot position set to 0. + - Converting from raw counts to "theta" - Direction: +/- depending on phase connections - Sync machines: dq offset From d81c6918248b94f70c630e9842c667fd56be75ad Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Mon, 24 Jun 2024 01:00:48 -0500 Subject: [PATCH 06/59] Update doc --- .../control-with-amdc/encoder-fb/index.md | 69 ++++++++++--------- 1 file changed, 35 insertions(+), 34 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 82d49e6e..1a202210 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -10,9 +10,9 @@ Incremental encoders which are typically used with AMDC have a fixed number of c ### Converting from raw counts to angle information -As a first step, the user may use the AMDC `enc` driver function `encoder_get_position()` to get the count of the encoder reading. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft, if it is feasible. This document assumes a positive rotor angular position in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. Care must be taken by the user to ensure that angle is within the bounds of `0` and `2 $\pi$` by appropriately wrapping the variable. +As a first step, the user may use the AMDC `enc` driver function `encoder_get_position()` to get the count of the encoder reading. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and logging the position reported. This document assumes a positive rotor angular position in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. Care must be taken by the user to ensure that angle is within the bounds of 0 and 2 $\pi$ by appropriately wrapping the variable. -Example code for when encoder count is increasing with CCW rotation of shaft: +Example code to convert encoder to angular position in radians: ```C double task_get_theta_m(void) { @@ -20,58 +20,53 @@ double task_get_theta_m(void) uint32_t position; encoder_get_position(&position); - // Encoder count per revolution + int ENCODER_COUNT_PER_REV, CCW; + double enc_theta_m_offset; + + // User to set encoder count per revolution ENCODER_COUNT_PER_REV = 1024; + // Set 1 if encoder count increases with CCW rotation of shaft, Set 0 if encoder count increases with CW rotation of shaft + CCW = 1; + // Angular position to be computed double theta_m_enc; + // User to set encoder offset enc_theta_m_offset = 100; - // Convert to radians - theta_m_enc = (double) PI2 * ( ( (double)position - enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); - // Wrapping to ensure within bounds - while (theta_m_enc < 0) { - theta_m_enc += PI2; + // Convert to radians + if (CCW){ + theta_m_enc = (double) PI2 * ( ( (double)position - enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); } + else{ + theta_m_enc = (double) PI2 * ( ( (double)ENCODER_COUNT_PER_REV - (double)1 -(double)position + enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); + } + + // Mod by 2 pi + theta_m_enc = fmod(theta_m_enc,PI2 ); return theta_m_enc; } ``` -Example code for when encoder count is decreasing with CCW rotation of shaft: -```C -double task_get_theta_m(void) -{ - // Get raw encoder position - uint32_t position; - encoder_get_position(&position); - // Encoder count per revolution - ENCODER_COUNT_PER_REV = 1024; - - // Angular position to be computed - double theta_m_enc; - enc_theta_m_offset = 100; - - // Convert to radians - theta_m_enc = (double) PI2 * ( ( (double)ENCODER_COUNT_PER_REV - (double)1 -(double)position + enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); +### Finding the offset +The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the rotor d-axis is aligned with the phase U of the stator. - // Wrapping to ensure within bounds - while (theta_m_enc > PI2) { - theta_m_enc -= PI2; - } - return theta_m_enc; -} -``` +To get the rotor to align with the phase U of stator the user may have some current flow through phase U and out of phase V and phase W. Alternately, the user may also inject some current along the d-axis using the AMDC injection function but with the rotor position overridden by the user to 0. After obtaining the offset, the user needs to set the variable `enc_theta_m_offset` to the appropirate value in the `task_get_theta_m()` function. -### Finding the offset +The encoder offset maybe validated during operation of a permanent magnet synchrnous motor as follows: +1. Spin the motor up-to a steady speed under no load conditions +1. Measure the d-axis voltage commanded by the current regulator +1. Repeat the experiment for a few different motor speeds +1. Plot the d-axis voltage against the motor speed +1. The d-axis voltage if the offset is tuned correctly should be close to zero for all speeds. +1. In-case there is an error in the offset value, a significant speed dependent voltage will appear on the d-axis voltage -The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the rotor d-axis is aligned with the phase U of the stator. -To get the rotor to align with the phase U of stator the user may have some current flow through phase U and out of phase V and phase W. Alternately, the user may also inject some Id current with the AMDC injection function but with the rotot position set to 0. - Converting from raw counts to "theta" - Direction: +/- depending on phase connections @@ -79,6 +74,12 @@ To get the rotor to align with the phase U of stator the user may have some curr ## Computing Speed from Position +The user needs to compute a rotor speed signal from the obtained position signal to be used in the control algorithm. There are several ways to do this. A simple and straightforward way to do this would be to compute the discrete time derivative of the position signal in the controller as shown below. This can be referred to as $\Omega_{raw}$. + + +$\Omega_{raw}$ will be a choppy signal due to the derivative operation. A low pass filter may be applied to this signal as shown below to a filtered speed, $\Omega_{lpf}$. The user may select an appropriate bandwidth for the low pass filter. However, this signal will always be a lagging estimate of the actual rotor speed due to low pass filter characterstics. + +An observer which implements a mechanical model of the rotor as shown below will produce a no-lag estimate of the rotor speed. - LPF - State Filter - Observer From e0fbf68fe1ba721915a846f12e7ca7771aba5d6d Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Wed, 26 Jun 2024 00:27:27 -0500 Subject: [PATCH 07/59] Update docs --- .../control-with-amdc/encoder-fb/index.md | 47 +- .../resources/EncoderCodeBlockDiargam.svg | 257 +++++++ .../encoder-fb/resources/ObserverFigure.svg | 635 ++++++++++++++++++ 3 files changed, 920 insertions(+), 19 deletions(-) create mode 100644 source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg create mode 100644 source/getting-started/control-with-amdc/encoder-fb/resources/ObserverFigure.svg diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 1a202210..13bcd9de 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -2,15 +2,17 @@ ## Background -Encoders provide the rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the contrl algorithm. Consequently, few techniques to derive the rotor speed from the measured position is also proposed. For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). +Encoders provide rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the contrl algorithm. Consequently, few techniques to derive the rotor speed from the measured position are also proposed. For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). ## Calibration -Incremental encoders which are typically used with AMDC have a fixed number of counts per revolution (for example, 1024) and is denoted by `CPR`. The user needs needs to convert the count into usable angular information which maybe used in the code. +Incremental encoders which are typically used with AMDC have a fixed number of counts per revolution (for example, 1024) and is denoted by `CPR`. The user needs needs to write some code to obtaine the encoder count at a given instance and tconvert the count into usable angular information which can be used within the control code. -### Converting from raw counts to angle information +### Obtaining encoder count and translating it into rotor position -As a first step, the user may use the AMDC `enc` driver function `encoder_get_position()` to get the count of the encoder reading. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and logging the position reported. This document assumes a positive rotor angular position in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. Care must be taken by the user to ensure that angle is within the bounds of 0 and 2 $\pi$ by appropriately wrapping the variable. + + +As a first step, the user may use the AMDC `enc` driver function `encoder_get_position()` to get the count of the encoder reading. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. This document follows the convention of a positive rotor angle in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. The user must ensure that angle is within the bounds of 0 and 2 $\pi$ by appropriately wrapping the variable using the `mod` function. Example code to convert encoder to angular position in radians: ```C @@ -41,7 +43,7 @@ double task_get_theta_m(void) theta_m_enc = (double) PI2 * ( ( (double)position - enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); } else{ - theta_m_enc = (double) PI2 * ( ( (double)ENCODER_COUNT_PER_REV - (double)1 -(double)position + enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); + theta_m_enc = (double) PI2 * ( ( (double)ENCODER_COUNT_PER_REV - (double)1 -(double)position + enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); } // Mod by 2 pi @@ -54,34 +56,41 @@ double task_get_theta_m(void) ### Finding the offset -The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the rotor d-axis is aligned with the phase U of the stator. +The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the d-axis of the rotor is aligned with the phase U winding of the stator. + +To get the rotor to align with the phase U winding, the user may have some current flow through phase U and out of phase V and phase W. This can done by using a DC supply, with phase U connected to the positive terminal and phases V and W connected to the negative terminal. Alternately, the user may also inject some current along the d-axis using the AMDC injection function, but with the rotor position overridden by the user to 0. After obtaining the offset, the user needs to set the variable `enc_theta_m_offset` to the appropirate value in the `task_get_theta_m()` function. -To get the rotor to align with the phase U of stator the user may have some current flow through phase U and out of phase V and phase W. Alternately, the user may also inject some current along the d-axis using the AMDC injection function but with the rotor position overridden by the user to 0. After obtaining the offset, the user needs to set the variable `enc_theta_m_offset` to the appropirate value in the `task_get_theta_m()` function. +To ensure that the obtained encoder offset is correct, the user may perform additional validation. For a permanent magnet synchronous motor, this can be done as follows: -The encoder offset maybe validated during operation of a permanent magnet synchrnous motor as follows: 1. Spin the motor up-to a steady speed under no load conditions 1. Measure the d-axis voltage commanded by the current regulator 1. Repeat the experiment for a few different motor speeds 1. Plot the d-axis voltage against the motor speed -1. The d-axis voltage if the offset is tuned correctly should be close to zero for all speeds. +1. The d-axis voltage if the offset is tuned correctly, should be close to zero for all speeds. 1. In-case there is an error in the offset value, a significant speed dependent voltage will appear on the d-axis voltage -- Converting from raw counts to "theta" -- Direction: +/- depending on phase connections -- Sync machines: dq offset - ## Computing Speed from Position The user needs to compute a rotor speed signal from the obtained position signal to be used in the control algorithm. There are several ways to do this. A simple and straightforward way to do this would be to compute the discrete time derivative of the position signal in the controller as shown below. This can be referred to as $\Omega_{raw}$. +$$ +\Omega_\text{raw}[k] = \frac{\theta_m[k] - \theta_m[k-1]}{T_s} +$$ + + +$\Omega_\text{raw}$ will be a choppy and noisy signal due to the derivative operation. A low pass filter may be applied to this signal as shown below to get a filtered speed, $\Omega_\text{lpf}$. The user may select an appropriate bandwidth, $\omega_b$ for the low pass filter to eliminate the noise introduced by the derivative operation. However, this signal will always be a lagging estimate of the actual rotor speed due to the characterstics of a low pass filter. + +$$ + \Omega_\text{lpf}[k] = \Omega_\text{raw}[k](1 - e^{\omega_b T_s}) + \Omega_\text{lpf}[k-1]e^{\omega_b T_s} +$$ +An observer which implements a mechanical model of the rotor as shown below will produce a no-lag estimate of the rotor speed, denoted by $\Omega_\text{sf}$. To implement an observer, the user needs to know the system parameters - `J` - the inertia of the rotor shaft and `b` - the damping coefficient of the rotor shaft. Further, to obtain a no-lag estimate it is necessary to provide the electromechanical torque, $T_{em}$ as input to the mechanical model. The `P-I` part of the observer closes the loop on the speed with $\Omega_\text{raw}$ being the reference input. The recommended tuning approach is as follows: -$\Omega_{raw}$ will be a choppy signal due to the derivative operation. A low pass filter may be applied to this signal as shown below to a filtered speed, $\Omega_{lpf}$. The user may select an appropriate bandwidth for the low pass filter. However, this signal will always be a lagging estimate of the actual rotor speed due to low pass filter characterstics. +$$ +K_p = \omega_{sf}b, K_i = \omega_{sf}J +$$ -An observer which implements a mechanical model of the rotor as shown below will produce a no-lag estimate of the rotor speed. -- LPF -- State Filter -- Observer +This tuning ensures a pole zero cancellation in the closed transfer function, resulting in a unity transfer function for speed tracking under ideal parameter estimates of `J` and `b` -Anirudh will added content here... \ No newline at end of file + diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg b/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg new file mode 100644 index 00000000..8e5f6b1a --- /dev/null +++ b/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg @@ -0,0 +1,257 @@ + + + + + + + + + + + + + + + + + Determineencoder counts per revolution + Determineencoder offset + Determinedirectionality of encoder count + task_get_theta_m() + Get encodercount usingencoder_get_position()function + + + + + + θm + A,B,Z pulses + + diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/ObserverFigure.svg b/source/getting-started/control-with-amdc/encoder-fb/resources/ObserverFigure.svg new file mode 100644 index 00000000..6306e1a2 --- /dev/null +++ b/source/getting-started/control-with-amdc/encoder-fb/resources/ObserverFigure.svg @@ -0,0 +1,635 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Ki + + + + + 1 + s + + + + + + + + + + + + + + + + + + 1 + J + + + + + + + + + + b + + + + Kp + + + + + + + + + + + + + + + 1 + s + + + + + + + + + + + + + + + + + + + + + + + + Ωraw + Ωsf + Tem + + From cbc72d10a6603fac6419295ea4ca2a4e38362f3e Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Wed, 26 Jun 2024 00:28:57 -0500 Subject: [PATCH 08/59] Update docs --- source/getting-started/control-with-amdc/encoder-fb/index.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 13bcd9de..d703a3b5 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -10,7 +10,7 @@ Incremental encoders which are typically used with AMDC have a fixed number of c ### Obtaining encoder count and translating it into rotor position - + As a first step, the user may use the AMDC `enc` driver function `encoder_get_position()` to get the count of the encoder reading. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. This document follows the convention of a positive rotor angle in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. The user must ensure that angle is within the bounds of 0 and 2 $\pi$ by appropriately wrapping the variable using the `mod` function. @@ -74,6 +74,7 @@ To ensure that the obtained encoder offset is correct, the user may perform addi ## Computing Speed from Position The user needs to compute a rotor speed signal from the obtained position signal to be used in the control algorithm. There are several ways to do this. A simple and straightforward way to do this would be to compute the discrete time derivative of the position signal in the controller as shown below. This can be referred to as $\Omega_{raw}$. + $$ \Omega_\text{raw}[k] = \frac{\theta_m[k] - \theta_m[k-1]}{T_s} $$ @@ -93,4 +94,4 @@ $$ This tuning ensures a pole zero cancellation in the closed transfer function, resulting in a unity transfer function for speed tracking under ideal parameter estimates of `J` and `b` - + From 655f2b18976961e11d609572cea6ce36f7a0e5bc Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Fri, 28 Jun 2024 16:11:05 -0500 Subject: [PATCH 09/59] Update doc --- .../control-with-amdc/encoder-fb/index.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index d703a3b5..47617e66 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -6,13 +6,13 @@ Encoders provide rotor position feedback to the control system in a motor drive. ## Calibration -Incremental encoders which are typically used with AMDC have a fixed number of counts per revolution (for example, 1024) and is denoted by `CPR`. The user needs needs to write some code to obtaine the encoder count at a given instance and tconvert the count into usable angular information which can be used within the control code. +Incremental encoders which are typically used with AMDC have a fixed number of counts per revolution (for example, 1024) and is denoted by `CPR`. The user needs needs to write some code to obtain the encoder count at a given instance and convert the count into usable angular information which can be used within the control code. ### Obtaining encoder count and translating it into rotor position -As a first step, the user may use the AMDC `enc` driver function `encoder_get_position()` to get the count of the encoder reading. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. This document follows the convention of a positive rotor angle in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. The user must ensure that angle is within the bounds of 0 and 2 $\pi$ by appropriately wrapping the variable using the `mod` function. +As a first step, the user may use the AMDC `drv/encoder` driver module `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted the rotor position in radians. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. This document follows the convention of a positive rotor angle in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. The user must ensure that angle is within the bounds of 0 and 2 $\pi$ by appropriately wrapping the variable using the `mod` function. Example code to convert encoder to angular position in radians: ```C @@ -56,9 +56,9 @@ double task_get_theta_m(void) ### Finding the offset -The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the d-axis of the rotor is aligned with the phase U winding of the stator. +The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the d-axis of the rotor is aligned with the phase U winding axis of the stator. -To get the rotor to align with the phase U winding, the user may have some current flow through phase U and out of phase V and phase W. This can done by using a DC supply, with phase U connected to the positive terminal and phases V and W connected to the negative terminal. Alternately, the user may also inject some current along the d-axis using the AMDC injection function, but with the rotor position overridden by the user to 0. After obtaining the offset, the user needs to set the variable `enc_theta_m_offset` to the appropirate value in the `task_get_theta_m()` function. +To get the rotor to align with the phase U winding, the user may have some current flow through phase U and out of phase V and phase W. This can done by using a DC supply, with phase U connected to the positive terminal and phases V and W connected to the negative terminal. Alternately, the user may also inject some current along the d-axis using the AMDC [Signal Injection](https://docs.amdc.dev/getting-started/user-guide/injection/index.html) module. While injecting d-axis current, the user must ensure that the rotor position is set to zero in the control code. After obtaining the offset, the user needs to set the variable `enc_theta_m_offset` to the appropriate value in the `task_get_theta_m()` function. To ensure that the obtained encoder offset is correct, the user may perform additional validation. For a permanent magnet synchronous motor, this can be done as follows: @@ -80,7 +80,7 @@ $$ $$ -$\Omega_\text{raw}$ will be a choppy and noisy signal due to the derivative operation. A low pass filter may be applied to this signal as shown below to get a filtered speed, $\Omega_\text{lpf}$. The user may select an appropriate bandwidth, $\omega_b$ for the low pass filter to eliminate the noise introduced by the derivative operation. However, this signal will always be a lagging estimate of the actual rotor speed due to the characterstics of a low pass filter. +$\Omega_\text{raw}$ will be a choppy and noisy signal due to the derivative operation and the digital nature of the incremental encoder. A low pass filter may be applied to this signal as shown below to get a filtered speed, $\Omega_\text{lpf}$. The user may select an appropriate bandwidth, $\omega_b$ for the low pass filter to eliminate the noise introduced by the derivative operation. A recommended bandwidth for the low pass filter is 10 Hz. However, this signal will always be a lagging estimate of the actual rotor speed due to the characterstics of a low pass filter. $$ \Omega_\text{lpf}[k] = \Omega_\text{raw}[k](1 - e^{\omega_b T_s}) + \Omega_\text{lpf}[k-1]e^{\omega_b T_s} From cbd2100c5b2a9731aaa78d36ee1552f8732e0a78 Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Sun, 30 Jun 2024 09:21:46 -0500 Subject: [PATCH 10/59] Update block diagram --- .../control-with-amdc/encoder-fb/index.md | 6 +- .../resources/EncoderCodeBlockDiargam.svg | 527 +++++++++++++----- 2 files changed, 394 insertions(+), 139 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 47617e66..413334a5 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -12,7 +12,7 @@ Incremental encoders which are typically used with AMDC have a fixed number of c -As a first step, the user may use the AMDC `drv/encoder` driver module `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted the rotor position in radians. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. This document follows the convention of a positive rotor angle in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. The user must ensure that angle is within the bounds of 0 and 2 $\pi$ by appropriately wrapping the variable using the `mod` function. +As a first step, the user may use the AMDC `drv/encoder` driver module `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted the rotor position in radians. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. This document follows the convention of a positive rotor angle in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. The user must ensure that angle is within the bounds of 0 and 2$\pi$ by appropriately wrapping the variable using the `mod` function. Example code to convert encoder to angular position in radians: ```C @@ -80,7 +80,7 @@ $$ $$ -$\Omega_\text{raw}$ will be a choppy and noisy signal due to the derivative operation and the digital nature of the incremental encoder. A low pass filter may be applied to this signal as shown below to get a filtered speed, $\Omega_\text{lpf}$. The user may select an appropriate bandwidth, $\omega_b$ for the low pass filter to eliminate the noise introduced by the derivative operation. A recommended bandwidth for the low pass filter is 10 Hz. However, this signal will always be a lagging estimate of the actual rotor speed due to the characterstics of a low pass filter. +$\Omega_\text{raw}$ will be a choppy and noisy signal due to the derivative operation and the digital nature of the incremental encoder. A low pass filter may be applied to this signal as shown below to get a filtered speed, $\Omega_\text{lpf}$. The user may select an appropriate bandwidth, $\omega_b$ for the low pass filter to eliminate the noise introduced by the derivative operation. A recommended bandwidth for the low pass filter is 10 Hz. This would be a good bandwidth to try for the user. The user can reduce the bandwidth if the filtered signal still has signficant noise for the application. However, $\Omega_\text{lpf}$ will always be a lagging estimate of the actual rotor speed due to the characterstics of a low pass filter. $$ \Omega_\text{lpf}[k] = \Omega_\text{raw}[k](1 - e^{\omega_b T_s}) + \Omega_\text{lpf}[k-1]e^{\omega_b T_s} @@ -92,6 +92,6 @@ $$ K_p = \omega_{sf}b, K_i = \omega_{sf}J $$ -This tuning ensures a pole zero cancellation in the closed transfer function, resulting in a unity transfer function for speed tracking under ideal parameter estimates of `J` and `b` +This tuning ensures a pole zero cancellation in the closed transfer function, resulting in a unity transfer function for speed tracking under ideal parameter estimates of `J` and `b`. A recommended bandwidth for the observer is 10 Hz. diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg b/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg index 8e5f6b1a..9c3b51c1 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg +++ b/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg @@ -3,8 +3,8 @@ @@ -52,11 +52,11 @@ transform="scale(0.5)" style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:1pt" d="M 5.77,0 -2.88,5 V -5 Z" - id="path3250" /> + id="path135" /> + id="path135-7" /> + + + + + + + + + + + + + + + - - Determine + encoder counts per revolution + x="114.87061" + y="21.049625" + id="tspan2800" /> task_get_theta_m() + + + Get encodercount usingencoder_get_position()function + + + Determineencoder offset + x="203.05502" + y="18.744692" + id="tspan2672-3">θm Determinedirectionality of Encoder raw encoder count + x="10.457352" + y="24.011608" + id="tspan15343">signals + + + + 2π( (count - offset)/ENCODER_COUNT_PER_REV) + if CCW + else + 2π( (ENCODER_COUNT_PER_REV - 1 - count + offset)/ENCODER_COUNT_PER_REV) + + + + + + + + mod by 2π + + + + + + + task_get_theta_m() + style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:3.52778px;font-family:'Times New Roman';-inkscape-font-specification:'Times New Roman, Normal';font-variant-ligatures:normal;font-variant-caps:normal;font-variant-numeric:normal;font-variant-east-asian:normal;stroke-width:0.264583" + x="69.787239" + y="20.100161" + id="tspan2672-3-7-8">count Get encoderoffset* count using + encoder_get_position()ENCODER_COUNT_PER_REV* function - - - - - + style="stroke-width:0.264583" + x="38.037342" + y="49.542728" + id="tspan15336" /> rotor θm + x="166.22415" + y="19.171022" + id="tspan15372">position + * User input + CCW* A,B,Z pulses + x="57.219265" + y="59.622509" + id="tspan15340-4" /> From d971d20e660e859b4d48ab047cc4da4fd8f9d706 Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya <90214161+anirudhupadhyaya@users.noreply.github.com> Date: Sun, 30 Jun 2024 12:23:06 -0500 Subject: [PATCH 11/59] Apply suggestions from code review Co-authored-by: Eric Severson --- .../control-with-amdc/encoder-fb/index.md | 31 +++++++++++++++---- 1 file changed, 25 insertions(+), 6 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 413334a5..4a36c66b 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -6,7 +6,7 @@ Encoders provide rotor position feedback to the control system in a motor drive. ## Calibration -Incremental encoders which are typically used with AMDC have a fixed number of counts per revolution (for example, 1024) and is denoted by `CPR`. The user needs needs to write some code to obtain the encoder count at a given instance and convert the count into usable angular information which can be used within the control code. +Incremental encoders are typically used with the AMDC and have a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. ### Obtaining encoder count and translating it into rotor position @@ -73,25 +73,44 @@ To ensure that the obtained encoder offset is correct, the user may perform addi ## Computing Speed from Position -The user needs to compute a rotor speed signal from the obtained position signal to be used in the control algorithm. There are several ways to do this. A simple and straightforward way to do this would be to compute the discrete time derivative of the position signal in the controller as shown below. This can be referred to as $\Omega_{raw}$. +The user needs to compute a rotor speed signal from the obtained position signal to be used in the control algorithm. There are several ways to do this. + +### Difference Equation Approach + +A simple, but naive, way to do this would be to compute the discrete time derivative of the position signal in the controller as shown below. This can be referred to as $\Omega_{raw}$. $$ \Omega_\text{raw}[k] = \frac{\theta_m[k] - \theta_m[k-1]}{T_s} $$ -$\Omega_\text{raw}$ will be a choppy and noisy signal due to the derivative operation and the digital nature of the incremental encoder. A low pass filter may be applied to this signal as shown below to get a filtered speed, $\Omega_\text{lpf}$. The user may select an appropriate bandwidth, $\omega_b$ for the low pass filter to eliminate the noise introduced by the derivative operation. A recommended bandwidth for the low pass filter is 10 Hz. This would be a good bandwidth to try for the user. The user can reduce the bandwidth if the filtered signal still has signficant noise for the application. However, $\Omega_\text{lpf}$ will always be a lagging estimate of the actual rotor speed due to the characterstics of a low pass filter. +Unfortunately, using this approach results in noise in $\Omega_\text{raw}$ due to the derivative operation and the digital nature of the incremental encoder. + +### Low Pass Filter Approach + +To solve this, _a low pass filter_ may be applied to this signal. This is shown below to obtain a filtered speed, $\Omega_\text{lpf}$. $$ \Omega_\text{lpf}[k] = \Omega_\text{raw}[k](1 - e^{\omega_b T_s}) + \Omega_\text{lpf}[k-1]e^{\omega_b T_s} $$ -An observer which implements a mechanical model of the rotor as shown below will produce a no-lag estimate of the rotor speed, denoted by $\Omega_\text{sf}$. To implement an observer, the user needs to know the system parameters - `J` - the inertia of the rotor shaft and `b` - the damping coefficient of the rotor shaft. Further, to obtain a no-lag estimate it is necessary to provide the electromechanical torque, $T_{em}$ as input to the mechanical model. The `P-I` part of the observer closes the loop on the speed with $\Omega_\text{raw}$ being the reference input. The recommended tuning approach is as follows: +### Observer Approach + +To obtain a no-lag estimate of the rotor speed, users may create an observer which implements a mechanical model of the rotor as shown below. + + + +The estimate of rotor speed is denoted by $\Omega_\text{sf}$. To implement this observer, the user needs to know the system parameters: +- `J`: the inertia of the rotor +- `b` the damping coefficient of the rotor. + +It is also necessary to provide the electromechanical torque, $T_{em}$ as input to the mechanical model. + +The `PI` portion of the observer closes the loop on the speed, with $\Omega_\text{raw}$ being the reference input. The recommended tuning approach is as follows: $$ K_p = \omega_{sf}b, K_i = \omega_{sf}J $$ -This tuning ensures a pole zero cancellation in the closed transfer function, resulting in a unity transfer function for speed tracking under ideal parameter estimates of `J` and `b`. A recommended bandwidth for the observer is 10 Hz. +This tuning ensures a pole zero cancellation in the closed transfer function, resulting in a unity transfer function for speed tracking under ideal parameter estimates of `J` and `b`. An observer bandwidth of 10 Hz is typical of most systems, but similar to the low pass filter approach, users may need to alter this based on the unique aspects of their system. - From 63600c65d2a44e5a57752b17e5d80587119f9578 Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Sun, 30 Jun 2024 13:42:56 -0500 Subject: [PATCH 12/59] Update doc to address review comments --- .../control-with-amdc/encoder-fb/index.md | 34 +++++++++++++------ 1 file changed, 23 insertions(+), 11 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 4a36c66b..34b693a8 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -2,17 +2,23 @@ ## Background -Encoders provide rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the contrl algorithm. Consequently, few techniques to derive the rotor speed from the measured position are also proposed. For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). +Encoders provide rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the contrl algorithm. Next, useful methods to obtain rotor speed from the measured position is presented. For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). ## Calibration -Incremental encoders are typically used with the AMDC and have a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. +Incremental encoders are typically used with the AMDC and have a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. ### Obtaining encoder count and translating it into rotor position +The recommended approach to reading the shaft position from the encoder is illustrated in the figure below: + -As a first step, the user may use the AMDC `drv/encoder` driver module `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted the rotor position in radians. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done by manually rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. This document follows the convention of a positive rotor angle in the counter clockwise (CCW) direction of shaft rotation. Using this information, along with the offset and total encoder counts per revolution, the obtained count can be translated into angular position using a simple linear equation. The user must ensure that angle is within the bounds of 0 and 2$\pi$ by appropriately wrapping the variable using the `mod` function. +As a first step, the user may use the AMDC `drv/encoder` driver module `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted to rotor position in radians. + + Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done manually by rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. In the figure, the signal `CCW` indicates this directionality. It must be set to `1`, if the encoder count increases with the counter clockwise rotation of shaft and `0` otherwise. Additionally, the user needs to provide the encoder offset, `offset` and the encoder counts per revolution, `ENCODER_COUNT_PER_REV`. A method to get the value of offset is described in the next [subsection](#finding-the-offset). Using all of this quantities, the obtained count can be translated into angular position using a simple linear equation. Note that, this document follows the convention of a positive rotor angle in the counter clockwise direction of shaft rotation while caclulating rotor position from the count signal. + + Finally, the user must ensure that angle is within the bounds of $0$ and $2\pi$ by appropriately wrapping the `rotor position` signal using the `mod` function. This is shown in the final block in the diagram. Example code to convert encoder to angular position in radians: ```C @@ -47,7 +53,7 @@ double task_get_theta_m(void) } // Mod by 2 pi - theta_m_enc = fmod(theta_m_enc,PI2 ); + theta_m_enc = fmod(theta_m_enc,PI2); return theta_m_enc; } ``` @@ -56,18 +62,20 @@ double task_get_theta_m(void) ### Finding the offset -The example code shown above makes uses of an encoder offset value. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the d-axis of the rotor is aligned with the phase U winding axis of the stator. +The example code shown above makes uses of an encoder offset value, `enc_theta_m_offset`. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the d-axis of the rotor is aligned with the phase U winding axis of the stator. + +To determine the appropriate offset value, eliminate any source of load torque on the shaft and apply a large current vector at 0 degrees ($I_u = I_0$, $I_v = I_w = -\frac{1}{2} I_0$). This should cause the rotor to align with the phase U winding axis. The offset value can now be obtained as `enc_theta_m_offset = encoder_get_position()`. Alternately, the user may also inject a current along the d-axis using the AMDC [Signal Injection](https://docs.amdc.dev/getting-started/user-guide/injection/index.html) module. While injecting d-axis current, the user must ensure that the rotor position is set to zero in the control code. -To get the rotor to align with the phase U winding, the user may have some current flow through phase U and out of phase V and phase W. This can done by using a DC supply, with phase U connected to the positive terminal and phases V and W connected to the negative terminal. Alternately, the user may also inject some current along the d-axis using the AMDC [Signal Injection](https://docs.amdc.dev/getting-started/user-guide/injection/index.html) module. While injecting d-axis current, the user must ensure that the rotor position is set to zero in the control code. After obtaining the offset, the user needs to set the variable `enc_theta_m_offset` to the appropriate value in the `task_get_theta_m()` function. +After obtaining the offset, the user needs to set the variable `enc_theta_m_offset` to the appropriate value in the `task_get_theta_m()` function. To ensure that the obtained encoder offset is correct, the user may perform additional validation. For a permanent magnet synchronous motor, this can be done as follows: 1. Spin the motor up-to a steady speed under no load conditions 1. Measure the d-axis voltage commanded by the current regulator -1. Repeat the experiment for a few different motor speeds -1. Plot the d-axis voltage against the motor speed -1. The d-axis voltage if the offset is tuned correctly, should be close to zero for all speeds. -1. In-case there is an error in the offset value, a significant speed dependent voltage will appear on the d-axis voltage +1. Repeat the experiment for a few different rotor speeds +1. Plot the d-axis voltage against the rotor speed +1. The d-axis voltage should be close to zero for all speeds, if the offset is tuned correctly +1. In-case there is an error in the offset value, a significant speed dependent voltage will appear on the d-axis voltage. In this case, the user may have to re-measure the encoder offset. @@ -96,7 +104,7 @@ $$ ### Observer Approach -To obtain a no-lag estimate of the rotor speed, users may create an observer which implements a mechanical model of the rotor as shown below. +To obtain a no-lag estimate of the rotor speed, users may create an observer [[1]](#1), which implements a mechanical model of the rotor as shown below. @@ -114,3 +122,7 @@ $$ This tuning ensures a pole zero cancellation in the closed transfer function, resulting in a unity transfer function for speed tracking under ideal parameter estimates of `J` and `b`. An observer bandwidth of 10 Hz is typical of most systems, but similar to the low pass filter approach, users may need to alter this based on the unique aspects of their system. + +# References + 1. R. D. Lorenz and K. W. Van Patten, "High-resolution velocity estimation for all-digital, AC servo drives," in IEEE Transactions on Industry Applications, vol. 27, no. 4, pp. 701-705, July-Aug. 1991, doi: 10.1109/28.85485. keywords: {Servomechanisms;Optical feedback;Optical signal processing;Transducers;Signal resolution;Velocity measurement;Position control;Feedback loop;Velocity control;Noise reduction} + From 3a1ca7bf9e6a2a553e35a9022d5a3b1e41de6a69 Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya Date: Sun, 30 Jun 2024 18:39:44 -0500 Subject: [PATCH 13/59] Add line on low pass filter --- source/getting-started/control-with-amdc/encoder-fb/index.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 34b693a8..493bf6d3 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -102,6 +102,8 @@ $$ \Omega_\text{lpf}[k] = \Omega_\text{raw}[k](1 - e^{\omega_b T_s}) + \Omega_\text{lpf}[k-1]e^{\omega_b T_s} $$ +10 Hz is a good bandwidth for the low-pass filter to start with, but users may need to alter this based on the unique aspects of their system. However, this approach will always produce a lagging speed estimate. + ### Observer Approach To obtain a no-lag estimate of the rotor speed, users may create an observer [[1]](#1), which implements a mechanical model of the rotor as shown below. From 04c349060b11e8cf059ee4a14cbb43f42bbffcdd Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya <90214161+anirudhupadhyaya@users.noreply.github.com> Date: Sun, 30 Jun 2024 19:30:07 -0500 Subject: [PATCH 14/59] Update source/getting-started/control-with-amdc/encoder-fb/index.md Co-authored-by: Eric Severson --- source/getting-started/control-with-amdc/encoder-fb/index.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 493bf6d3..3a6d4c1d 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -102,7 +102,9 @@ $$ \Omega_\text{lpf}[k] = \Omega_\text{raw}[k](1 - e^{\omega_b T_s}) + \Omega_\text{lpf}[k-1]e^{\omega_b T_s} $$ -10 Hz is a good bandwidth for the low-pass filter to start with, but users may need to alter this based on the unique aspects of their system. However, this approach will always produce a lagging speed estimate. +Here, $T_{\rm s}$ is the control sample rate and $\omega_b$ is the low pass filter bandwidth. The user must select this bandwidth to obtain a sufficiently clean speed signal. The optimal bandwidth to use is going to vary based on the motor system. Typically, a bandwidth of 10 Hz is a reasonable starting point. This can be reduced if the speed signal remains too noisy, or increased for higher speed controls. + +Note that this low pass filter approach will always produce a lagging speed estimate due to phase delay in the filter transfer function. This may be unacceptable higher performance motor control algorithms. ### Observer Approach From 40243038701ae9a70cac7df13d31a061ceea29d3 Mon Sep 17 00:00:00 2001 From: Anirudh Upadhyaya <90214161+anirudhupadhyaya@users.noreply.github.com> Date: Mon, 1 Jul 2024 11:03:34 -0500 Subject: [PATCH 15/59] Add current sensor calibration documentation (#95) * Initial commit * Update readme * Update readme * Update readme * Add files * Update files * Changes * Changes * Update files * Get rif of scope image * Minor updates * Address review comments * Remove resources * Add back resources * Address review comments * Address review comments * Update index.md * Edit current sensor calibration method section * Edit calibration method section * Add section on Recalcilating current sensor offset * Clarify that we measure a voltage. * Edit conclusion * Update index.md * Update index.md * Address review comments * Update index.md * Update index.md * Update index.md * Apply suggestions from code review Co-authored-by: Eric Severson * Update source/getting-started/control-with-amdc/current-sensor-cal/index.md * Update source/getting-started/control-with-amdc/current-sensor-cal/index.md --------- Co-authored-by: Nathan Petersen Co-authored-by: Eric Severson --- .../current-sensor-cal/index.md | 56 +- ...urrent_sensor_calibration-checkpoint.ipynb | 243 ++++ .../current_sensor_calibration.ipynb | 243 ++++ .../resources/current_sensor_drawing.svg | 1145 +++++++++++++++++ .../current-sensor-cal/resources/exp_data.csv | 8 + .../current-sensor-cal/resources/fit.svg | 1117 ++++++++++++++++ 6 files changed, 2811 insertions(+), 1 deletion(-) create mode 100644 source/getting-started/control-with-amdc/current-sensor-cal/resources/.ipynb_checkpoints/current_sensor_calibration-checkpoint.ipynb create mode 100644 source/getting-started/control-with-amdc/current-sensor-cal/resources/current_sensor_calibration.ipynb create mode 100644 source/getting-started/control-with-amdc/current-sensor-cal/resources/current_sensor_drawing.svg create mode 100644 source/getting-started/control-with-amdc/current-sensor-cal/resources/exp_data.csv create mode 100644 source/getting-started/control-with-amdc/current-sensor-cal/resources/fit.svg diff --git a/source/getting-started/control-with-amdc/current-sensor-cal/index.md b/source/getting-started/control-with-amdc/current-sensor-cal/index.md index 2bfe373d..a835f55f 100644 --- a/source/getting-started/control-with-amdc/current-sensor-cal/index.md +++ b/source/getting-started/control-with-amdc/current-sensor-cal/index.md @@ -1,4 +1,58 @@ # Current Sensor Calibration -How to calibrate current sensor feedback +## Background +Motor drives typically require current sensors to provide feedback to the control system. This document describes a method to calibrate the current sensors to a linear model during commissioning of a motor drive. The calibration is characterized by two parameters, a gain and an offset, that describe how the sensed current appears as a voltage to the AMDC. + +Current sensors are transducers which produce an output signal (either current or voltage) proportional to the primary current flowing through the sensor. There are different types of current sensors relying on different physical phenomenons such as shunt resistors and hall-effect. For the purpose of this document, the specific type of sensor does not matter---just that the output signal is linear with the primary current, and that it is measured as a voltage by the control system. The current sensor needs to be calibrated against an appropriate reference before it can be used in the control system. This reference is a known, trusted current sensor, such as a precision digital multimeter (preferred), hall-effect current clamp, or the setpoint of a DC power supply. While the manufacturer datasheet provides nominal parameters, calibration of the current sensor is necessary to get accurate measurements to account for any deviation due to process variation. + +## Calibration Method + +A method is now provided to calibrate the current sensors in a motor drive. An example of the assumed system for a three phase motor is shown in the figure below. + + + +Typically, each phase has a current sensor associated with it that needs to be calibrated. This method assumes that the signal measured by the AMDC for each sensor is a voltage that must be converted into a current value. + +1. Connect the reference curent sensor (i.e. precision digital multimeter) to the phase U cable of the motor. +1. Set up your AMDC system to enable you to log the raw reading of the drive's current sensor attached to phase U (presumably, by sampling an ADC channel). It is recommended to use the AMDC's logging functionality so that data can be collected over a period of time (e.g. 100 ms) and post-processed to find the average value. +1. Record the drive's sensor reading when there is no current flowing through phase U. _Hint:_ remember to calculate this value as the average over a period of time. +1. Cause a "small" curent to flow through phase U (i.e., apply a voltage across phase U). The value of current is left to the discretion of the user based on the system nominal ratings. +1. Record the drive's sensor reading as well as the reference sensor's reading of the current flowing through the phase U cable. +1. Progressively increase the phase U current and record the readings. Do this over the full range of rated current, both positive and negative. +1. Tabulate the measurements as shown in this example [`exp_data.csv` file](./resources/exp_data.csv). +1. Fit a linear expression of the form $\text{Reading [V]} = \text{Gain [V/A]} \times \text{Current [A]} + \text{Offset [V]}$ to the obtained measurements. This [example Jupyter notebook](./resources/current_sensor_calibration.ipynb) is provided to illustrate the process. +1. Repeat the exercise for the remaining phases of the system. + +An example of the results are shown in the plot below. The obtained gain and offset can be used directly in the control code to convert the sensor reading into the actual current measurement. + + + + +```{tip} +Be sure to conduct the calibration process over the full range of current data (both positive and negative current) to account for any variation in the current sensor reading due to directionality of current. +``` +## Use of Calibration Data + +The below codeblock can be utilized by the user to convert between raw measurements from the sensor and the actual currents. + +```C +#define INV_GAIN (1.0/0.621) // Inverse of gain obtained from curve fit (1/0.621) +double offset = 4.739; // [V], offset from curve fit. This is a variable so that the drive can remeasure and adjust the offset at startup + +double current_measurement; // Actual current measurement, to be used in control algorithm + +current_measurement = (sensor_reading - offset)*INV_GAIN; // sensor_reading is the raw measurement and needs to be obtained by the user + +``` + +## Recalculate Offset At Startup +The offset value of the current sensors can drift over time. It is recommended that drive developers include code in their control logic to automatically re-zero the current sensor at startup, as follows: + +1. Prior to enabling the PWM, when it is known that there is no current flowing in the motor, record approximately 100 ms of sensor data on each phase. +2. For each phase, calculate the average of this data and use it as the new `offset` value in the code block above. +3. Proceed with starting-up the drive. + +## Conclusion + +The current sensor calibration method presented in this article should be viewed as a best-practice for motor drive development. Readers are welcome to directly use the provided code and Jupyter notebook in their motor drives. diff --git a/source/getting-started/control-with-amdc/current-sensor-cal/resources/.ipynb_checkpoints/current_sensor_calibration-checkpoint.ipynb b/source/getting-started/control-with-amdc/current-sensor-cal/resources/.ipynb_checkpoints/current_sensor_calibration-checkpoint.ipynb new file mode 100644 index 00000000..9fbd8ad8 --- /dev/null +++ b/source/getting-started/control-with-amdc/current-sensor-cal/resources/.ipynb_checkpoints/current_sensor_calibration-checkpoint.ipynb @@ -0,0 +1,243 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "125fae80", + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "df = pd.read_csv('exp_data.csv')" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1ba56894", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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Reference Current [A]Sensor Reading [V]
0-10.11-1.55
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\n", + "
" + ], + "text/plain": [ + " Reference Current [A] Sensor Reading [V]\n", + "0 -10.11 -1.55\n", + "1 -6.93 0.44\n", + "2 -2.15 3.42\n", + "3 0.00 4.70\n", + "4 2.95 6.60\n", + "5 6.06 8.53\n", + "6 9.44 10.58" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Lets look at the imported experimental data file\n", + "df" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "aab59367", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Sensor Reading [V]')" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(df['Reference Current [A]'], df['Sensor Reading [V]'], 'x')\n", + "plt.xlabel('Reference Current [A]')\n", + "plt.ylabel('Sensor Reading [V]')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1a6b2d9f", + "metadata": {}, + "outputs": [], + "source": [ + "# Lets fit a first order function to our experimental data\n", + "\n", + "x= np.polyfit(df['Reference Current [A]'],df['Sensor Reading [V]'],1 );" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b9be90e3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gain: 0.6213316322731629\n", + "Offset: 4.739969343983164\n" + ] + } + ], + "source": [ + "# Lets print out the gain and the offset\n", + "\n", + "print(\"Gain: \", x[0])\n", + "print(\"Offset: \", x[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "7d6aa0c3", + "metadata": {}, + "outputs": [], + "source": [ + "# Lets get an expression using the obtained gain and offset\n", + "\n", + "fit = df['Reference Current [A]']*x[0] + x[1];" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "c8253993", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Reference Current [A]Sensor Reading [V]
0-10.11-1.55
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\n", + "
" + ], + "text/plain": [ + " Reference Current [A] Sensor Reading [V]\n", + "0 -10.11 -1.55\n", + "1 -6.93 0.44\n", + "2 -2.15 3.42\n", + "3 0.00 4.70\n", + "4 2.95 6.60\n", + "5 6.06 8.53\n", + "6 9.44 10.58" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Lets look at the imported experimental data file\n", + "df" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "aab59367", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Sensor Reading [V]')" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(df['Reference Current [A]'], df['Sensor Reading [V]'], 'x')\n", + "plt.xlabel('Reference Current [A]')\n", + "plt.ylabel('Sensor Reading [V]')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1a6b2d9f", + "metadata": {}, + "outputs": [], + "source": [ + "# Lets fit a first order function to our experimental data\n", + "\n", + "x= np.polyfit(df['Reference Current [A]'],df['Sensor Reading [V]'],1 );" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b9be90e3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gain: 0.6213316322731629\n", + "Offset: 4.739969343983164\n" + ] + } + ], + "source": [ + "# Lets print out the gain and the offset\n", + "\n", + "print(\"Gain: \", x[0])\n", + "print(\"Offset: \", x[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "7d6aa0c3", + "metadata": {}, + "outputs": [], + "source": [ + "# Lets get an expression using the obtained gain and offset\n", + "\n", + "fit = df['Reference Current [A]']*x[0] + x[1];" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "c8253993", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(df['Reference Current [A]'], df['Sensor Reading [V]'], 'x')\n", + "plt.plot(df['Reference Current [A]'], fit)\n", + "plt.xlabel('Reference Current [A]')\n", + "plt.ylabel('Sensor Reading [V]')\n", + "plt.legend(['Raw data', 'Fit'])\n", + "plt.savefig('Fit.svg')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "03acc820", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/source/getting-started/control-with-amdc/current-sensor-cal/resources/current_sensor_drawing.svg b/source/getting-started/control-with-amdc/current-sensor-cal/resources/current_sensor_drawing.svg new file mode 100644 index 00000000..4c549c3b --- /dev/null +++ b/source/getting-started/control-with-amdc/current-sensor-cal/resources/current_sensor_drawing.svg @@ -0,0 +1,1145 @@ + + + +InductorInductorInductorInductorInductorInductorPhase UPhase VPhase WThree phase motorCurrent sensorMotor DriveVDCIu Iv Iw diff --git a/source/getting-started/control-with-amdc/current-sensor-cal/resources/exp_data.csv b/source/getting-started/control-with-amdc/current-sensor-cal/resources/exp_data.csv new file mode 100644 index 00000000..6564cb49 --- /dev/null +++ b/source/getting-started/control-with-amdc/current-sensor-cal/resources/exp_data.csv @@ -0,0 +1,8 @@ +Reference Current [A],Sensor Reading [V] +-10.11,-1.55 +-6.93,0.44 +-2.15,3.42 +0,4.7 +2.95,6.6 +6.06,8.53 +9.44,10.58 diff --git a/source/getting-started/control-with-amdc/current-sensor-cal/resources/fit.svg b/source/getting-started/control-with-amdc/current-sensor-cal/resources/fit.svg new file mode 100644 index 00000000..e690e36c --- /dev/null +++ b/source/getting-started/control-with-amdc/current-sensor-cal/resources/fit.svg @@ -0,0 +1,1117 @@ + + + + + + + + 2024-06-05T23:19:51.533373 + image/svg+xml + + + Matplotlib v3.5.3, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From 7bdd0aa9c11da1020725c980b78e88086c2d5766 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Fri, 1 Nov 2024 20:26:40 -0500 Subject: [PATCH 16/59] Edit background --- source/getting-started/control-with-amdc/encoder-fb/index.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 3a6d4c1d..b977a3ac 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -2,7 +2,9 @@ ## Background -Encoders provide rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the contrl algorithm. Next, useful methods to obtain rotor speed from the measured position is presented. For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). +Encoders provide rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the control algorithm. Methods to obtain rotor speed from the measured position are also presented. + +For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). ## Calibration From c249ab3d82dc4a07dbaa80dbc7b371feb3bd4d8b Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Fri, 1 Nov 2024 20:27:18 -0500 Subject: [PATCH 17/59] Fix file name type-o --- source/getting-started/control-with-amdc/encoder-fb/index.md | 2 +- ...{EncoderCodeBlockDiargam.svg => EncoderCodeBlockDiagram.svg} | 0 2 files changed, 1 insertion(+), 1 deletion(-) rename source/getting-started/control-with-amdc/encoder-fb/resources/{EncoderCodeBlockDiargam.svg => EncoderCodeBlockDiagram.svg} (100%) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index b977a3ac..f3e1e0d2 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -14,7 +14,7 @@ Incremental encoders are typically used with the AMDC and have a fixed number of The recommended approach to reading the shaft position from the encoder is illustrated in the figure below: - + As a first step, the user may use the AMDC `drv/encoder` driver module `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted to rotor position in radians. diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg b/source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiagram.svg similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiargam.svg rename to source/getting-started/control-with-amdc/encoder-fb/resources/EncoderCodeBlockDiagram.svg From 52556e65cae8dabb65c15f93baa0c62221ad75fd Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Fri, 1 Nov 2024 21:58:42 -0500 Subject: [PATCH 18/59] Fix type-os --- source/getting-started/control-with-amdc/encoder-fb/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index f3e1e0d2..8510093c 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -16,9 +16,9 @@ The recommended approach to reading the shaft position from the encoder is illus -As a first step, the user may use the AMDC `drv/encoder` driver module `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted to rotor position in radians. +As a first step, the user may use the AMDC `drv/encoder` driver module function `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted to rotor position in radians. - Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done manually by rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. In the figure, the signal `CCW` indicates this directionality. It must be set to `1`, if the encoder count increases with the counter clockwise rotation of shaft and `0` otherwise. Additionally, the user needs to provide the encoder offset, `offset` and the encoder counts per revolution, `ENCODER_COUNT_PER_REV`. A method to get the value of offset is described in the next [subsection](#finding-the-offset). Using all of this quantities, the obtained count can be translated into angular position using a simple linear equation. Note that, this document follows the convention of a positive rotor angle in the counter clockwise direction of shaft rotation while caclulating rotor position from the count signal. + Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done manually by rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. In the figure, the signal `CCW` indicates this directionality. It must be set to `1` if the encoder count increases with counter clockwise rotation of shaft and `0` otherwise. Additionally, the user needs to provide the encoder offset, `offset`, and the encoder counts per revolution, `ENCODER_COUNT_PER_REV`. A method to get the value of offset is described in the next [subsection](#finding-the-offset). Using all of these quantities, the obtained count can be translated into angular position using a simple linear equation. Note that this document follows the convention of a positive rotor angle in the counter clockwise direction of shaft rotation while calculating rotor position from the count signal. Finally, the user must ensure that angle is within the bounds of $0$ and $2\pi$ by appropriately wrapping the `rotor position` signal using the `mod` function. This is shown in the final block in the diagram. From 5ac7ce6056da6e764fe7be2687d9a9f98b18b181 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Fri, 1 Nov 2024 22:19:41 -0500 Subject: [PATCH 19/59] Add config instructions --- .../control-with-amdc/encoder-fb/index.md | 17 ++++++++++++++++- 1 file changed, 16 insertions(+), 1 deletion(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 8510093c..4a813be3 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -6,10 +6,25 @@ Encoders provide rotor position feedback to the control system in a motor drive. For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). -## Calibration +## Obtaining Position Incremental encoders are typically used with the AMDC and have a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. +### Configuring the encoder +Upon powerup, the AMDC configures the encoder to a default number of pulses per revolution. This is handled in `encoder.c`, which is part of the core AMDC-Firmware. When using an encoder that has a different number pulses per revolution, the user must inform the driver by calling `encoder_set_pulses_per_rev()`. + +Example code for a 10 bit encoder: + +``` C +#define USER_ENCODER_PULSES_PER_REV_BITS (10) +#define USER_ENCODER_PULSES_PER_REV (1 << USER_ENCODER_PULSES_PER_REV_BITS) + +int task_user_app_init(void) +{ + encoder_set_pulses_per_rev_bits(USER_ENCODER_PULSES_PER_REV_BITS); + ... +``` + ### Obtaining encoder count and translating it into rotor position The recommended approach to reading the shaft position from the encoder is illustrated in the figure below: From 1532f0a15f86b8e17ff825718f044670df14e25e Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sat, 2 Nov 2024 21:09:33 -0500 Subject: [PATCH 20/59] Edit first 1/3 of document --- .../control-with-amdc/encoder-fb/index.md | 26 +++++++++++++------ 1 file changed, 18 insertions(+), 8 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 4a813be3..3bf68649 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -2,16 +2,20 @@ ## Background -Encoders provide rotor position feedback to the control system in a motor drive. This document describes a method to convert the raw readings of an encoder into meaningful position information which can be used by the control algorithm. Methods to obtain rotor speed from the measured position are also presented. +Encoders are used to determine the rotor position and speed, and are the typical method of feedback to the control system in a motor drive. This document explains how to use the AMDC's encoder interface to extract high quality rotor position and speed data. -For more information on how an encoder works and how they may be interfaced with the AMDC please refer to this [document](https://docs.amdc.dev/hardware/subsystems/encoder.html#). +For more information: -## Obtaining Position +- on how encoders work and are interfaced with the AMDC, see the [encoder hardware subsystem page](https://docs.amdc.dev/hardware/subsystems/encoder.html#) +- on the driver functionality included with the AMDC firmware, see the [encoder driver architecture page](https://docs.amdc.dev/firmware/arch/drivers/encoder.html). -Incremental encoders are typically used with the AMDC and have a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. +## Rotor Position + +The AMDC supports [incremental encoders with quadrature ABZ outputs](https://en.wikipedia.org/wiki/Incremental_encoder#Quadrature_outputs) and a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. ### Configuring the encoder -Upon powerup, the AMDC configures the encoder to a default number of pulses per revolution. This is handled in `encoder.c`, which is part of the core AMDC-Firmware. When using an encoder that has a different number pulses per revolution, the user must inform the driver by calling `encoder_set_pulses_per_rev()`. + +Upon powerup, the AMDC configures the encoder to a default number of pulses per revolution. This is handled in `encoder.c` as part of the standard firmware package. When using an encoder that has a different number pulses per revolution, the user must inform the driver by calling `encoder_set_pulses_per_rev()`. Example code for a 10 bit encoder: @@ -21,11 +25,17 @@ Example code for a 10 bit encoder: int task_user_app_init(void) { - encoder_set_pulses_per_rev_bits(USER_ENCODER_PULSES_PER_REV_BITS); - ... + encoder_set_pulses_per_rev(USER_ENCODER_PULSES_PER_REV); + + // other user app one-time initialization code + // ... +``` + +```{tip} +The AMDC provides a convenience function that can be used as an alternate to `encoder_set_pulses_per_rev()` when the encoder is specified as a number of bits: `encoder_set_pulses_per_rev_bits(USER_ENCODER_PULSES_PER_REV_BITS).` ``` -### Obtaining encoder count and translating it into rotor position +### Converting the encoder count into rotor position The recommended approach to reading the shaft position from the encoder is illustrated in the figure below: From 3bb86ef381b028cae5a165bfbb352be7da96d944 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sat, 7 Dec 2024 21:27:21 -0600 Subject: [PATCH 21/59] Fix current calibration images (#116) --- .../control-with-amdc/current-sensor-cal/index.md | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/source/getting-started/control-with-amdc/current-sensor-cal/index.md b/source/getting-started/control-with-amdc/current-sensor-cal/index.md index a835f55f..783b7cfb 100644 --- a/source/getting-started/control-with-amdc/current-sensor-cal/index.md +++ b/source/getting-started/control-with-amdc/current-sensor-cal/index.md @@ -10,7 +10,7 @@ Current sensors are transducers which produce an output signal (either current o A method is now provided to calibrate the current sensors in a motor drive. An example of the assumed system for a three phase motor is shown in the figure below. - +![Current Sensor Configuration](resources/current_sensor_drawing.svg) Typically, each phase has a current sensor associated with it that needs to be calibrated. This method assumes that the signal measured by the AMDC for each sensor is a voltage that must be converted into a current value. @@ -26,8 +26,7 @@ Typically, each phase has a current sensor associated with it that needs to be c An example of the results are shown in the plot below. The obtained gain and offset can be used directly in the control code to convert the sensor reading into the actual current measurement. - - +![Example Results](resources/fit.svg) ```{tip} Be sure to conduct the calibration process over the full range of current data (both positive and negative current) to account for any variation in the current sensor reading due to directionality of current. 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+pole_2_Hz = -100; + +w1 = 2*pi*pole_1_Hz; +w2 = 2*pi*pole_2_Hz; + +Tend = 10; +Tsim = 1e-5; + +finit = 0.1; % initial frequency of chirp [Hz] +ftarget = 1000; % chirp frequency at target time [Hz] + +%% Run simulation +out = sim('pll_test_sim.slx'); + +%% System ID +sim_data = [out.theta_in.Time,out.theta_in.Data,out.theta_out.Data]; + +den = sim_data(:,2); % input signal +num = sim_data(:,3); % output signal + +[freq,mag,phase,coh] = generateFRF(num,den,Tsim,100000,'hann'); + +% Curve Fit Current Command Tracking FRF +% Find where frequency goes positive +idx_f_pos = find(freq >= 0,1); + +G_CL = tf([-w1-w2, w1*w2], [1, -w1-w2, w1*w2]); % CL transfer function +disp('---') +disp('System Poles (Hz):') +my_poles_Hz = pole(G_CL) ./ (2*pi); +disp(my_poles_Hz(1)) +disp(my_poles_Hz(2)) + +mag_pos = mag(idx_f_pos:end); +phase_pos = phase(idx_f_pos:end); +freq_pos = freq(idx_f_pos:end); +[~,index] = min(abs(mag_pos - 1/sqrt(2))); +freq_check = freq_pos(index); +mag_check = mag_pos(index); +phase_check = phase_pos(index); + +%% Plot +markersize = 3; +linewidth = 1; + +% Bode diagram +figure + +f1 = 0.1; +f2 = 1000; + +tiledlayout(3,1); +ax1 = nexttile; +ax2 = nexttile; +ax3 = nexttile; + +% Bode plot by System ID +plot(ax1,freq,20*log10(mag),'oc','markersize',markersize); +plot(ax2,freq,phase,'oc','markersize',markersize); +plot(ax3,freq,coh,'.','markersize',6); +hold (ax1,'on'); +hold (ax2,'on'); + +% Bode plot with ideal Closed-loop transfer function +freq_bode = transpose(linspace(0.1,1/(4*Tsim),10/(4*Tsim))); +[mag_G_CL,phase_G_CL] = bode(G_CL,freq_bode*2*pi); +plot(ax1,freq_bode,squeeze(20*log10(mag_G_CL)),'r','linewidth',linewidth); +plot(ax2,freq_bode,wrapTo180(squeeze(phase_G_CL)),'r','linewidth',linewidth); + +% Set figure limit, label, etc. +xlim(ax1,[f1 f2]); +xlim(ax2,[f1 f2]); +xlim(ax3,[f1 f2]); +ylim(ax3,[0 1]); + +xlabel(ax3,"Frequency (Hz)"); +ylabel(ax1,"Magnitude (dB)"); +ylabel(ax2,"Phase (deg)"); +ylabel(ax3,"Coherence"); + +grid(ax1,'on'); +grid(ax2,'on'); +grid(ax3,'on'); + +set(ax1,'xscale','log'); +set(ax2,'xscale','log'); +set(ax3,'xscale','log'); + +legend(ax1,'System ID','PLL','Location','southwest'); +legend(ax2,'System ID','PLL','Location','southwest'); + +%% +function [freq,mag,phase,coh] = generateFRF(num,den,T,lines,win) + + fs = 1/T; + overlap = lines/2; + averages = floor(length(num)/(lines-overlap)); + windowType = window(win,lines); + + [FRF,freq] = tfestimate(den,num,windowType,overlap,lines,fs); + [coh,freq] = mscohere(den,num,windowType,overlap,lines,fs); + + FRF = fftshift(FRF); + coh = fftshift(coh); + freq = freq - max(freq)/2; + mag = abs(FRF); + phase = angle(FRF) * 180/pi; + +end \ No newline at end of file diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/pll_test_sim.slx b/source/getting-started/control-with-amdc/encoder-fb/resources/pll_test_sim.slx new file mode 100644 index 0000000000000000000000000000000000000000..d84461dfc8f0c1bfff181a6ebd432563d08df1f5 GIT binary patch literal 44200 zcmaHRV~{A_mTcQLPTRI^K>VBp0R3A~hWkB*7t7^Zpv1ec%&!JU{)nH}D;grEc)g_UO?Z#R0N-BhL@r zAZjssqacg^o=u;3a7jqxJ#}mox7G;zyM@RZm}&zTQN<=6U&gMlu;WP25d>|)w?bH0 zvYT=B6b8r~zmKf0VuyFk{9iP45s#|S(u(xG_aH-9JMH%2>^`~ShXF9AM-i1s$$)hR zA6ZLu+bGx@aWLqNkXB+4#5>*oWVkf*6oU%rJ*HR$a9ggwxK_NqBk?E-Yjhnz&4sQf zHnW%ssIUkjE8`XU@Fw4!mCSxMz)YS@KwY%SN3ZQMm6iF3#rU1ktJ7H_?SM(QGU zpN=|*-3$C`>I3&SSF|{$5UEi|binm710mxnKQQEs-8!*KXGzyt1))#li z@=1C5_#9jwtFznV2qp|fSyv(wMIE3KK^W%VPg}$Nn@NN`Lp^=iUEP4XUdxr=N+=)6 z9*ReJ0W=VBLAx#Do;l#hS zK43IS!jCWBCjo;kP-W4b@BAz<8hLU|BWeTzgQGWyUZ8*}}5 zYLG5h5qo!wC~B_+W*2AMs|-_rp#_cpCsO{7__(1G*?575;Ph#2wbJwQkg`1-@tBLQ zl-1?L7XO3_ALdO#)E3FONpaW~;{(dRj#X#f3Ys-J?mfR&QjB-qL(};1waMn9>kDWf zl`RZ!@|nUXCmw?b10L`DZTNl7j{@xJb`*#I6b-)u`_Ji#CBKQ~1B%~+D1WE5a4vXE zFS9z&k%%v31oq(NAPE9V#z6GcrDO9qWD;SSk1b(UiRNn`9s*rK2q!59tE7Io?D z>0%U8^@(pz!^3%6Y}by4p$j6>OoWJA%Mug;mpE?M4O1Saj@iLD|d7Ib5k{HyrZ8M;)d6s=?r6jJ)m zL2M*?JSvXWq)wNm0l$)Z49}XnmjC(zEuxG66_1ml8S&U7dm)TXhDa9EU{9l9WcdgY z4WcEOK2W@Z>}c5a*v?|>qoa`fAlmqIv&$GAx8j!)HG~bZUKO;ND8kui?-PbFV#9RJ z*DfoKW6Gy*7!1&5s~#CaSH|{g6nKm-4M2i5z;$Au)AEXo@F0 zWkb4bCXF4z0#9hlUcA@RSa{+j|4`Kr=nxU1(3*R~7U5)Vke{w>yatPkM+qWjZzKO! zyF3~{JEcHd)UQ^T{(4%+iR%QX8iA8KX|jV`nK*@S!j)w|U>QwR?JbG253@p(@vd`! zbP04xeL$Jvm~K6F-PGDoVp9fCgPhh_MK3%Im^XvU#X}FQA3}O zLp{S4eBH$5Wf#=%Sj1+E#dmV^y5q;cq5P%t3p8S(mKCF*@eZ;Lxb+mrthdplhQb8n zt@zODs;o(>vnkhH*V9ll_@fzUsLAtUI0Cf+*?ukj*GXJV2{kcW=0z%k8giB3XOZ`d zc2V&1ju5(pVCqMQnRmgd4I5f(xN39G4rVi2M_xzI%~=j`mEuSfVB~H#u^#e$Atkh=IL=(waB*Tx@?T zpy#(y_W46TQ1BFbFHZA7OUb!WAkhQ$N&TXJBTLaKwh9It`IPx_(Dg}MY+xV${F;?!*pWXw}3LA}zLv7sPpLbka-$3&J zurJ|*gRzW20083P|GRx*U}0hWmwic6wzgfPNBG*()o<0+N64TL!B65;fenW(#Fsf^ zmNBsO#&_$ zxPssXaZRwJBOVRp0wATj;Tao6p;h}OaS0lj1F;L&mwY0!@XBS-?OsDZ9?q>df2vwzUC$iJw(FYLJ85(OnUro#{HCgTPC8z5T}9r33v0R z0}eBRcb#DTyWU6V4tAIR!~?BU6{tOYLcH1~8Jyg8Ckj?nj5Gb#w73)npG8uzCy}|k z6Riu6MK0(u0M@zFT0hF}-lohbuh6eoW;JM&Ok^Kvy%=RJA+iCBvZjCrMzCx=#pnVy zQxLFbYMchh0=XAENx5FqtzQLE{(g#)feRz-pjjNnIz6ieQ{L|vxfqK{;m8UvnUaqo zHcldm#QYm{v<~B4sc>mToi6Z^A8d{RCwh^?IGd!KdhB@En&+UpK#O#EDIEN8E@f6S zVgSeHpRC{W8Vh>m2hYQ)#i&u=fO*S7X4XlK*>j1a@wbK*nK85;pv}?;dS+*w^hD-k zQ6Eid!hxD?D-T|m&MP@_w>9=<*`c$K&%Lg8>V=6NhSwaF(}vzUJQ~k!euklw(&CnZ zo$rY;a)DO8TBRwAHj=9y8p3qMOr153uF-1IwAC-10Shm0&GU_wzv$F(P&f0DzI<1D zX-0MYMQB$frhU-A0smQV2U|%9wm&vm4G;i;>EG?LfswVFk-n2YowT`ugT8~iqOG%o zp|QM!t&y{#lkR_%pS7F5gM+@iq29xTF#r%R{*#`Oo*wYrFaC)E0KiIlULvHBuzGq3 z{#P*mU-F4L3h7#VDXAGy$)R^y_loo{ylI0ZdhgU22v2|Y{>B22@&c0cu`@L@lQGd{ zz+2GqeoB+SrC|hk<9|u>&kcu(;MMVsHi85EbNroAJbxB`#t!~t`H_FduPJ0}<78~( zq^sm^XY8o`uNG-cl5_lNk-=*(sMu(XB(!@fj$xq$;VW{oC;q~MlzCLOvk^O&G3(=3W_8T1N?=@u$-Y933oGXsHcwlhiGY(cN)+*a~N#8|akq?Ov!j z$LrczUN73#x^|ZJP9*xd*(@OdS^Hb-5Lm^w-shyA#u}nMHSw&imTN|wxaVelGTr$* z7Y9UN*@=4*1IusQhT31T%H*upAEzF%vodpub&|AO{D|;MvEuu@-!Ow7P+?l_0wIZs zcdG1`PVbiYa@skGr)dE)7JWrsg*v%~nv0(4w|^4}cQhxpb5Hdavw@t&U~j@CmE+N8 z5x)@aW)+^GzAQJ%<$1GMl<#p*vWI(=3tRG|%i?u_x1}E{?9+I6-tP!0=PYoQ#Y2A| zT{+njkcq3AH;;)3W!?|Sjx_h>;CcFEAw<{F!MtF$r#vwnwz?QFDD!^{I^uRJsI)0_ zbN3i_eMZWGb^o^_mLHjX@cAhMJTL$N=$|6cbuhMaq@(@UwP<0}CV(CV{KhjU|Fjb& zZB3&l+RJEyltZ%CpZ52w zWO+2mF`mqjqHLLv$1sTNI|mkGQSDGjrqzy6@sNC@3i+h4m|ryK&W9w=hx`F@s9P zi&FIKU@Noe=<_<|k4e`?!#It+M9fUQX6%3tS!RJXL)Q-bATD?(UobHF34AW8D?kyP ze%Y*W%FeA?L|j?MhECA8#lW*QLbYzQF z`&;P$>{S6Q<4m_7nZ`i?0Eqv6uK7>B46JMoEsf0eO&#>D|JAqupDO~bah`pAdQqO(wAwXyRFoK-rD}Nh zNN@b~A^y3PzfQv6u93t0`I>qv3PBLtT*BB^D|&HzrmJY&+JIEJ;JGD%LKHj)^&z!y zCCU>doS-O+hcYHI7le5t^m4GyAN%Xx{VinAB^2W+crh3eK6+^T-q$lpM5DfsM_RvN z&x!#zUE~HtOMi4X*wW|^QGUNUQRR=B?o?cMJCf#f7~zJS;Zq_pX{tR3ryt;ziwg{{xqqLh z!Z42^Yc?T;Rz;#8{>$Yxcb1Mj`YRHns8%gilgc)1&s0+OO)JdVag?RC*br7NQ&$V$ z3pWJ4@)-t$%aB#=o-r!A#h>mjW zve}?x7oZWtCOvwS@1NjZR*~EXe?U|GfT#F(@QzOUPR1rywyt#lS-{r%hGynA#{Yi; 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.../pll_test.m => simulink/computing-speed.m} | 0 .../computing-speed.slx} | Bin .../{resources => simulink}/pll_encoder.slx | Bin 3 files changed, 0 insertions(+), 0 deletions(-) rename source/getting-started/control-with-amdc/encoder-fb/{resources/pll_test.m => simulink/computing-speed.m} (100%) rename source/getting-started/control-with-amdc/encoder-fb/{resources/pll_test_sim.slx => simulink/computing-speed.slx} (100%) rename source/getting-started/control-with-amdc/encoder-fb/{resources => simulink}/pll_encoder.slx (100%) diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/pll_test.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.m similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/resources/pll_test.m rename to source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.m diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/pll_test_sim.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.slx similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/resources/pll_test_sim.slx rename to source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.slx diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/pll_encoder.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/pll_encoder.slx similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/resources/pll_encoder.slx rename to source/getting-started/control-with-amdc/encoder-fb/simulink/pll_encoder.slx From f9a610c58a438d60df37618be6b364d11b374e2c Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sat, 7 Jun 2025 12:25:38 -0500 Subject: [PATCH 25/59] Rename fiels --- .../{computing-speed.m => computing_speed.m} | 0 .../{computing-speed.slx => computing_speed.slx} | Bin 2 files changed, 0 insertions(+), 0 deletions(-) rename source/getting-started/control-with-amdc/encoder-fb/simulink/{computing-speed.m => computing_speed.m} (100%) rename source/getting-started/control-with-amdc/encoder-fb/simulink/{computing-speed.slx => computing_speed.slx} (100%) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.m similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.m rename to source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.m diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/simulink/computing-speed.slx rename to source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx From d55c6fab98214b9c524d1bb64091f4cbfbdc1adb Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sat, 7 Jun 2025 12:32:18 -0500 Subject: [PATCH 26/59] Rename files --- .../encoder-fb/simulink/computing_speed.slx | Bin 44200 -> 46690 bytes .../simulink/{computing_speed.m => setup.m} | 0 2 files changed, 0 insertions(+), 0 deletions(-) rename source/getting-started/control-with-amdc/encoder-fb/simulink/{computing_speed.m => setup.m} (100%) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx index d84461dfc8f0c1bfff181a6ebd432563d08df1f5..e6682b3f15641f2b59908ab2f5cc91abe685caf0 100644 GIT binary patch delta 29180 zcmV)0K+eCY*#hG10vJ$B0|XQR000O8001EX1}IlhR_cl6o zmmu9JB1lO|gA5@kNOwy&44u-AK}kr7fJjLULx+IUA>G~G{hs;$-uJ$Dt$W}9?^^da z%UR+upYu6qpS_>`Jp1gAQE!#y32>=#ArJ_`D+Q<;1cGvcd}CvRPkP4YqrqP|&I-D2 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--git a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index 35c59524..c05f2d7f 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -7,107 +7,158 @@ w1 = 2*pi*pole_1_Hz; w2 = 2*pi*pole_2_Hz; -Tend = 10; +Tend = 0.2; Tsim = 1e-5; -finit = 0.1; % initial frequency of chirp [Hz] -ftarget = 1000; % chirp frequency at target time [Hz] +p = 1; % number of pole +speed_cmd = 3000; % fundmental frequency [Hz] %% Run simulation -out = sim('pll_test_sim.slx'); - -%% System ID -sim_data = [out.theta_in.Time,out.theta_in.Data,out.theta_out.Data]; - -den = sim_data(:,2); % input signal -num = sim_data(:,3); % output signal - -[freq,mag,phase,coh] = generateFRF(num,den,Tsim,100000,'hann'); - -% Curve Fit Current Command Tracking FRF -% Find where frequency goes positive -idx_f_pos = find(freq >= 0,1); - -G_CL = tf([-w1-w2, w1*w2], [1, -w1-w2, w1*w2]); % CL transfer function -disp('---') -disp('System Poles (Hz):') -my_poles_Hz = pole(G_CL) ./ (2*pi); -disp(my_poles_Hz(1)) -disp(my_poles_Hz(2)) - -mag_pos = mag(idx_f_pos:end); -phase_pos = phase(idx_f_pos:end); -freq_pos = freq(idx_f_pos:end); -[~,index] = min(abs(mag_pos - 1/sqrt(2))); -freq_check = freq_pos(index); -mag_check = mag_pos(index); -phase_check = phase_pos(index); - -%% Plot -markersize = 3; -linewidth = 1; - -% Bode diagram -figure - -f1 = 0.1; -f2 = 1000; - -tiledlayout(3,1); -ax1 = nexttile; -ax2 = nexttile; -ax3 = nexttile; - -% Bode plot by System ID -plot(ax1,freq,20*log10(mag),'oc','markersize',markersize); -plot(ax2,freq,phase,'oc','markersize',markersize); -plot(ax3,freq,coh,'.','markersize',6); -hold (ax1,'on'); -hold (ax2,'on'); - -% Bode plot with ideal Closed-loop transfer function -freq_bode = transpose(linspace(0.1,1/(4*Tsim),10/(4*Tsim))); -[mag_G_CL,phase_G_CL] = bode(G_CL,freq_bode*2*pi); -plot(ax1,freq_bode,squeeze(20*log10(mag_G_CL)),'r','linewidth',linewidth); -plot(ax2,freq_bode,wrapTo180(squeeze(phase_G_CL)),'r','linewidth',linewidth); - -% Set figure limit, label, etc. -xlim(ax1,[f1 f2]); -xlim(ax2,[f1 f2]); -xlim(ax3,[f1 f2]); -ylim(ax3,[0 1]); - -xlabel(ax3,"Frequency (Hz)"); -ylabel(ax1,"Magnitude (dB)"); -ylabel(ax2,"Phase (deg)"); -ylabel(ax3,"Coherence"); - -grid(ax1,'on'); -grid(ax2,'on'); -grid(ax3,'on'); - -set(ax1,'xscale','log'); -set(ax2,'xscale','log'); -set(ax3,'xscale','log'); - -legend(ax1,'System ID','PLL','Location','southwest'); -legend(ax2,'System ID','PLL','Location','southwest'); - -%% -function [freq,mag,phase,coh] = generateFRF(num,den,T,lines,win) - - fs = 1/T; - overlap = lines/2; - averages = floor(length(num)/(lines-overlap)); - windowType = window(win,lines); - - [FRF,freq] = tfestimate(den,num,windowType,overlap,lines,fs); - [coh,freq] = mscohere(den,num,windowType,overlap,lines,fs); - - FRF = fftshift(FRF); - coh = fftshift(coh); - freq = freq - max(freq)/2; - mag = abs(FRF); - phase = angle(FRF) * 180/pi; - -end \ No newline at end of file +out = sim('computing_speed.slx'); +% + +%% Post processing +% Extract simulation data +runObj = Simulink.sdi.Run.getLatest; + +% List of variables to extract +obj2ext = {'time','theta_m','omega_raw', 'omega_pll'}; + +% Get signal IDs and store signals into array +for idx = 2:length(obj2ext) + sigID = getSignalIDsByName(runObj,obj2ext{idx}); + sig_obj.(obj2ext{idx}) = Simulink.sdi.getSignal(sigID); + sig_val.(obj2ext{idx}) = sig_obj.(obj2ext{idx}).Values.Data; +end + +time = sig_obj.(obj2ext{2}).Values.Time; + +%% Plot figure +width = 2*5.43; +height = 1.2*3*4.38 / 3; +set(0,'units','inches'); +Inch_SS = get(0,'screensize'); +lw = 1; % line width + +figure1 = figure; +% Plot theta_in +subplot(2,1,1); +hold on; +plot(time, squeeze(sig_val.theta_m), 'Color', 'k', 'LineWidth', lw); +xlabel('Time [s]','Interpreter','latex'); +ylabel('$\theta_{\mathrm{m}}$ (rad)','Interpreter','latex'); +xlim([0 Tend]); +ylim([0 7]); + +% Plot theta_out +subplot(2,1,2); +hold on; +plot(time, squeeze(sig_val.omega_raw), 'Color', 'k', 'LineWidth', lw); +plot(time, squeeze(sig_val.omega_pll), 'Color', 'r', 'LineWidth', lw); +xlabel('Time [s]','Interpreter','latex'); +ylabel('$\Omega$ (rad/s)','Interpreter','latex'); +xlim([0 Tend]); +ylim([0 400]); +legend('$\Omega_{\mathrm{raw}}$','$\Omega_{\mathrm{pll}}$', 'Interpreter','latex','Location','east'); + +set(findall(gcf, '-property', 'FontName'), 'FontName', 'Times New Roman'); + +set(figure1,'Units','inches','Position',[(Inch_SS(3)-width)/2 (Inch_SS(4)-height)/2 width height]); +print(figure1, '-dsvg','-noui','plot_results'); +print(figure1, '-dpng','-r300','plot_results'); + +% %% System ID +% sim_data = [out.theta_in.Time,out.theta_in.Data,out.theta_out.Data]; +% +% den = sim_data(:,2); % input signal +% num = sim_data(:,3); % output signal +% +% [freq,mag,phase,coh] = generateFRF(num,den,Tsim,100000,'hann'); +% +% % Curve Fit Current Command Tracking FRF +% % Find where frequency goes positive +% idx_f_pos = find(freq >= 0,1); +% +% G_CL = tf([-w1-w2, w1*w2], [1, -w1-w2, w1*w2]); % CL transfer function +% disp('---') +% disp('System Poles (Hz):') +% my_poles_Hz = pole(G_CL) ./ (2*pi); +% disp(my_poles_Hz(1)) +% disp(my_poles_Hz(2)) +% +% mag_pos = mag(idx_f_pos:end); +% phase_pos = phase(idx_f_pos:end); +% freq_pos = freq(idx_f_pos:end); +% [~,index] = min(abs(mag_pos - 1/sqrt(2))); +% freq_check = freq_pos(index); +% mag_check = mag_pos(index); +% phase_check = phase_pos(index); +% +% %% Plot +% markersize = 3; +% linewidth = 1; +% +% % Bode diagram +% figure +% +% f1 = 0.1; +% f2 = 1000; +% +% tiledlayout(3,1); +% ax1 = nexttile; +% ax2 = nexttile; +% ax3 = nexttile; +% +% % Bode plot by System ID +% plot(ax1,freq,20*log10(mag),'oc','markersize',markersize); +% plot(ax2,freq,phase,'oc','markersize',markersize); +% plot(ax3,freq,coh,'.','markersize',6); +% hold (ax1,'on'); +% hold (ax2,'on'); +% +% % Bode plot with ideal Closed-loop transfer function +% freq_bode = transpose(linspace(0.1,1/(4*Tsim),10/(4*Tsim))); +% [mag_G_CL,phase_G_CL] = bode(G_CL,freq_bode*2*pi); +% plot(ax1,freq_bode,squeeze(20*log10(mag_G_CL)),'r','linewidth',linewidth); +% plot(ax2,freq_bode,wrapTo180(squeeze(phase_G_CL)),'r','linewidth',linewidth); +% +% % Set figure limit, label, etc. +% xlim(ax1,[f1 f2]); +% xlim(ax2,[f1 f2]); +% xlim(ax3,[f1 f2]); +% ylim(ax3,[0 1]); +% +% xlabel(ax3,"Frequency (Hz)"); +% ylabel(ax1,"Magnitude (dB)"); +% ylabel(ax2,"Phase (deg)"); +% ylabel(ax3,"Coherence"); +% +% grid(ax1,'on'); +% grid(ax2,'on'); +% grid(ax3,'on'); +% +% set(ax1,'xscale','log'); +% set(ax2,'xscale','log'); +% set(ax3,'xscale','log'); +% +% legend(ax1,'System ID','PLL','Location','southwest'); +% legend(ax2,'System ID','PLL','Location','southwest'); +% +% %% +% function [freq,mag,phase,coh] = generateFRF(num,den,T,lines,win) +% +% fs = 1/T; +% overlap = lines/2; +% averages = floor(length(num)/(lines-overlap)); +% windowType = window(win,lines); +% +% [FRF,freq] = tfestimate(den,num,windowType,overlap,lines,fs); +% [coh,freq] = mscohere(den,num,windowType,overlap,lines,fs); +% +% FRF = fftshift(FRF); +% coh = fftshift(coh); +% freq = freq - max(freq)/2; +% mag = abs(FRF); +% phase = angle(FRF) * 180/pi; +% +% end \ No newline at end of file From 199299da7cc37171828c5aac3c7920f390c4cc8a Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sat, 7 Jun 2025 14:04:59 -0500 Subject: [PATCH 28/59] Add low pass fileter --- .../encoder-fb/simulink/computing_speed.slx | Bin 50660 -> 52685 bytes .../encoder-fb/simulink/setup.m | 12 +++++++++--- 2 files changed, 9 insertions(+), 3 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx index 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z1IPN!O7(vSy{rKM+W&+g{X>P!;W@u4;2(Z-0~4JQPGun66+x)rSeu+cW)Fmu68>(J z3z*{h4_bskb$#H2ZhUauEfyfDFI;%b1UTypPur3JqWHrXw*-JC0dQ*XmvE777GPW; z+cm z;r?MDxaA%T5FZYY+XGYm{|+($fc(F*=uLnNMN`7ve&fNB_9=jU>F}SmMDUMEsBr#$ z7NAHA!b=7BLpTpw-~n|n;KK-KRU7|F3Q%0m%M~36^1aTMq?1`4A7yYVU8z{{VI=q^JM@ diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index ef7b5d7b..994a87f2 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -70,7 +70,7 @@ plot(time, squeeze(sig_val.omega_raw), 'Color', 'k', 'LineWidth', lw); plot(time, squeeze(sig_val.omega_lpf), 'Color', 'r', 'LineWidth', lw); plot(time, squeeze(sig_val.omega_pll), 'Color', 'b', 'LineWidth', lw); -plot(time, squeeze(sig_val.omega_sf), 'Color', 'g', 'LineWidth', lw); +plot(time, squeeze(sig_val.omega_sf), '--', 'Color', 'g', 'LineWidth', lw); 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1e-4; -Tsim = 1e-6; +Tsim = 1e-5; p = 1; % number of pole speed_cmd = 3000; % fundmental frequency [Hz] @@ -27,6 +27,10 @@ b_o_sf = wb_sf*J_z; K_io_sf = wb_sf*b; +% Parameters for chirp signal +f_init = 0.1; % initial frequency of chirp [Hz] +f_target = 1000; % chirp frequency at target time [Hz] + %% Run simulation out = sim('computing_speed.slx'); % @@ -83,98 +87,89 @@ print(figure1, '-dsvg','-noui','plot_results'); print(figure1, '-dpng','-r300','plot_results'); -% %% System ID -% sim_data = [out.theta_in.Time,out.theta_in.Data,out.theta_out.Data]; -% -% den = sim_data(:,2); % input signal -% num = sim_data(:,3); % output signal -% -% [freq,mag,phase,coh] = generateFRF(num,den,Tsim,100000,'hann'); -% -% % Curve Fit Current Command Tracking FRF -% % Find where frequency goes positive -% idx_f_pos = find(freq >= 0,1); -% -% G_CL = tf([-w1-w2, w1*w2], [1, -w1-w2, w1*w2]); % CL transfer function -% disp('---') -% disp('System Poles (Hz):') -% my_poles_Hz = pole(G_CL) ./ (2*pi); -% disp(my_poles_Hz(1)) -% disp(my_poles_Hz(2)) -% -% mag_pos = mag(idx_f_pos:end); -% phase_pos = phase(idx_f_pos:end); -% freq_pos = freq(idx_f_pos:end); -% [~,index] = min(abs(mag_pos - 1/sqrt(2))); -% freq_check = freq_pos(index); -% mag_check = mag_pos(index); -% phase_check = phase_pos(index); -% -% %% Plot -% markersize = 3; -% linewidth = 1; -% -% % Bode diagram -% figure -% -% f1 = 0.1; -% f2 = 1000; -% -% tiledlayout(3,1); -% ax1 = nexttile; -% ax2 = nexttile; -% ax3 = nexttile; -% -% % Bode plot by System ID -% plot(ax1,freq,20*log10(mag),'oc','markersize',markersize); -% plot(ax2,freq,phase,'oc','markersize',markersize); -% plot(ax3,freq,coh,'.','markersize',6); -% hold (ax1,'on'); -% hold (ax2,'on'); -% +%% System ID +den = squeeze(sig_val.omega_raw); % input signal +num = squeeze(sig_val.omega_lpf); % output signal + +[freq,mag,phase,coh] = generateFRF(num,den,Ts,10000,'hann'); + +% Curve Fit Current Command Tracking FRF +% Find where frequency goes positive +idx_f_pos = find(freq >= 0,1); + +mag_pos = mag(idx_f_pos:end); +phase_pos = phase(idx_f_pos:end); +freq_pos = freq(idx_f_pos:end); +[~,index] = min(abs(mag_pos - 1/sqrt(2))); +freq_check = freq_pos(index); +mag_check = mag_pos(index); +phase_check = phase_pos(index); + +%% Plot +markersize = 3; +linewidth = 1; + +% Bode diagram +figure + +f1 = 0.1; +f2 = 1000; + +tiledlayout(3,1); +ax1 = nexttile; +ax2 = nexttile; +ax3 = nexttile; + +% Bode plot by System ID +plot(ax1,freq,20*log10(mag),'oc','markersize',markersize); +plot(ax2,freq,phase,'oc','markersize',markersize); +plot(ax3,freq,coh,'.','markersize',6); +hold (ax1,'on'); +hold (ax2,'on'); + % % Bode plot with ideal Closed-loop transfer function % freq_bode = transpose(linspace(0.1,1/(4*Tsim),10/(4*Tsim))); % [mag_G_CL,phase_G_CL] = bode(G_CL,freq_bode*2*pi); % plot(ax1,freq_bode,squeeze(20*log10(mag_G_CL)),'r','linewidth',linewidth); % plot(ax2,freq_bode,wrapTo180(squeeze(phase_G_CL)),'r','linewidth',linewidth); -% -% % Set figure limit, label, etc. -% xlim(ax1,[f1 f2]); -% xlim(ax2,[f1 f2]); -% xlim(ax3,[f1 f2]); -% ylim(ax3,[0 1]); -% -% xlabel(ax3,"Frequency (Hz)"); -% ylabel(ax1,"Magnitude (dB)"); -% ylabel(ax2,"Phase (deg)"); -% ylabel(ax3,"Coherence"); -% -% grid(ax1,'on'); -% grid(ax2,'on'); -% grid(ax3,'on'); -% -% set(ax1,'xscale','log'); -% set(ax2,'xscale','log'); -% set(ax3,'xscale','log'); -% -% legend(ax1,'System ID','PLL','Location','southwest'); -% legend(ax2,'System ID','PLL','Location','southwest'); -% -% %% -% function [freq,mag,phase,coh] = generateFRF(num,den,T,lines,win) -% -% fs = 1/T; -% overlap = lines/2; -% averages = floor(length(num)/(lines-overlap)); -% windowType = window(win,lines); -% -% [FRF,freq] = tfestimate(den,num,windowType,overlap,lines,fs); -% [coh,freq] = mscohere(den,num,windowType,overlap,lines,fs); -% -% FRF = fftshift(FRF); -% coh = fftshift(coh); -% freq = freq - max(freq)/2; -% mag = abs(FRF); -% phase = angle(FRF) * 180/pi; -% -% end \ No newline at end of file + +% Set figure limit, label, etc. +xlim(ax1,[f1 f2]); +xlim(ax2,[f1 f2]); +xlim(ax3,[f1 f2]); +ylim(ax3,[0 1]); + +xlabel(ax3,"Frequency (Hz)"); +ylabel(ax1,"Magnitude (dB)"); +ylabel(ax2,"Phase (deg)"); +ylabel(ax3,"Coherence"); + +grid(ax1,'on'); +grid(ax2,'on'); +grid(ax3,'on'); + +set(ax1,'xscale','log'); +set(ax2,'xscale','log'); +set(ax3,'xscale','log'); + +legend(ax1,'System ID','PLL','Location','southwest'); +legend(ax2,'System ID','PLL','Location','southwest'); + +%% +function [freq,mag,phase,coh] = generateFRF(num,den,T,lines,win) + + fs = 1/T; + overlap = lines/2; + averages = floor(length(num)/(lines-overlap)); + windowType = window(win,lines); + + [FRF,freq] = tfestimate(den,num,windowType,overlap,lines,fs); + [coh,freq] = mscohere(den,num,windowType,overlap,lines,fs); + + FRF = fftshift(FRF); + coh = fftshift(coh); + freq = freq - max(freq)/2; + mag = abs(FRF); + phase = angle(FRF) * 180/pi; + +end \ No newline at end of file From 6239d599d262238aa829b9cb73ad2f3c55211771 Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sat, 7 Jun 2025 16:31:00 -0500 Subject: [PATCH 33/59] Rename file --- .../{computing_speed.slx => compute_speed.slx} | Bin .../control-with-amdc/encoder-fb/simulink/setup.m | 3 +-- 2 files changed, 1 insertion(+), 2 deletions(-) rename source/getting-started/control-with-amdc/encoder-fb/simulink/{computing_speed.slx => compute_speed.slx} (100%) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/simulink/computing_speed.slx rename to source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index 52dc6d16..e8e0067f 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -32,8 +32,7 @@ f_target = 1000; % chirp frequency at target time [Hz] %% Run simulation -out = sim('computing_speed.slx'); -% +out = sim('compute_speed.slx'); %% Post processing % Extract simulation data From 860b2711ee67f4cfe75aedd9fce7bc8271dd30cf Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sat, 7 Jun 2025 16:46:15 -0500 Subject: [PATCH 34/59] Update code --- .../encoder-fb/simulink/compute_speed.slx | Bin 61475 -> 64627 bytes .../encoder-fb/simulink/setup.m | 6 ++++-- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx index a244c2280090b3166e4b267f245ac4d8b67bcb24..b446a02714506ae1fb868e5c91a254135139cc67 100644 GIT binary patch delta 43402 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zW~cwJ7s?gkKPU|bd4l|Z-n}H;tUbDoo}IltQW6s0UoD0657M0q?SRt*!O^_;^WnGS{F^o3 zkM--5yyt`Rm!r)cqJSUZ>Du3tNjn#jocUMq45h#yYRk}S$V?!_3=Ue z$0*R%_0GEwOr;-e9(y0@ly7$S$_r6HKF#^Dy!yVpVNYD>bUE}d`TC^_`kyYE?E*k{ zZTHUHMbS!sl}B4I8pu3_c=+VmdemjZjs3jPh0dCLF_z()i*+|omU6M(XAjlg?B z&$lAr=OF$&9*9(8Pz5nHDEp2c!j}{jPf7zi|15fufnvxQKo9q5AdPzh@C1<4y*5NL z1<3iH6m)z~^yR;+7Cw3T`^i4xe_8tfS^G%|>ZT+Di9FCls8WL*Xb3?94_Kh=2LcFv zn$KHW(8ec4miE6CPg+zE*CRc+6v+5d41zEf#FR=1>iGm(K_`#W;L{+^CwjvFWaM{X z!N9(2fPvxvudc#C-cOR?`JkRBaR|&IP<<&Dh~SwWd;p~ItN`u=%6^ssPX_HhYk-%6 t_+R89vL-=4CrLq-FZAGKpuaC{g#SCW|36Ltk9^HRq^}GxmDm5l{tp1K$yNXW diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index a174a02a..1336c88e 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -87,74 +87,80 @@ print(figure1, '-dpng','-r300','plot_results'); %% System ID -den = squeeze(sig_val.omega_raw); % input signal -% num = squeeze(sig_val.omega_lpf); % output signal -num = squeeze(sig_val.omega_pll); % output signal -% num = squeeze(sig_val.omega_sf); % output signal - -[freq,mag,phase,coh] = generateFRF(num,den,Ts,10000,'hann'); - -% Curve Fit Current Command Tracking FRF -% Find where frequency goes positive -idx_f_pos = find(freq >= 0,1); - -mag_pos = mag(idx_f_pos:end); -phase_pos = phase(idx_f_pos:end); -freq_pos = freq(idx_f_pos:end); -[~,index] = min(abs(mag_pos - 1/sqrt(2))); -freq_check = freq_pos(index); -mag_check = mag_pos(index); -phase_check = phase_pos(index); - -%% Plot +den = squeeze(sig_val.omega_raw); % input signal +outputs = { + squeeze(sig_val.omega_lpf), 'Low-pass filter', '--'; + squeeze(sig_val.omega_pll), 'PLL', '-'; + squeeze(sig_val.omega_sf), 'Observer', '-.' +}; % output signals + markersize = 3; linewidth = 1; +colors = lines(size(outputs, 1)); % set color map -% Bode diagram -figure - -f1 = 0.1; -f2 = 1000; +% Bode plot +f1 = f_init; +f2 = f_target; +figure; tiledlayout(3,1); -ax1 = nexttile; -ax2 = nexttile; -ax3 = nexttile; - -% Bode plot by System ID -plot(ax1,freq,20*log10(mag),'oc','markersize',markersize); -plot(ax2,freq,phase,'oc','markersize',markersize); -plot(ax3,freq,coh,'.','markersize',6); -hold (ax1,'on'); -hold (ax2,'on'); - -% % Bode plot with ideal Closed-loop transfer function -% freq_bode = transpose(linspace(0.1,1/(4*Tsim),10/(4*Tsim))); -% [mag_G_CL,phase_G_CL] = bode(G_CL,freq_bode*2*pi); -% plot(ax1,freq_bode,squeeze(20*log10(mag_G_CL)),'r','linewidth',linewidth); -% plot(ax2,freq_bode,wrapTo180(squeeze(phase_G_CL)),'r','linewidth',linewidth); - -% Set figure limit, label, etc. -xlim(ax1,[f1 f2]); -xlim(ax2,[f1 f2]); -xlim(ax3,[f1 f2]); -ylim(ax3,[0 1]); - -xlabel(ax3,"Frequency (Hz)"); -ylabel(ax1,"Magnitude (dB)"); -ylabel(ax2,"Phase (deg)"); -ylabel(ax3,"Coherence"); - -grid(ax1,'on'); -grid(ax2,'on'); -grid(ax3,'on'); - -set(ax1,'xscale','log'); -set(ax2,'xscale','log'); -set(ax3,'xscale','log'); - -legend(ax1,'System ID','PLL','Location','southwest'); -legend(ax2,'System ID','PLL','Location','southwest'); +ax1 = nexttile; % Magnitude +ax2 = nexttile; % Phase +ax3 = nexttile; % Coherence + +hold(ax1, 'on'); +hold(ax2, 'on'); +hold(ax3, 'on'); + +% Compute magnitude and phase for each signal +for i = 1:size(outputs, 1) + num = outputs{i, 1}; + label = outputs{i, 2}; + linestyle = outputs{i, 3}; + + [freq, mag, phase, coh] = generateFRF(num, den, Ts, 10000, 'hann'); + + plot(ax1, freq, 20*log10(mag), ... + 'LineStyle', 'none', 'Marker', 'o', ... + 'Color', colors(i,:), 'MarkerSize', markersize, ... + 'DisplayName', label); + + plot(ax2, freq, phase, ... + 'LineStyle', 'none', 'Marker', 'o', ... + 'Color', colors(i,:), 'MarkerSize', markersize, ... + 'DisplayName', label); + + plot(ax3, freq, coh, ... + 'LineStyle', 'none', 'Marker', 'o', ... + 'Color', colors(i,:), 'MarkerSize', markersize, ... + 'DisplayName', label); +end + +xlim(ax1, [f1 f2]); +xlim(ax2, [f1 f2]); +xlim(ax3, [f1 f2]); +ylim(ax3, [0 1]); + +set(ax1, 'xscale', 'log'); +set(ax2, 'xscale', 'log'); +set(ax3, 'xscale', 'log'); + +xlabel(ax3, "Frequency (Hz)"); +ylabel(ax1, "Magnitude (dB)"); +ylabel(ax2, "Phase (deg)"); +ylabel(ax3, "Coherence"); + +grid(ax1, 'on'); +grid(ax2, 'on'); +grid(ax3, 'on'); + +legend(ax1, 'Location', 'southwest'); + +set(findall(gcf, '-property', 'FontName'), 'FontName', 'Times New Roman'); + +set(figure1,'Units','inches','Position',[(Inch_SS(3)-width)/2 (Inch_SS(4)-height)/2 width height]); +print(figure1, '-dsvg','-noui','bode_plot'); +print(figure1, '-dpng','-r300','bode_plot'); %% function [freq,mag,phase,coh] = generateFRF(num,den,T,lines,win) From 36971f0e9b4c342cc007d03428d0cf3042a2e86c Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sat, 7 Jun 2025 17:04:06 -0500 Subject: [PATCH 36/59] Add encoder angle diagram, first edits of text to use it. --- .../control-with-amdc/encoder-fb/index.md | 18 +- .../resources/MotorCrossSection.svg | 165 ++++++++++++++++++ 2 files changed, 176 insertions(+), 7 deletions(-) create mode 100644 source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.svg diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 3bf68649..4142868f 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -13,35 +13,39 @@ For more information: The AMDC supports [incremental encoders with quadrature ABZ outputs](https://en.wikipedia.org/wiki/Incremental_encoder#Quadrature_outputs) and a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. +This document assumes the configuration shown in the figure below, where the control code expects a measurement of the angle of the rotor's north pole relative to the phase $u$ magnetic axis, labeled as $\theta_{\rm m}$. The encoder provides $\theta_{\rm enc}$, which is the number of counts since the last z-pulse. The user's code needs to convert $\theta_{\rm enc}$ (in units of counts) into $\theta_{\rm m}$ (likely in units of radians) and handle an offset angle $\theta_{\rm off}$ between the encoder's 0 position and the phase $u$ axis. + +![Motor Cross-Section with Encoder Angles](resources/MotorCrossSection.svg) + ### Configuring the encoder -Upon powerup, the AMDC configures the encoder to a default number of pulses per revolution. This is handled in `encoder.c` as part of the standard firmware package. When using an encoder that has a different number pulses per revolution, the user must inform the driver by calling `encoder_set_pulses_per_rev()`. +Upon powerup, the AMDC configures the encoder to a default number of counts per revolution. This is handled in `encoder.c` as part of the standard firmware package. When using an encoder that has a different number counts per revolution, the user must inform the driver by calling `encoder_set_counts_per_rev()`. Example code for a 10 bit encoder: ``` C -#define USER_ENCODER_PULSES_PER_REV_BITS (10) -#define USER_ENCODER_PULSES_PER_REV (1 << USER_ENCODER_PULSES_PER_REV_BITS) +#define USER_ENCODER_COUNTS_PER_REV_BITS (10) +#define USER_ENCODER_COUNTS_PER_REV (1 << USER_ENCODER_COUNTS_PER_REV_BITS) int task_user_app_init(void) { - encoder_set_pulses_per_rev(USER_ENCODER_PULSES_PER_REV); + encoder_set_counts_per_rev(USER_ENCODER_COUNTS_PER_REV); // other user app one-time initialization code // ... ``` ```{tip} -The AMDC provides a convenience function that can be used as an alternate to `encoder_set_pulses_per_rev()` when the encoder is specified as a number of bits: `encoder_set_pulses_per_rev_bits(USER_ENCODER_PULSES_PER_REV_BITS).` +The AMDC provides a convenience function that can be used as an alternate to `encoder_set_counts_per_rev()` when the encoder is specified as a number of bits: `encoder_set_counts_per_rev_bits(USER_ENCODER_COUNTS_PER_REV_BITS).` ``` ### Converting the encoder count into rotor position The recommended approach to reading the shaft position from the encoder is illustrated in the figure below: - + -As a first step, the user may use the AMDC `drv/encoder` driver module function `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted to rotor position in radians. +First, the user uses the AMDC [`drv/encoder`](/firmware/arch/drivers/encoder.md) driver module function `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted to rotor position in radians. Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done manually by rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. In the figure, the signal `CCW` indicates this directionality. It must be set to `1` if the encoder count increases with counter clockwise rotation of shaft and `0` otherwise. Additionally, the user needs to provide the encoder offset, `offset`, and the encoder counts per revolution, `ENCODER_COUNT_PER_REV`. A method to get the value of offset is described in the next [subsection](#finding-the-offset). Using all of these quantities, the obtained count can be translated into angular position using a simple linear equation. Note that this document follows the convention of a positive rotor angle in the counter clockwise direction of shaft rotation while calculating rotor position from the count signal. diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.svg b/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.svg new file mode 100644 index 00000000..fc53967c --- /dev/null +++ b/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.svg @@ -0,0 +1,165 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From 8dc006bbdd70ff845ccdf183321f155223906ea2 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sat, 7 Jun 2025 17:54:40 -0500 Subject: [PATCH 37/59] Add latex source for motor cross section --- .../resources/MotorCrossSection.tex | 259 ++++++++++++++++++ 1 file changed, 259 insertions(+) create mode 100644 source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.tex diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.tex b/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.tex new file mode 100644 index 00000000..e5822bae --- /dev/null +++ b/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.tex @@ -0,0 +1,259 @@ +\documentclass[class=IEEEtran]{standalone}%[conference,10pt]{IEEEtran} +\usepackage{amsmath} +\ifCLASSINFOpdf +\usepackage[pdftex]{graphicx} +\else +\usepackage[dvips]{graphicx} +\fi + +\usepackage{color} % required for `\textcolor' (yatex added) + +%ERIC ADDED: +\usepackage{xcolor, tikz, pgfplots, ifthen} +\usepackage[american,cuteinductors,smartlabels]{circuitikz} +\pgfplotsset{compat=newest} +\usetikzlibrary{intersections,calc,backgrounds} + +\begin{document} + + + \centering + \newcommand{\thisScale}{.09} + + +%THE CALLING TEX FILE MUST DEFINE TWO COMMANDS: +%\thisScale and \setupFig +%for example: +% \newcommand{\setupFig} +%{ +% \def\TopLayerLabels{{"v", "v", "-u", "w", "w", "-v", "u", "u", "-w", "v", "v", "-u", "w", "w", "-v", "u", "u", "-w","v", "v", "-u", "w", "w", "-v", "u", "u", "-w","v", "v", "-u", "w", "w", "-v", "u", "u", "-w"}} +% \def\BotLayerLabels{{"v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w", "v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w","v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w","v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w"}} +%} +\definecolor{motoGreen}{RGB}{34, 139, 34} +\definecolor{motoRed}{RGB}{196,0,100} % HEX #fedeed +\definecolor{motoBlue}{RGB}{0,110,191} + +%PREAMBLE: +% \usetikzlibrary{intersections} +% \usetikzlibrary{calc} +% +% \newcommand{\setupFig}{\def\showX{0}} +% \newcommand{\thisScale}{1/10} +% +\scalebox{3}{ +\begin{tikzpicture}[font=\tiny,scale=\thisScale,remember picture, >=stealth] + + +%default values: +\def\StatorOR{25} +\def\StatorIR{17.5} + +\def\IntraSlotDepth{.3} +\def\IntraSlotWidth{2} +\def\SlotWidth{2} +\def\SlotDepth{4.1} +\def\NumSlots{36} +\def\CondRadius{1.25} +\def\UseCond{0} +\def\NumberSlots{0} +\def\StatorRotOffset{5} %angle that slot 1 should be at with respect to the x axis +\def\TopLayerLabels{{"v", "v", "-u", "w", "w", "-v", "u", "u", "-w", "v", "v", "-u", "w", "w", "-v", "u", "u", "-w","v", "v", "-u", "w", "w", "-v", "u", "u", "-w","v", "v", "-u", "w", "w", "-v", "u", "u", "-w"}} +\def\BotLayerLabels{{"v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w", "v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w","v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w","v", "-u", "-u", "w", "-v", "-v", "u", "-w", "-w"}} +\def\phaseUcolor{"motoBlue!30!white"} +\def\phaseVcolor{"motoRed!30!white"} +\def\phaseWcolor{"motoGreen!30!white"} +\def\TopCondColors{{\phaseUcolor,\phaseUcolor,\phaseVcolor,\phaseVcolor,\phaseWcolor,\phaseWcolor,\phaseUcolor,\phaseUcolor,\phaseVcolor,\phaseVcolor,\phaseWcolor,\phaseWcolor}} +\def\BotCondColors{{\phaseVcolor,\phaseVcolor,\phaseWcolor,\phaseWcolor,\phaseWcolor,\phaseWcolor,\phaseUcolor,\phaseUcolor,\phaseWcolor,\phaseVcolor,\phaseWcolor,\phaseWcolor}} +\def\nodeFontSize{\tiny} + +%draw rotor: +\def\drawPMrotor{0} +\def\PMrotorPoles{4} +\def\PMrotorRotation{15} +\def\PMrotorPMthick{2} +\def\PMrotorAG{1} +\def\PMnorthColor{red!20!white} +\def\PMsouthColor{green!20!white} +\def\showRotorAngle{1} +\def\rotorAngleLabel{$\theta$} +\def\showRotorAngleTwo{0} +\def\rotorAngleTwoStart{15} +\def\rotorAngleTwoLabel{$\theta_b$} +\def\showAlpha{1} + + +% Overrides for this image +\newcommand{\setupFig} +{ + \def\TopLayerLabels{{ + " ", " ", " "," "," "," ", + " "," "," "," "," "," "}} %back of the slot + \def\BotLayerLabels{{ + " ", " "," "," "," "," ", + " "," "," "," "," "," "}} %front of the slot + \def\TopCondColors{{\phaseUcolor,\phaseVcolor,\phaseWcolor,\phaseUcolor,\phaseVcolor, + \phaseWcolor,\phaseUcolor,\phaseVcolor,\phaseWcolor,\phaseUcolor,\phaseVcolor,\phaseWcolor}} %back of slot + \def\BotCondColors{{\phaseWcolor,\phaseUcolor,\phaseVcolor,\phaseWcolor,\phaseUcolor,\phaseVcolor, + \phaseWcolor,\phaseUcolor,\phaseVcolor,\phaseWcolor,\phaseUcolor,\phaseVcolor}} %front of slot + \def\NumSlots{0} + \def\SlotWidth{3.6} + \def\SlotDepth{6.0} + \def\IntraSlotDepth{.75} + \def\StatorRotOffset{-60} %angle that slot 1 should be at with respect to the x axis + \def\StatorOR{16} + \def\StatorIR{12} + \def\drawPMrotor{1} + \def\PMrotorPoles{8} + \def\PMnorthColor{red!20!white} + \def\PMsouthColor{green!20!white} + \def\showRotorAngle{1} + \def\showRotorAngleTwo{1} + \def\rotorAngleTwoStart{-30} + \def\PMrotorRotation{15} + \def\showAlpha{0} + \def\NumberSlots{0} + \def\UseCond{0} + \def\rotorAngleTwoLabel{$\theta_{\rm enc}$} + \def\rotorAngleLabel{$\theta_{\rm m}$} +} + +\setupFig %must be defined, this can overwrite the above definitions + + + +%Stator laminations +\filldraw[fill=gray!40!white] circle(\StatorOR); +\filldraw[fill=white,very thin] circle (\StatorIR); + + +%make slots: +%find x y coordinate for slot + \pgfmathparse{(\SlotWidth/4.5)/\StatorOR}; %was: \SlotWidth/6 + \edef\slope{\pgfmathresult}; + \pgfmathparse{sqrt((\StatorIR)^2/(1+\slope^2))}; + \edef\xcord{\pgfmathresult}; + \pgfmathparse{sqrt((\StatorIR)^2/(1+(1/\slope)^2))}; + \edef\ycord{\pgfmathresult}; + + \pgfmathparse{sqrt((\StatorIR-1)^2/(1+\slope^2))}; + \edef\xcordsnip{\pgfmathresult}; + \pgfmathparse{sqrt((\StatorIR-1)^2/(1+(1/\slope)^2))}; + \edef\ycordsnip{\pgfmathresult}; + + \ifthenelse{\NumSlots = 0}{}{ + \begin{scope} + \foreach \x in {1,2,...,\NumSlots} + { + \path[fill= white,draw=black,rotate=360/\NumSlots*(\x-1)+\StatorRotOffset, name path =slotPath] (\xcord, \ycord) -- ++(\IntraSlotDepth,0) -- ++(0, \SlotWidth/3) -- ++(\SlotDepth, 0) -- ++(0,-\SlotWidth) -- ++(-\SlotDepth,0) -- ++(0, \SlotWidth/3) -- ++(-\IntraSlotDepth,0) -- cycle; + } + \end{scope} + + \begin{scope} + \foreach \x in {1,2,...,\NumSlots} + { + \pgfmathparse{\TopLayerLabels[\x-1]}; + \edef\TopLayerLabel{\pgfmathresult}; + \pgfmathparse{\BotLayerLabels[\x-1]}; + \edef\BotLayerLabel{\pgfmathresult}; + \path[fill= white,rotate=360/\NumSlots*(\x-1)+\StatorRotOffset, name path =slotPath](\xcordsnip, \ycordsnip) -- ++(\IntraSlotDepth+1,0) -- ++(0, \SlotWidth/3) -- ++(\SlotDepth, 0) -- ++(0,-\SlotWidth) -- ++(-\SlotDepth,0) -- ++(0, \SlotWidth/3) -- ++(-\IntraSlotDepth-1,0) -- cycle; + \ifthenelse{\UseCond = 1} + { + \pgfmathparse{\TopCondColors[\x-1]} + \edef\TopCondColor{\pgfmathresult} + \pgfmathparse{\BotCondColors[\x-1]} + \edef\BotCondColor{\pgfmathresult} + + \filldraw[fill = \BotCondColor, very thin,rotate=360/\NumSlots*(\x-1)+\StatorRotOffset-.5] (\StatorIR+\IntraSlotDepth+\CondRadius+.25,0) circle(\CondRadius) node[font=\tiny]{\BotLayerLabel}; + \filldraw[fill = \TopCondColor, very thin, rotate=360/\NumSlots*(\x-1)+\StatorRotOffset-.5] (\StatorIR+\IntraSlotDepth+\SlotDepth-\CondRadius-.25,0) circle(\CondRadius) node[font=\nodeFontSize]{\TopLayerLabel}; + } + { + \draw[rotate=360/\NumSlots*(\x-1)+\StatorRotOffset] (\StatorIR + \IntraSlotDepth+\SlotDepth/2, -\SlotWidth/2) -- +(0, \SlotWidth); + \draw [rotate=360/\NumSlots*(\x-1)+\StatorRotOffset](\StatorIR + \IntraSlotDepth + \SlotDepth/4, 0) node{\BotLayerLabel}; + \draw [rotate=360/\NumSlots*(\x-1)+\StatorRotOffset](\StatorIR + \IntraSlotDepth + 3*\SlotDepth/4, 0) node{\TopLayerLabel}; + } + \ifthenelse{\NumberSlots = 1} + { + \draw [rotate=360/\NumSlots*(\x-1)+\StatorRotOffset](\StatorIR + \IntraSlotDepth + 5*\SlotDepth/4, 0) node{\x}; + }{} + } + \end{scope}} + + \begin{scope}[rotate = \PMrotorRotation] + + \ifthenelse{\drawPMrotor = 1} + { + \edef\rotorPMOR{\StatorIR-\PMrotorAG} + \edef\rotorShaftOR{\rotorPMOR - \PMrotorPMthick} + \edef\PMangle{180/\PMrotorPoles} + + \fill[gray!40!white] (0,0) circle(\rotorShaftOR); + \foreach \x in {1,2,...,\PMrotorPoles} + { + \begin{scope}[rotate=(\x-1)*\PMangle*2] + \pgfmathparse{int(mod(\x,2))} + \edef\NorthPole{\pgfmathresult} + + \def\pmColor{\PMnorthColor} + \def\pmColor{\PMsouthColor} + \ifthenelse{\NorthPole = 1} + { + \def\pmColor{\PMnorthColor} + } + { + \def\pmColor{\PMsouthColor} + } + %\filldraw[gray!40!white,draw=black] ([shift=(-180\PMrotorPoles:\rotorShaftOR)]0,0) arc (-180/\PMrotorPoles:180/\PMrotorPole:\rotorShaftOR); + \fill[\pmColor] ([shift=(-\PMangle:\rotorShaftOR)]0,0) arc (-\PMangle:\PMangle:\rotorShaftOR) + -- (\PMangle:\rotorPMOR) + -- ([shift=(\PMangle:\rotorPMOR)]0,0) arc (\PMangle:-\PMangle:\rotorPMOR) + -- (-\PMangle:\rotorShaftOR); + \draw([shift=(-\PMangle:\rotorShaftOR)]0,0) arc (-\PMangle:\PMangle:\rotorShaftOR) + -- (\PMangle:\rotorPMOR) + -- ([shift=(\PMangle:\rotorPMOR)]0,0) arc (\PMangle:-\PMangle:\rotorPMOR); + + + \ifthenelse{\NorthPole = 1} + { + \draw[->] (\rotorShaftOR+.25, 0) -- (\rotorPMOR-.25, 0); + } + { + \draw[<-] (\rotorShaftOR+.25, 0) -- (\rotorPMOR-.25, 0); + } + \end{scope} + } + + } + {} +\end{scope} + +\ifthenelse{\showRotorAngle = 1} + { + \draw(\PMrotorRotation:\StatorIR-\PMrotorAG/2) -- (\PMrotorRotation:\StatorOR+5); + \draw(0:\StatorOR+.5) -- (0:\StatorOR+9) node[right]{phase $u$ axis}; + %\draw[dashed](0:\StatorOR+5) -- (0:\StatorOR+10) node[right]{phase $u$ axis}; + \draw[->]([shift=(0:\StatorOR+2.5)]0,0) arc (0:\PMrotorRotation:\StatorOR+2.5) node[xshift=-3,pos=0.5, right]{\rotorAngleLabel}; + } + {} + +\ifthenelse{\showRotorAngleTwo = 1} +{ + \draw(\PMrotorRotation:\StatorIR-\PMrotorAG/2) -- (\PMrotorRotation:\StatorOR+10); + \draw(\rotorAngleTwoStart:\StatorOR+.5) -- (\rotorAngleTwoStart:\StatorOR+10) node[pos=1, right,rotate=\rotorAngleTwoStart] {z-pulse}; + \draw[->]([shift=(\rotorAngleTwoStart:\StatorOR+7.5)]0,0) arc (\rotorAngleTwoStart:\PMrotorRotation:\StatorOR+7.5) node[xshift=-2,pos=0.85, right]{\rotorAngleTwoLabel}; + \draw[->]([shift=(\rotorAngleTwoStart:\StatorOR+2.5)]0,0) arc (\rotorAngleTwoStart:0:\StatorOR+2.5) node[xshift=-3,pos=0.5, right]{$\theta_{\rm off}$}; +} +{} + +\ifthenelse{\showAlpha = 1} +{ + \draw(0,0) -- (60:\StatorIR-\PMrotorAG-\PMrotorPMthick*1.5); + \draw(0,0) -- (0:\StatorIR-\PMrotorAG-\PMrotorPMthick*1.5); + %\draw(0:\StatorOR+.5) -- (0:\StatorOR+5); + \draw[->]([shift=(0:\StatorIR-\PMrotorAG-\PMrotorPMthick*1.5-2.5)]0,0) arc (0:60:\StatorIR-\PMrotorAG-\PMrotorPMthick*1.5-2.5) node[pos=0.95, right]{$\alpha$}; +} +{} +\showAlpha{1} +\end{tikzpicture} +} +\end{document} + From cb1c257d687b4eb4d1978a4e6d05edcc60b52a52 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sat, 7 Jun 2025 17:55:03 -0500 Subject: [PATCH 38/59] add test code --- .../control-with-amdc/encoder-fb/index.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 4142868f..690863f9 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -1,5 +1,17 @@ # Encoder Feedback +[the encoder](/firmware/arch/drivers/encoder.md) + +[firmware](/firmware/index.rst) + +[arch](/firmware/arch/index.md) + +[timing manager](/firmware/arch/timing-manager.md) + +[drivers](/firmware/arch/drivers/index.md) + +[logging](/getting-started/user-guide/logging/index.md) + ## Background Encoders are used to determine the rotor position and speed, and are the typical method of feedback to the control system in a motor drive. This document explains how to use the AMDC's encoder interface to extract high quality rotor position and speed data. From 41096e6bee2468ed3602ba1cd3944db4daa6e35e Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sat, 7 Jun 2025 22:28:48 -0500 Subject: [PATCH 39/59] - Edit everything before finding the offset - Fix links --- .../control-with-amdc/encoder-fb/index.md | 83 +++++++++---------- 1 file changed, 41 insertions(+), 42 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index 690863f9..ed3130dc 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -1,25 +1,13 @@ # Encoder Feedback -[the encoder](/firmware/arch/drivers/encoder.md) - -[firmware](/firmware/index.rst) - -[arch](/firmware/arch/index.md) - -[timing manager](/firmware/arch/timing-manager.md) - -[drivers](/firmware/arch/drivers/index.md) - -[logging](/getting-started/user-guide/logging/index.md) - ## Background Encoders are used to determine the rotor position and speed, and are the typical method of feedback to the control system in a motor drive. This document explains how to use the AMDC's encoder interface to extract high quality rotor position and speed data. For more information: -- on how encoders work and are interfaced with the AMDC, see the [encoder hardware subsystem page](https://docs.amdc.dev/hardware/subsystems/encoder.html#) -- on the driver functionality included with the AMDC firmware, see the [encoder driver architecture page](https://docs.amdc.dev/firmware/arch/drivers/encoder.html). +- on how encoders work and are interfaced with the AMDC, see the [encoder hardware subsystem page](/hardware/subsystems/encoder.md); +- on the driver functionality included with the AMDC firmware, see the [encoder driver architecture page](/firmware/arch/drivers/encoder.md). ## Rotor Position @@ -57,52 +45,63 @@ The recommended approach to reading the shaft position from the encoder is illus -First, the user uses the AMDC [`drv/encoder`](/firmware/arch/drivers/encoder.md) driver module function `encoder_get_position()` to get the count of the encoder reading. The`drv/encoder` driver module also has a function called `encoder_get_steps()` which gives the incremental change in the encoder position. Whereas, `encoder_get_position()` gives the actual position of the shaft and this can be converted to rotor position in radians. +First, the AMDC [`drv/encoder`](/firmware/arch/drivers/encoder.md) driver module function `encoder_get_position()` is used to obtain the the encoder's count $\theta_{\rm enc}$ since the last z-pulse. + +```{tip} +The [`drv/encoder`](/firmware/arch/drivers/encoder.md) driver module also has a function called `encoder_get_steps()` which returns the encoder's count since power-on. One rotation direction increments, the other decrements. This value does not wrap around (it ignores `encoder_set_counts_per_rev()` and the z-pulse). Users are advised to use `encoder_get_position()`, which does wrap around and tracks the z-pulse. +``` + +Next, the user should calculate $\theta_{\rm m}$ from $\theta_{\rm enc}$. This is done by 1) removing the offset and 2) converting counts into radians. For the the angles defined as shown in the image above, this is simply calculated as + +$$ +\theta_{\rm m} = \tfrac{2\pi}{\rm COUNTS\_PER\_REV} \left( \theta_{\rm enc} - \theta_{\rm off} \right) +$$ (eq:convCCW) + +In this case, a counter-clockwise rotation of the rotor causes the $\theta_{\rm enc}$ to increase. However, in some teststands a clockwise rotation causes $\theta_{\rm enc}$ to increment. For these encoders, $\theta_{\rm m}$ is calculated as + +$$ +\theta_{\rm m} &= \tfrac{2\pi}{\rm COUNTS\_PER\_REV} \left({\scriptstyle \rm COUNTS\_PER\_REV} - \theta_{\rm enc} + \theta_{\rm off} \right) \\ &= 2\pi - \theta_{\rm m, CCW} +$$ (eq:convCW) + +```{tip} +The user can experimentally determine whether the encoder count increases with counter-clockwise rotation of the shaft by rotating the shaft and using [logging](/getting-started/user-guide/logging/index.md) to observe the trend of $\theta_{\rm enc}$. +``` - Next, the user needs to verify if the encoder count is increasing or decreasing with counter-clock wise rotation of shaft. This may be done manually by rotating the shaft and observing the trend of the reported position with respect to the direction of rotation. In the figure, the signal `CCW` indicates this directionality. It must be set to `1` if the encoder count increases with counter clockwise rotation of shaft and `0` otherwise. Additionally, the user needs to provide the encoder offset, `offset`, and the encoder counts per revolution, `ENCODER_COUNT_PER_REV`. A method to get the value of offset is described in the next [subsection](#finding-the-offset). Using all of these quantities, the obtained count can be translated into angular position using a simple linear equation. Note that this document follows the convention of a positive rotor angle in the counter clockwise direction of shaft rotation while calculating rotor position from the count signal. - - Finally, the user must ensure that angle is within the bounds of $0$ and $2\pi$ by appropriately wrapping the `rotor position` signal using the `mod` function. This is shown in the final block in the diagram. +Finally, the user must ensure that angle is within the bounds of $0$ and $2\pi$ by appropriately wrapping the $\theta_{\rm m}$. This can be accomplished in C by using the `mod` function. This is shown in the final block in the diagram. -Example code to convert encoder to angular position in radians: +Here is example code to convert the encoder to angular position in radians (note that this assumes the encoder offset $\theta_{\rm off}$ is already know; a procedure to determine this is described in the next [subsection](#finding-the-offset)): ```C double task_get_theta_m(void) { - // Get raw encoder position - uint32_t position; - encoder_get_position(&position); - - int ENCODER_COUNT_PER_REV, CCW; - double enc_theta_m_offset; + // User to set encoder offset + double theta_off = 100; // User to set encoder count per revolution - ENCODER_COUNT_PER_REV = 1024; + double ENCODER_COUNT_PER_REV = 1024; - // Set 1 if encoder count increases with CCW rotation of shaft, Set 0 if encoder count increases with CW rotation of shaft - CCW = 1; + // User to set 1 if encoder count increases with CCW rotation of shaft, set 0 if encoder count increases with CW rotation of shaft + int CCW_ROTATION_FLAG = 1; // Angular position to be computed - double theta_m_enc; - - // User to set encoder offset - enc_theta_m_offset = 100; + double theta_m; + // Get raw encoder position + uint32_t theta_enc; + encoder_get_position(&theta_enc); // Convert to radians - if (CCW){ - theta_m_enc = (double) PI2 * ( ( (double)position - enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); - } - else{ - theta_m_enc = (double) PI2 * ( ( (double)ENCODER_COUNT_PER_REV - (double)1 -(double)position + enc_theta_m_offset )/ (double) ENCODER_COUNT_PER_REV); + theta_m = (double) PI2 * ( ((double)theta_enc - theta_off) / (double) ENCODER_COUNT_PER_REV); + + if (!CCW_ROTATION_FLAG){ + theta_m = PI2 - theta_m; } - + // Mod by 2 pi - theta_m_enc = fmod(theta_m_enc,PI2); - return theta_m_enc; + theta_m = fmod(theta_m,PI2); + return theta_m; } ``` - - ### Finding the offset The example code shown above makes uses of an encoder offset value, `enc_theta_m_offset`. It is necessary for the user to find this offset experimentally for their machine. For synchronous machines, this offset is the count value measured by the encoder when the d-axis of the rotor is aligned with the phase U winding axis of the stator. From 9e7a82b686c06c158b99001652bf46b2af7d2356 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sat, 7 Jun 2025 22:40:42 -0500 Subject: [PATCH 40/59] change image naming to dash-case --- source/getting-started/control-with-amdc/encoder-fb/index.md | 2 +- .../{MotorCrossSection.svg => motor-cross-section.svg} | 0 .../{MotorCrossSection.tex => motor-cross-section.tex} | 0 3 files changed, 1 insertion(+), 1 deletion(-) rename source/getting-started/control-with-amdc/encoder-fb/resources/{MotorCrossSection.svg => motor-cross-section.svg} (100%) rename source/getting-started/control-with-amdc/encoder-fb/resources/{MotorCrossSection.tex => motor-cross-section.tex} (100%) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index ed3130dc..b475c5c3 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -15,7 +15,7 @@ The AMDC supports [incremental encoders with quadrature ABZ outputs](https://en. This document assumes the configuration shown in the figure below, where the control code expects a measurement of the angle of the rotor's north pole relative to the phase $u$ magnetic axis, labeled as $\theta_{\rm m}$. The encoder provides $\theta_{\rm enc}$, which is the number of counts since the last z-pulse. The user's code needs to convert $\theta_{\rm enc}$ (in units of counts) into $\theta_{\rm m}$ (likely in units of radians) and handle an offset angle $\theta_{\rm off}$ between the encoder's 0 position and the phase $u$ axis. -![Motor Cross-Section with Encoder Angles](resources/MotorCrossSection.svg) +![Motor Cross-Section with Encoder Angles](resources/motor-cross-section.svg) ### Configuring the encoder diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.svg b/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.svg similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.svg rename to source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.svg diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.tex b/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.tex similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/resources/MotorCrossSection.tex rename to source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.tex From cf35e6c2edd5d19bfef427a805fc2299cc2696bd Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sun, 8 Jun 2025 06:47:38 -0500 Subject: [PATCH 41/59] Update simulink --- .../encoder-fb/simulink/compute_speed.slx | Bin 64593 -> 64991 bytes .../encoder-fb/simulink/setup.m | 5 +++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx index 9df26a3fd1de007f28cbcd71407231245c12db60..25b18e60e0c9fae1d2cc91c99952bca566045d53 100644 GIT binary patch delta 45624 zcmV)#K##xC_ygbj0~}CG0|XQR000O8001EXjl=8q18V>PwRHdh766lB_!xieyLC{N z;s5?gC|wfLAR-~s-6*Lvf*{@94Tn@pkW#u8lp`KOy1S)?LwEO~JN7=G&wh7)v$KEg 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a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index 1336c88e..97312224 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -6,7 +6,7 @@ Tsim = 1e-5; p = 1; % number of pole -speed_cmd = 3000; % fundmental frequency [Hz] +speed_cmd = 3000; % rotational speed [r/min] % Parameters for low pass filter f_lpf = 10; % low pass fileter cut-off frequency (Hz) @@ -90,7 +90,7 @@ den = squeeze(sig_val.omega_raw); % input signal outputs = { squeeze(sig_val.omega_lpf), 'Low-pass filter', '--'; - squeeze(sig_val.omega_pll), 'PLL', '-'; + % squeeze(sig_val.omega_pll), 'PLL', '-'; squeeze(sig_val.omega_sf), 'Observer', '-.' }; % output signals @@ -139,6 +139,7 @@ xlim(ax1, [f1 f2]); xlim(ax2, [f1 f2]); xlim(ax3, [f1 f2]); +% ylim(ax2, [-180 0]); ylim(ax3, [0 1]); set(ax1, 'xscale', 'log'); From 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--git a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index a4030eb5..6cd0ed97 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -21,7 +21,7 @@ end p = 1; % number of pole -speed_cmd = 3000; % rotational speed [r/min] +speed_cmd = 3000; % rotational speed (r/min) % Parameters for low pass filter f_lpf = 10; % low pass fileter cut-off frequency (Hz) @@ -46,6 +46,12 @@ f_init = 0.1; % initial frequency of chirp [Hz] f_target = 1000; % chirp frequency at target time [Hz] +% Parameters for speed control +fb_speed = 100; +omega_b_speed = 2*pi*fb_speed; +Kp_speed = omega_b_speed*J_z; +Ki_speed = omega_b_speed*b; + %% Run simulation out = sim('compute_speed.slx'); From 600fc24b1cd17d63223e7ed61319af501d64f339 Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sun, 8 Jun 2025 09:01:43 -0500 Subject: [PATCH 44/59] Improve typesetting around the image --- .../getting-started/control-with-amdc/encoder-fb/index.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/index.md b/source/getting-started/control-with-amdc/encoder-fb/index.md index b475c5c3..40ae502d 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/index.md +++ b/source/getting-started/control-with-amdc/encoder-fb/index.md @@ -13,9 +13,13 @@ For more information: The AMDC supports [incremental encoders with quadrature ABZ outputs](https://en.wikipedia.org/wiki/Incremental_encoder#Quadrature_outputs) and a fixed number of counts per revolution `CPR` (for example, `CPR = 1024`). The user needs to provide code that interfaces to the AMDC's drivers to read the encoder count and convert it into usable angular information that is suitable for use within the control code. -This document assumes the configuration shown in the figure below, where the control code expects a measurement of the angle of the rotor's north pole relative to the phase $u$ magnetic axis, labeled as $\theta_{\rm m}$. The encoder provides $\theta_{\rm enc}$, which is the number of counts since the last z-pulse. The user's code needs to convert $\theta_{\rm enc}$ (in units of counts) into $\theta_{\rm m}$ (likely in units of radians) and handle an offset angle $\theta_{\rm off}$ between the encoder's 0 position and the phase $u$ axis. +```{image} resources/motor-cross-section.svg +:alt: Motor Cross-Section with Encoder Angles +:width: 350px +:align: right +``` -![Motor Cross-Section with Encoder Angles](resources/motor-cross-section.svg) +This document assumes the configuration shown to the right, where the control code expects a measurement of the angle of the rotor's north pole relative to the phase $u$ magnetic axis, labeled as $\theta_{\rm m}$. The encoder provides $\theta_{\rm enc}$, which is the number of counts since the last z-pulse. The user's code needs to convert $\theta_{\rm enc}$ (in units of counts) into $\theta_{\rm m}$ (likely in units of radians) and handle an offset angle $\theta_{\rm off}$ between the encoder's 0 position and the phase $u$ axis. ### Configuring the encoder From 5e845e77a3c2d70c957482848c99b630f2afe2be Mon Sep 17 00:00:00 2001 From: Eric Severson Date: Sun, 8 Jun 2025 11:12:54 -0500 Subject: [PATCH 45/59] Make motor cross-section plot 2 poles, add phave v and w axes --- .../resources/motor-cross-section.svg | 266 +++++++++++------- .../resources/motor-cross-section.tex | 4 +- 2 files changed, 165 insertions(+), 105 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.svg b/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.svg index fc53967c..6c6b7b65 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.svg +++ b/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.svg @@ -1,5 +1,5 @@ - + @@ -30,136 +30,194 @@ - + - + - + - + - + - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.tex b/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.tex index e5822bae..d5878df3 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.tex +++ b/source/getting-started/control-with-amdc/encoder-fb/resources/motor-cross-section.tex @@ -103,7 +103,7 @@ \def\StatorOR{16} \def\StatorIR{12} \def\drawPMrotor{1} - \def\PMrotorPoles{8} + \def\PMrotorPoles{2} \def\PMnorthColor{red!20!white} \def\PMsouthColor{green!20!white} \def\showRotorAngle{1} @@ -230,6 +230,8 @@ { \draw(\PMrotorRotation:\StatorIR-\PMrotorAG/2) -- (\PMrotorRotation:\StatorOR+5); \draw(0:\StatorOR+.5) -- (0:\StatorOR+9) node[right]{phase $u$ axis}; + \draw[rotate=120](0:\StatorOR+.5) -- (0:\StatorOR+9) node[right, xshift=-2, yshift=9, rotate=120+180]{phase $v$ axis}; + \draw[rotate=240](0:\StatorOR+.5) -- (0:\StatorOR+9) node[right, xshift=-7, yshift=-8, rotate=240+180]{phase $w$ axis}; %\draw[dashed](0:\StatorOR+5) -- (0:\StatorOR+10) node[right]{phase $u$ axis}; \draw[->]([shift=(0:\StatorOR+2.5)]0,0) arc (0:\PMrotorRotation:\StatorOR+2.5) node[xshift=-3,pos=0.5, right]{\rotorAngleLabel}; } From 5b96b3c9d77e5199789eed466a000220462077c3 Mon Sep 17 00:00:00 2001 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a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -8,23 +8,13 @@ load_system('compute_speed') % load Simulink model -if ENABLE_SYSTEM_ID == 0 - Tend = 0.2; - % Comment out Chirp Signal block - set_param('compute_speed/Chirp Signal', 'Commented', 'on'); - set_param('compute_speed/Theta to Omega', 'Commented', 'off'); -elseif ENABLE_SYSTEM_ID == 1 - Tend = 10; - % Comment out Theta to Omega block - set_param('compute_speed/Chirp Signal', 'Commented', 'off'); - set_param('compute_speed/Theta to Omega', 'Commented', 'on'); -end +Tend = 0.2; p = 1; % number of pole speed_cmd = 3000; % rotational speed (r/min) % Parameters for low pass filter -f_lpf = 10; % low pass fileter cut-off frequency (Hz) +f_lpf = 100; % low pass fileter cut-off frequency (Hz) omega_lpf = 2*pi*f_lpf; % low pass fileter cut-off frequency (rad/s) % Parameters for PLL @@ -87,6 +77,7 @@ ylabel('$\theta_{\mathrm{m}}$ (rad)','Interpreter','latex'); xlim([0 Tend]); ylim([0 7]); +yticks([0 2 4 6]); % Plot theta_out subplot(2,1,2); From 88edda45116e7bd9d25ffa2a2f41a2070ce96cfb Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sun, 8 Jun 2025 12:04:35 -0500 Subject: [PATCH 47/59] Remove unneccesary code --- .../encoder-fb/simulink/compute_speed.slx | Bin 66265 -> 66170 bytes .../encoder-fb/simulink/setup.m | 117 +----------------- 2 files changed, 3 insertions(+), 114 deletions(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx index 9e8d8e39d5ed711037aefeb29a1d05c1db1749f3..75e57ea08a23babbfeaa968e1f4e0e91a096f515 100644 GIT binary patch delta 13170 zcmZv@1yr0t&nOIwLveR0?(PK^_u}qS+@<*9?ps`2ytuo&ySqavR@^V``~LSk-#!1c z=Q$_IWRpy0CYjmIEQdfp21Da1$w5J5K|nyjzrW-V{-HpUWdH<(KMEL4jReee4G)eM zj{x~0q8q}wP*D<*OB#ILyeNntsoSPS-ep7t7i|P?!fEGE?5nhs2)}sUQ2BT~qti0) 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-ENABLE_SYSTEM_ID = 0; - Ts = 1e-4; Tsim = 1e-5; @@ -50,7 +48,7 @@ runObj = Simulink.sdi.Run.getLatest; % List of variables to extract -obj2ext = {'time','theta_m','omega_raw', 'omega_lpf', 'omega_pll', 'omega_sf'}; +obj2ext = {'time', 'omega_raw', 'omega_lpf', 'omega_pll', 'omega_sf'}; % Get signal IDs and store signals into array for idx = 2:length(obj2ext) @@ -63,24 +61,13 @@ %% Plot figure width = 2*5.43; -height = 1.2*3*4.38 / 3; +height = 1.2*3*4.38/3/2; set(0,'units','inches'); Inch_SS = get(0,'screensize'); lw = 1; % line width figure1 = figure; -% Plot theta_in -subplot(2,1,1); -hold on; -plot(time, squeeze(sig_val.theta_m), 'Color', 'k', 'LineWidth', lw); -xlabel('Time [s]','Interpreter','latex'); -ylabel('$\theta_{\mathrm{m}}$ (rad)','Interpreter','latex'); -xlim([0 Tend]); -ylim([0 7]); -yticks([0 2 4 6]); - -% Plot theta_out -subplot(2,1,2); +% Plot omega hold on; plot(time, squeeze(sig_val.omega_raw), 'Color', 'k', 'LineWidth', lw); plot(time, squeeze(sig_val.omega_lpf), 'Color', 'r', 'LineWidth', lw); @@ -97,101 +84,3 @@ set(figure1,'Units','inches','Position',[(Inch_SS(3)-width)/2 (Inch_SS(4)-height)/2 width height]); print(figure1, '-dsvg','-noui','plot_results'); print(figure1, '-dpng','-r300','plot_results'); - -%% System ID -if ENABLE_SYSTEM_ID == 1 - den = squeeze(sig_val.omega_raw); % input signal - outputs = { - squeeze(sig_val.omega_lpf), 'Low-pass filter', '--'; - % squeeze(sig_val.omega_pll), 'PLL', '-'; - squeeze(sig_val.omega_sf), 'Observer', '-.' - }; % output signals - - markersize = 3; - linewidth = 1; - colors = lines(size(outputs, 1)); % set color map - - % Bode plot - f1 = f_init; - f2 = f_target; - - figure; - tiledlayout(3,1); - ax1 = nexttile; % Magnitude - ax2 = nexttile; % Phase - ax3 = nexttile; % Coherence - - hold(ax1, 'on'); - hold(ax2, 'on'); - hold(ax3, 'on'); - - % Compute magnitude and phase for each signal - for i = 1:size(outputs, 1) - num = outputs{i, 1}; - label = outputs{i, 2}; - linestyle = outputs{i, 3}; - - [freq, mag, phase, coh] = generateFRF(num, den, Ts, 10000, 'hann'); - - plot(ax1, freq, 20*log10(mag), ... - 'LineStyle', 'none', 'Marker', 'o', ... - 'Color', colors(i,:), 'MarkerSize', markersize, ... - 'DisplayName', label); - - plot(ax2, freq, phase, ... - 'LineStyle', 'none', 'Marker', 'o', ... - 'Color', colors(i,:), 'MarkerSize', markersize, ... - 'DisplayName', label); - - plot(ax3, freq, coh, ... - 'LineStyle', 'none', 'Marker', 'o', ... - 'Color', colors(i,:), 'MarkerSize', markersize, ... - 'DisplayName', label); - end - - xlim(ax1, [f1 f2]); - xlim(ax2, [f1 f2]); - xlim(ax3, [f1 f2]); - % ylim(ax2, [-180 0]); - ylim(ax3, [0 1]); - - set(ax1, 'xscale', 'log'); - set(ax2, 'xscale', 'log'); - set(ax3, 'xscale', 'log'); - - xlabel(ax3, "Frequency (Hz)"); - ylabel(ax1, "Magnitude (dB)"); - ylabel(ax2, "Phase (deg)"); - ylabel(ax3, "Coherence"); - - grid(ax1, 'on'); - grid(ax2, 'on'); - grid(ax3, 'on'); - - legend(ax1, 'Location', 'southwest'); - - set(findall(gcf, '-property', 'FontName'), 'FontName', 'Times New Roman'); - - set(figure1,'Units','inches','Position',[(Inch_SS(3)-width)/2 (Inch_SS(4)-height)/2 width height]); - print(figure1, '-dsvg','-noui','bode_plot'); - print(figure1, '-dpng','-r300','bode_plot'); -end - -%% -function [freq,mag,phase,coh] = generateFRF(num,den,T,lines,win) - - fs = 1/T; - overlap = lines/2; - averages = floor(length(num)/(lines-overlap)); - windowType = window(win,lines); - - [FRF,freq] = tfestimate(den,num,windowType,overlap,lines,fs); - [coh,freq] = mscohere(den,num,windowType,overlap,lines,fs); - - FRF = fftshift(FRF); - coh = fftshift(coh); - freq = freq - max(freq)/2; - mag = abs(FRF); - phase = angle(FRF) * 180/pi; - -end \ No newline at end of file From f5c907f9a8bc5963f803951ec089a36b338aa170 Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Sun, 8 Jun 2025 12:28:35 -0500 Subject: [PATCH 48/59] Update simulink, cleaning up everything --- .../encoder-fb/simulink/compute_speed.slx | Bin 66170 -> 64072 bytes 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b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index 628de531..34daf621 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -41,24 +41,41 @@ Ki_speed = omega_b_speed*b; %% Run simulation -out = sim('compute_speed.slx'); +set_param('compute_speed/Speed Controller LPF', 'Commented', 'off'); +set_param('compute_speed/Speed Controller PLL', 'Commented', 'on'); +set_param('compute_speed/Speed Control Observer', 'Commented', 'on'); +sim('compute_speed.slx'); +run1 = Simulink.sdi.Run.getLatest; + +set_param('compute_speed/Speed Controller LPF', 'Commented', 'on'); +set_param('compute_speed/Speed Controller PLL', 'Commented', 'off'); +set_param('compute_speed/Speed Control Observer', 'Commented', 'on'); +sim('compute_speed.slx'); +run2 = Simulink.sdi.Run.getLatest; + +set_param('compute_speed/Speed Controller LPF', 'Commented', 'on'); +set_param('compute_speed/Speed Controller PLL', 'Commented', 'on'); +set_param('compute_speed/Speed Control Observer', 'Commented', 'off'); +sim('compute_speed.slx'); +run3 = Simulink.sdi.Run.getLatest; %% Post processing -% Extract simulation data -runObj = Simulink.sdi.Run.getLatest; - % List of variables to extract obj2ext = {'time', 'omega_raw', 'omega_lpf', 'omega_pll', 'omega_sf'}; - -% Get signal IDs and store signals into array -for idx = 2:length(obj2ext) - sigID = getSignalIDsByName(runObj,obj2ext{idx}); - sig_obj.(obj2ext{idx}) = Simulink.sdi.getSignal(sigID); - sig_val.(obj2ext{idx}) = sig_obj.(obj2ext{idx}).Values.Data; +runs = {run1, run2, run3}; + +for r = 1:3 + runObj = runs{r}; + for i = 1:length(obj2ext) + sigID = getSignalIDsByName(runObj, obj2ext{i}); + if ~isempty(sigID) + sig_obj{r}.(obj2ext{i}) = Simulink.sdi.getSignal(sigID); + sig_val{r}.(obj2ext{i}) = sig_obj{r}.(obj2ext{i}).Values.Data; + time{r} = sig_obj{r}.(obj2ext{i}).Values.Time; + end + end end -time = sig_obj.(obj2ext{2}).Values.Time; - %% Plot figure width = 2*5.43; height = 1.2*3*4.38/3/2; @@ -69,10 +86,10 @@ figure1 = figure; % Plot omega hold on; -plot(time, squeeze(sig_val.omega_raw), 'Color', 'k', 'LineWidth', lw); -plot(time, squeeze(sig_val.omega_lpf), 'Color', 'r', 'LineWidth', lw); -plot(time, squeeze(sig_val.omega_pll), 'Color', 'b', 'LineWidth', lw); -plot(time, squeeze(sig_val.omega_sf), '--', 'Color', 'g', 'LineWidth', lw); +plot(time{3}, squeeze(sig_val{3}.omega_raw), 'Color', 'k', 'LineWidth', lw); +plot(time{1}, squeeze(sig_val{1}.omega_lpf), 'Color', 'r', 'LineWidth', lw); +plot(time{2}, squeeze(sig_val{2}.omega_pll), 'Color', 'b', 'LineWidth', lw); +plot(time{3}, squeeze(sig_val{3}.omega_sf), '--', 'Color', 'g', 'LineWidth', lw); xlabel('Time [s]','Interpreter','latex'); ylabel('$\Omega$ (rad/s)','Interpreter','latex'); xlim([0 Tend]); From 4f094cac363b0126f7f15d03b7bcc20662048a90 Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Fri, 19 Dec 2025 15:23:28 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From b08749685fbfb01c7220d228f1426b8e98268ec3 Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Fri, 19 Dec 2025 16:02:20 -0600 Subject: [PATCH 56/59] Rename simulink model --- ...compute_speed.slx => speedControlSimulation.slx} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename source/getting-started/control-with-amdc/encoder-fb/simulink/{compute_speed.slx => speedControlSimulation.slx} (100%) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx b/source/getting-started/control-with-amdc/encoder-fb/simulink/speedControlSimulation.slx similarity index 100% rename from source/getting-started/control-with-amdc/encoder-fb/simulink/compute_speed.slx rename to source/getting-started/control-with-amdc/encoder-fb/simulink/speedControlSimulation.slx From 06a3b2fcee6dcd00a4cbe4decd674802c3464e4c Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Fri, 19 Dec 2025 16:03:12 -0600 Subject: [PATCH 57/59] Add gitignore --- .../encoder-fb/simulink/.gitignore | 32 +++++++++++++++++++ 1 file changed, 32 insertions(+) create mode 100644 source/getting-started/control-with-amdc/encoder-fb/simulink/.gitignore diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/.gitignore b/source/getting-started/control-with-amdc/encoder-fb/simulink/.gitignore new file mode 100644 index 00000000..1f886b6c --- /dev/null +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/.gitignore @@ -0,0 +1,32 @@ +########## +# MATLAB # +########## + +# Windows default autosave extension +*.asv + +# OSX / *nix default autosave extension +*.m~ + +# Compiled MEX binaries (all platforms) +*.mex* + +# Packaged app and toolbox files +*.mlappinstall +*.mltbx + +# Generated helpsearch folders +helpsearch*/ + +# Simulink code generation folders +slprj/ +sccprj/ + +# Matlab code generation folders +codegen/ + +# Simulink autosave extension +*.autosave + +# Simulink cache files +*.slxc From 68d06b6b9661b68e51f137afe1932e05b0167c84 Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Fri, 19 Dec 2025 16:04:49 -0600 Subject: [PATCH 58/59] Update m file --- .../control-with-amdc/encoder-fb/simulink/setup.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index 13792228..8634526b 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -109,7 +109,7 @@ print(figure1, '-dpng','-r300','plot_results'); function switch_speed_calculation(speed_calculation_type) - % Define maps for plant and controller models + % Define maps for speed calculation models speed_calculation_models = containers.Map( ... {'lowPassFilter', 'pllEncoder', 'observer'}, ... {'lowPassFilter', 'pllEncoder', 'observer'} ... 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zJ*GLp>`Z@QKMXc9|AqK79AHznzwnq38EP|w_5UvR@SS-HcH{iVBUT6*+AzZiUgH1z zHcLSIFI64J6@(d>{rgiC`YY-kEYQD9@c$i%SPJSl%Srk#?e>2M*pz`uA%&{ELxQT! zVv+tAHSyoLUX2ZEgq=y zJR|s76)L991FeL?w)fCy?U(<=3WZxB2A_R|k}dFo6V;)!`m|851xD~!O=#hQDmX|B zT3PfGinS;X&ew*Xn^8iY7kRd5xN3_D^;ls9hnqo%?MVKndSZnb{LTs*`H2h)S!D#9*+O|&8A$(|Px3!i zNNf*dm&kybK0`Tth@gwGPi&K55D!YSMo9Xvnd$%5DOoa9c})>)oC5v6#!C7hi%XbE zD*gYI4hl?#e#v3{TZ;eMAA&#>{}re^4W>*IsOCC5SU(E}DWN6nj9~M;zplU6*}w?J mf3OOkyFw7r@b8oGgn6hHir&;J2sjp&2` diff --git a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m index 34daf621..13cc8780 100644 --- a/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m +++ b/source/getting-started/control-with-amdc/encoder-fb/simulink/setup.m @@ -11,6 +11,10 @@ p = 1; % number of pole speed_cmd = 3000; % rotational speed (r/min) +% Parameters for plant +J_z = 29.54e-6; +b = 4.28e-6; + % Parameters for low pass filter f_lpf = 100; % low pass fileter cut-off frequency (Hz) omega_lpf = 2*pi*f_lpf; % low pass fileter cut-off frequency (rad/s) @@ -21,10 +25,6 @@ w1 = 2*pi*pole_1_Hz; w2 = 2*pi*pole_2_Hz; -% Parameters for observer -J_z = 29.54e-6; -b = 4.28e-6; - f_sf = 10; % motion state fileter cut-off frequency (Hz) wb_sf = 2*pi*f_sf; b_o_sf = wb_sf*J_z; @@ -41,30 +41,32 @@ Ki_speed = omega_b_speed*b; %% Run simulation -set_param('compute_speed/Speed Controller LPF', 'Commented', 'off'); -set_param('compute_speed/Speed Controller PLL', 'Commented', 'on'); -set_param('compute_speed/Speed Control Observer', 'Commented', 'on'); +% set_param('compute_speed/Speed Controller LPF', 'Commented', 'off'); +% set_param('compute_speed/Speed Controller PLL', 'Commented', 'on'); +% set_param('compute_speed/Speed Control Observer', 'Commented', 'on'); sim('compute_speed.slx'); run1 = Simulink.sdi.Run.getLatest; -set_param('compute_speed/Speed Controller LPF', 'Commented', 'on'); -set_param('compute_speed/Speed Controller PLL', 'Commented', 'off'); -set_param('compute_speed/Speed Control Observer', 'Commented', 'on'); -sim('compute_speed.slx'); -run2 = Simulink.sdi.Run.getLatest; - -set_param('compute_speed/Speed Controller LPF', 'Commented', 'on'); -set_param('compute_speed/Speed Controller PLL', 'Commented', 'on'); -set_param('compute_speed/Speed Control Observer', 'Commented', 'off'); -sim('compute_speed.slx'); -run3 = Simulink.sdi.Run.getLatest; +% set_param('compute_speed/Speed Controller LPF', 'Commented', 'on'); +% set_param('compute_speed/Speed Controller PLL', 'Commented', 'off'); +% set_param('compute_speed/Speed Control Observer', 'Commented', 'on'); +% sim('compute_speed.slx'); +% run2 = Simulink.sdi.Run.getLatest; +% +% set_param('compute_speed/Speed Controller LPF', 'Commented', 'on'); +% set_param('compute_speed/Speed Controller PLL', 'Commented', 'on'); +% set_param('compute_speed/Speed Control Observer', 'Commented', 'off'); +% sim('compute_speed.slx'); +% run3 = Simulink.sdi.Run.getLatest; %% Post processing % List of variables to extract -obj2ext = {'time', 'omega_raw', 'omega_lpf', 'omega_pll', 'omega_sf'}; -runs = {run1, run2, run3}; +% obj2ext = {'time', 'omega_raw', 'omega_lpf', 'omega_pll', 'omega_sf'}; +obj2ext = {'time', 'omega'}; +% runs = {run1, run2, run3}; +runs = {run1}; -for r = 1:3 +for r = 1:1 runObj = runs{r}; for i = 1:length(obj2ext) sigID = getSignalIDsByName(runObj, obj2ext{i}); @@ -86,15 +88,15 @@ figure1 = figure; % Plot omega hold on; -plot(time{3}, squeeze(sig_val{3}.omega_raw), 'Color', 'k', 'LineWidth', lw); -plot(time{1}, squeeze(sig_val{1}.omega_lpf), 'Color', 'r', 'LineWidth', lw); -plot(time{2}, squeeze(sig_val{2}.omega_pll), 'Color', 'b', 'LineWidth', lw); -plot(time{3}, squeeze(sig_val{3}.omega_sf), '--', 'Color', 'g', 'LineWidth', lw); +% plot(time{3}, squeeze(sig_val{3}.omega_raw), 'Color', 'k', 'LineWidth', lw); +plot(time{1}, squeeze(sig_val{1}.omega), 'Color', 'r', 'LineWidth', lw); +% plot(time{2}, squeeze(sig_val{2}.omega_pll), 'Color', 'b', 'LineWidth', lw); +% plot(time{3}, squeeze(sig_val{3}.omega_sf), '--', 'Color', 'g', 'LineWidth', lw); xlabel('Time [s]','Interpreter','latex'); ylabel('$\Omega$ (rad/s)','Interpreter','latex'); xlim([0 Tend]); % ylim([0 400]); -legend('$\Omega_{\mathrm{raw}}$','$\Omega_{\mathrm{lpf}}$', '$\Omega_{\mathrm{pll}}$', '$\Omega_{\mathrm{sf}}$', 'Interpreter','latex','Location','east'); +% legend('$\Omega_{\mathrm{raw}}$','$\Omega_{\mathrm{lpf}}$', '$\Omega_{\mathrm{pll}}$', '$\Omega_{\mathrm{sf}}$', 'Interpreter','latex','Location','east'); set(findall(gcf, '-property', 'FontName'), 'FontName', 'Times New Roman'); From 48a28ad7d025b756f55d82f9dc730c0002dfba22 Mon Sep 17 00:00:00 2001 From: Takahiro Noguchi Date: Fri, 19 Dec 2025 15:34:19 -0600 Subject: [PATCH 51/59] Create Reference model of low pass filter --- .../encoder-fb/simulink/compute_speed.slx | Bin 58015 -> 54860 bytes .../encoder-fb/simulink/lowPassFilter.slx | Bin 0 -> 34586 bytes 2 files changed, 0 insertions(+), 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