-
Notifications
You must be signed in to change notification settings - Fork 38
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Fix lowpass & refactor filter structure
- Fixed second order lowpass - Made the crossover frequency and damping tuneble - Use the filtered signal for PID calculations - Add a derivative filter
- Loading branch information
Showing
13 changed files
with
455 additions
and
61 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,275 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# How to discretize a second order lowpass with Tustin's method\n", | ||
| "First a continous time filter is constructed. This filter will be discretized with Tustin's method and converted into C++ code." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from sympy import *" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 2, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "a, s, d, T, z = symbols('a,s,d,T,z')" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "First our continous time system" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# a = 2*pi*c\n", | ||
| "sys = 1 / (1/a**2 * s**2 + 2*d/a * s + 1)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Translate to discrete" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 4, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle \\frac{1}{1 + \\frac{4 d \\left(z - 1\\right)}{T a \\left(z + 1\\right)} + \\frac{4 \\left(z - 1\\right)^{2}}{T^{2} a^{2} \\left(z + 1\\right)^{2}}}$" | ||
| ], | ||
| "text/plain": [ | ||
| "1/(1 + 4*d*(z - 1)/(T*a*(z + 1)) + 4*(z - 1)**2/(T**2*a**2*(z + 1)**2))" | ||
| ] | ||
| }, | ||
| "execution_count": 4, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "sys = sys.subs(s, 2 / T * (z - 1) / (z + 1))\n", | ||
| "sys" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 5, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "(T**2*a**2*z**2 + 2*T**2*a**2*z + T**2*a**2)/(T**2*a**2*z**2 + 2*T**2*a**2*z + T**2*a**2 + 4*T*a*d*z**2 - 4*T*a*d + 4*z**2 - 8*z + 4)\n" | ||
| ] | ||
| }, | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle \\frac{T^{2} a^{2} z^{2} + 2 T^{2} a^{2} z + T^{2} a^{2}}{T^{2} a^{2} z^{2} + 2 T^{2} a^{2} z + T^{2} a^{2} + 4 T a d z^{2} - 4 T a d + 4 z^{2} - 8 z + 4}$" | ||
| ], | ||
| "text/plain": [ | ||
| "(T**2*a**2*z**2 + 2*T**2*a**2*z + T**2*a**2)/(T**2*a**2*z**2 + 2*T**2*a**2*z + T**2*a**2 + 4*T*a*d*z**2 - 4*T*a*d + 4*z**2 - 8*z + 4)" | ||
| ] | ||
| }, | ||
| "execution_count": 5, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "print(cancel(sys))\n", | ||
| "cancel(sys)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 6, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/plain": [ | ||
| "[T**2*a**2, 2*T**2*a**2, T**2*a**2]" | ||
| ] | ||
| }, | ||
| "execution_count": 6, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "num = Poly(T**2*a**2*z**2 + 2*T**2*a**2*z + T**2*a**2, z)\n", | ||
| "num.all_coeffs()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 7, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/plain": [ | ||
| "[T**2*a**2 + 4*T*a*d + 4, 2*T**2*a**2 - 8, T**2*a**2 - 4*T*a*d + 4]" | ||
| ] | ||
| }, | ||
| "execution_count": 7, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "den = Poly(T**2*a**2*z**2 + 2*T**2*a**2*z + T**2*a**2 + 4*T*a*d*z**2 - 4*T*a*d + 4*z**2 - 8*z + 4, z)\n", | ||
| "den.all_coeffs()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Try to simplify" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 8, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "(b**2*z**2 + 2*b**2*z + b**2)/(b**2*z**2 + 2*b**2*z + b**2 + 4*b*d*z**2 - 4*b*d + 4*z**2 - 8*z + 4)\n" | ||
| ] | ||
| }, | ||
| { | ||
| "data": { | ||
| "text/latex": [ | ||
| "$\\displaystyle \\frac{b^{2} z^{2} + 2 b^{2} z + b^{2}}{b^{2} z^{2} + 2 b^{2} z + b^{2} + 4 b d z^{2} - 4 b d + 4 z^{2} - 8 z + 4}$" | ||
| ], | ||
| "text/plain": [ | ||
| "(b**2*z**2 + 2*b**2*z + b**2)/(b**2*z**2 + 2*b**2*z + b**2 + 4*b*d*z**2 - 4*b*d + 4*z**2 - 8*z + 4)" | ||
| ] | ||
| }, | ||
| "execution_count": 8, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "b = symbols('b')\n", | ||
| "# a*T = b -> T = b/a\n", | ||
| "sys = sys.subs(T, b/a)\n", | ||
| "print(cancel(sys))\n", | ||
| "cancel(sys)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 9, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/plain": [ | ||
| "[b**2, 2*b**2, b**2]" | ||
| ] | ||
| }, | ||
| "execution_count": 9, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "num = Poly(b**2*z**2 + 2*b**2*z + b**2, z)\n", | ||
| "num.all_coeffs()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 10, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "data": { | ||
| "text/plain": [ | ||
| "[b**2 + 4*b*d + 4, 2*b**2 - 8, b**2 - 4*b*d + 4]" | ||
| ] | ||
| }, | ||
| "execution_count": 10, | ||
| "metadata": {}, | ||
| "output_type": "execute_result" | ||
| } | ||
| ], | ||
| "source": [ | ||
| "den = Poly(b**2*z**2 + 2*b**2*z + b**2 + 4*b*d*z**2 - 4*b*d + 4*z**2 - 8*z + 4, z)\n", | ||
| "den.all_coeffs()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Translate that to C++" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "```c++\n", | ||
| "auto a = 2 * M_PI * c;\n", | ||
| "auto b = T * a;\n", | ||
| "y_[0] = ((pow(b, 2)) * u_[0] + (2 * pow(b, 2)) * u_[1] + (pow(b, 2)) * u_[2] -\n", | ||
| " (2 * pow(b, 2) - 8) * y_[1] - (pow(b, 2) - 4 * T * a * d + 4) * y_[2]) /\n", | ||
| " (pow(b, 2) + 4 * T * a * d + 4);\n", | ||
| "```" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3", | ||
| "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": "3.8.10" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 4 | ||
| } |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,32 @@ | ||
| #pragma once | ||
|
|
||
| #include <path_tracking_pid/details/fifo_array.hpp> | ||
|
|
||
| namespace path_tracking_pid::details | ||
| { | ||
| /** | ||
| * @brief discrete time derivative filter | ||
| */ | ||
| class Derivative | ||
| { | ||
| public: | ||
| /** | ||
| * @brief Construct a Derivative instance | ||
| */ | ||
| Derivative(); | ||
|
|
||
| /** | ||
| * @brief filter one sample of a signal | ||
| * @param u signal to be filtered | ||
| * @param step_size | ||
| * @return derivative of the signal | ||
| */ | ||
| double filter(double u, double step_size); | ||
|
|
||
| void reset(); | ||
|
|
||
| private: | ||
| FifoArray<double, 2> u_ = {}; | ||
| }; | ||
|
|
||
| } // namespace path_tracking_pid::details |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Oops, something went wrong.