From a14b31a134af6bb78cf7c389efb0a70cef56013c Mon Sep 17 00:00:00 2001 From: nandard Date: Thu, 22 Sep 2022 16:23:31 +0700 Subject: [PATCH] Add assignment 6 --- Assignment 6 - Tuning PID/README.md | 34 ++++++ Assignment 6 - Tuning PID/assign_6_pso.m | 141 +++++++++++++++++++++++ 2 files changed, 175 insertions(+) create mode 100644 Assignment 6 - Tuning PID/README.md create mode 100644 Assignment 6 - Tuning PID/assign_6_pso.m diff --git a/Assignment 6 - Tuning PID/README.md b/Assignment 6 - Tuning PID/README.md new file mode 100644 index 0000000..3cf2d5f --- /dev/null +++ b/Assignment 6 - Tuning PID/README.md @@ -0,0 +1,34 @@ +# Derivative Effect on Control System +This dir is belong to Control System class contains with Tuning PID with ZN1 and PSO on motor system. + +## Software +This program ran in Matlab + +## Variables +`s = tf('s');` defines `s` as 'frequency domain' for transfer function and will be used further. +``` +J = 0.01; +b = 0.1; +K = 0.01; +R = 1; +L = 0.5; +``` +Those variable comes from BLDC control system. +``` +c1=2; c2=2; w_max = 1; w_min = 0.1; particles=50; iterations=100; +var=3; e_max = 1; e_min=0.1; + +% Search limit +lim_min = 0; +lim_max = 2500; +``` +Variable above is the constant for PSO tuning. + + +## Testing + +### Notes +Contact nanda.r.d@mail.ugm.ac.id for more information +### Links +You can access the source code here +[github.com/nandard/control-system.git](https://github.com/nandard/control-system.git) diff --git a/Assignment 6 - Tuning PID/assign_6_pso.m b/Assignment 6 - Tuning PID/assign_6_pso.m new file mode 100644 index 0000000..8ffbd89 --- /dev/null +++ b/Assignment 6 - Tuning PID/assign_6_pso.m @@ -0,0 +1,141 @@ +clc; clear all; close all +% system function +s = tf('s'); +J = 0.01; +b = 0.1; +K = 0.01; +R = 1; +L = 0.5; + +num_motor = [K]; +den_motor = [J*L J*R+b*L R*b+K*K]; +motor = tf(num_motor,den_motor); +motor_l = feedback(motor,1); +step(motor_l) +%step(motor_l/s); +%impulse(motor_l); +%step(motor_l/s^2); +hold on +stepinfo(motor_l) +[y,t] = step(motor_l); +ss_error = abs(1 - y(end)) + +tic +% Constant +c1=2; c2=2; w_max = 1; w_min = 0.1; particles=50; iterations=100; +var=3; e_max = 1; e_min=0.1; + +% Search limit +lim_min = 0; +lim_max = 2500; + +% imization steps +steps = 0; + +% Initialization +for m=1:particles + for n=1:var + v(m,n)=0; + x(m,n)=lim_min+rand*(lim_max-lim_min); + xp(m,n)=x(m,n); + end + + % Model Parameters + Kp = x(m,1); + Ki = x(m,2); + Kd = x(m,3); + + % Simulation Model + pid = tf([Kd Kp Ki],[0 1 0]); + motor_cl = feedback(motor * pid, 1); + y = step(motor_cl); + + % TIAE (Objective Function) + total = 0; + T = size(y); + for t=1:T + total=total+(t*abs(y(t)-1)); + end + ITAE(m) = total; +end + +% Find the best value +[prev_best, loc] = min(ITAE); +xg(1) = x(loc,1); +xg(2) = x(loc,2); +xg(3) = x(loc,3); + +for i=1:iterations + e = e_max - ((e_max - e_min)*i)/iterations; + w = w_min + ((iterations - i)*(w_max - w_min))/iterations; + for m=1:particles + for n=1:var + v(m,n) = w*v(m,n) + c1*rand*(xp(m,n)-x(m,n)) + c2*rand*(xg(n)-x(m,n)); + x(m,n) = x(m,n) + e*v(m,n); + % Constrain + if x(m,n) < lim_min + x(m,n) = lim_min; + end + if x(m,n) > lim_max + x(m,n) = lim_max; + end + end + + % Update Personal Best + Kp = x(m,1); + Ki = x(m,2); + Kd = x(m,3); + pid = tf([Kd Kp Ki],[0 1 0]); + motor_cl = feedback(motor * pid, 1); + y = step(motor_cl); + + total = 0; + T = size(y); + for t=1:T + total=total+(t*abs(y(t)-1)); + end + ITAEp(m) = total; + if ITAEp(m) < ITAE(m) + ITAE(m) = ITAEp(m); + xp(m,1) = x(m,1); + xp(m,2) = x(m,2); + xp(m,3) = x(m,3); + end + end + % Update Global best + [now_best, loc] = min(ITAE); + if now_best < prev_best + prev_best = now_best; + xg(1) = xp(loc,1); % actually this can change to x(loc,n) + xg(2) = xp(loc,2); + xg(3) = xp(loc,3); + end + steps = steps + 1; + best_value(steps) = prev_best; +end +toc +% Final Testing +ITAE_min = prev_best +Kp = xg(1) +Ki = xg(2) +Kd = xg(3) + +pid = tf([Kd Kp Ki],[0 1 0]); +motor_cl = feedback(motor * pid, 1); +step(motor_cl) +%step(motor_cl/s); +%impulse(motor_cl); +%step(motor_cl/s^2); +legend("Before Tuning","After tuning"); +title("Step Response"); +stepinfo(motor_cl) +[y,t] = step(motor_cl); +ss_error = abs(1 - y(end)) + +t = 1:steps; +figure +plot(t,best_value, 'r--','LineWidth',2); +xlabel('Iteration'); +ylabel('Cost Function (ITAE)'); +legend("ITAE for PSO-PID"); +title("ITAE with each iteration")