Add assignment 6

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)

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")