upadate documentation

Assignment 6 - Tuning PID/README.md

@@ -1,10 +1,10 @@
-# Improved Particle Swarm Optimization on PID Tuning
+# Improved Particle Swarm Optimization and Ziegler-Nicols 1 on PID Tuning
-This dir is belong to Control System class contains with Tuning PID with ZN1 and PSO on motor system.
+This dir is belong to Control System class contains with Tuning PID with ZN1 and IPSO on motor system.
 
 ## Software
 This program ran in Matlab
-
+## IPSO Method
-## Variables
+### Variables
 `s = tf('s');` defines `s` as 'frequency domain' for transfer function and will be used further. 
 ```
 J = 0.01;
@@ -25,23 +25,23 @@ lim_max = 2500;
 Variable above is the constant for PSO tuning.
 
 
-## Testing 
+### Testing 
-### ITAE Cost Function
+#### ITAE Cost Function
 ![itae](https://user-images.githubusercontent.com/77116615/191751929-89ff2f77-7e1a-45a4-b535-f8f3a768ecc6.png)
 
-### Step Response
+#### Step Response
 ![step](https://user-images.githubusercontent.com/77116615/191751960-eee905b9-e450-41de-8824-f2157e431238.png)
 
-### Ramp Response
+#### Ramp Response
 ![ramp](https://user-images.githubusercontent.com/77116615/191752006-63e2fe9b-69ad-48eb-881d-7adb2b630819.png)
 
-### Impulse Response
+#### Impulse Response
 ![impulse](https://user-images.githubusercontent.com/77116615/191752036-5e05bfd7-9448-437e-ada6-16d9744b1b89.png)
 
-### Acceleration Response
+#### Acceleration Response
 ![acceleration](https://user-images.githubusercontent.com/77116615/191752086-4f392de0-202b-429c-adc9-0935d10275b5.png)
 
-## Results
+### Results
 Elapsed time is 18.701024 seconds.
 
 ### Before PSO-PID
@@ -72,10 +72,120 @@ Kd = 2.4810e+03
             Peak: 0.9976
         PeakTime: 0.0036
          SSError: 0.0024
+       DelayTime: 0.000595
+```
+## ZN1 Method
+### 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.
+```
+tic
+timeVal=tic;
+[y,t] = step(motor);
+h = mean(diff(t));
+dy = gradient(y, h);                                            % Numerical Derivative
+[~,idx] = max(dy);                                              % Index Of Maximum
+b = [t([idx-1,idx+1]) ones(2,1)] \ y([idx-1,idx+1]);            % Regression Line Around Maximum Derivative
+tv = [-b(2)/b(1); (1-b(2))/b(1)];                               % Independent Variable Range For Tangent Line Plot
+f = [tv ones(2,1)] * b;                                         % Calculate Tangent Line
+
+L = tv(1);
+T = tv(2);
+
+figure(1)
+plot(t, y)
+hold on
+plot(tv, f, '-r')                                               % Tangent Line
+plot(t(idx), y(idx), '.r')
+title('Mencari tangent line plant ')% Maximum Vertical
+hold off
+grid
+```
+Process above is to find tangent line and L and T constant
+
+After L and T constant is obtained, the values is used to obtained Kp, Ki, and Kd constant
+```
+control = tf(zeros(1,1,5));
+sys=tf(zeros(1,1,5));
+complete=tf(zeros(1,1,5));
+
+% sistem dengan P
+kp = T/L
+control(:,:,1)= tf([0 kp 0],[1 0]);
+
+% sistem dengan PI
+kp = 0.9*T/L
+Ti= L/0.3;
+ki = kp/Ti
+control(:,:,2)= tf([0 kp ki],[1 0]);
+
+% sistem dengan PID
+kp = 1.2*T/L
+Ti= 2*L;
+ki = kp/Ti
+Td = 0.5*L;
+kd = kp*Td
+control(:,:,3)= tf([kd kp ki],[1 0]);
 ```
 
-### Notes
+### Testing 
+
+#### Step Response
+
+
+#### Ramp Response
+
+
+#### Impulse Response
+
+
+#### Acceleration Response
+
+
+### Results
+Elapsed time is 0.065802 - 0.455767 seconds.
+
+### Before ZN1-PID
+```
+        RiseTime: 1.0161
+    SettlingTime: 1.8471
+     SettlingMin: 0.0819
+     SettlingMax: 0.0907
+       Overshoot: 0
+      Undershoot: 0
+            Peak: 0.0907
+        PeakTime: 3.0168
+         SSError: 0.9095
+```
+### After ZN1-PID
+Control P:
+  Kp = 140.9417
+Control PI:
+  Kp = 126.8475 ; Ki = 711.9513
+Control PID:
+  Kp = 169.13; Ki = 1.5821e+03; Kd = 4.5201
+```
+        RiseTime: 0.0676
+    SettlingTime: 0.8486
+     SettlingMin: 0.8129
+     SettlingMax: 1.4349
+       Overshoot: 43.4944
+      Undershoot: 0
+            Peak: 1.4349
+        PeakTime: 0.17391
+         SSError: -0.0021
+       DelayTime: 0.0444
+```
+
+## Notes
 Contact nanda.r.d@mail.ugm.ac.id for more information
-### Links
+## Links
 You can access the source code here
 [github.com/nandard/control-system.git](https://github.com/nandard/control-system.git)