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Assignment 6 - Tuning PID/README.md
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# Improved Particle Swarm Optimization on PID Tuning
This dir is belong to Control System class contains with Tuning PID with ZN1 and PSO on motor system.
# 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 IPSO on motor system.
## Software
This program ran in Matlab
## Variables
## IPSO Method
### 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
### ITAE Cost Function
### Testing
#### 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)