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Assignment 4 - PI/README.md Normal file
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# Integral Effect on Control System
This dir is belong to Control System class contains with Integral Effect on Control System. This code 100% original made by my hand :), please leave some notes if you're going to use it. Thanks!
## Software
This program run 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.
```
Kp = 1;
% Ki = 1;
% Ki = 3;
% Ki = 5;
Ki = 7;
% Ki = 9;
```
Variable above is the constant from PI control, we're trying to varies the constant to analyze integral effect on control system
## Process
The BLDC motor control system should be defined as transfer function by initialize its numerator-denumerator and *tf()* function.
```
num_motor = [K];
den_motor = [J*L J*R+b*L R*b+K*K];
motor = tf(num_motor,den_motor)
```
Besides the plant function, the PI-control system defined by `C = tf([Kp Ki],[1 0])`. The vector is set according to PI formula which `PI = Kp * Ki/s`. After that, both of system are multiplied each others without feedback by `complete = feedback(motor*C,1);`
That system will be test with step, ramp, and impulse input by call below lines
```
subplot(311), impulse(complete); % Impulse reponse
subplot(312), step(complete); % Step Response
subplot(313), step(complete / s); % Ramp response
stepinfo(complete)
```
Since Matlab doesn't provide any steady-state error calculation, we process it by call below lines
```
[y,t] = step(complete); % Calculate Steady-State error
sse = abs(1 - y(end))
```
Last line works to limit the graph
```
xlim([0 50])
ylim([0 3])
```
## Testing
| Kp = 1 | Ki = 1 | Ki = 3 | Ki = 5 | Ki = 7 | Ki = 9 |
|--- |--- |--- |--- |--- |--- |
| Rise Time | 22.7723 | 6.7782 | 3.5914 | 2.3175 | 2.3175 |
| Settling Time | 40.3716 | 12.1907 | 6.3158 | 3.6779 | 3.6779 |
| Overshoot | 0 | 0 | 0 | 0.3523 | 0 |
| SSE | 1.7396e-06 | 0.0034 | 0.0033 | 0.0034 | 6.6536e-05 |
### Notes
Contact nanda.r.d@mail.ugm.ac.id for more information
### Links
You can access the source code here
[github.com/nandard/routh_table.git](https://github.com/nandard/routh_table.git)

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Assignment 4 - PI/integral_tf.m Normal file
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% Variable
s = tf('s');
J = 0.01;
b = 0.1;
K = 0.01;
R = 1;
L = 0.5;
Kp = 1;
% Ki = 1;
% Ki = 3;
% Ki = 5;
Ki = 7;
% Ki = 9;
% Define Transfer Function
num_motor = [K];
den_motor = [J*L J*R+b*L R*b+K*K];
motor = tf(num_motor,den_motor)
% Define Control Function
C = tf([Kp Ki],[1 0])
% Define Closed-Loop function
complete = feedback(motor*C,1);
% Process system responses
subplot(311), impulse(complete); % Impulse reponse
subplot(312), step(complete); % Step Response
subplot(313), step(complete / s); % Ramp response
stepinfo(complete)
% Calculate the Stead-State Error
[y,t] = step(complete); % Calculate Steady-State error
sse = abs(1 - y(end))
% Limit the graph
xlim([0 50])
ylim([0 3])