# Derivative Effect on Control System
This dir is belong to Control System class contains with Derivative 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 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.
```
Kp = 1;
Kd = 1;
% Kd = 3;
% Kd = 5;
% Kd = 7;
% Kd = 9;
```
Variable above is the constant from PD control, we're trying to varies the constant to analyze derivative 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 PD-control system defined by `C = tf([Kd Kp 0],[0 1 0])`. The vector is set according to PD formula which `PD = Kp + Kd * 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 
For Kp = 1
|   Param	|   Kd = 1	|   Kd = 3	|   Kd = 5	|   Kd = 7	|   Kd = 9	|
|---	|---	|---	|---	|---	|---	|
|   Rise Time	|   0.0540	|   0.0140	|   0.0081	|   0.0057	|   0.0044	|
|   Settling Time	|   2.1356	|   3.2085	|   3.9313	|   4.6494	|  5.3646 	|
|   Overshoot	|   50.9930	|   232.5791	|   359.4791	|   452.0385	|   522.2002	|
|   SSE	|   0.9088	|   0.9077	|   0.9075	|   0.9075	|   0.9069	|

### Kp = 1, Kd = 1

![Kp = 1, Kd = 1](https://user-images.githubusercontent.com/77116615/191516834-ff31ea45-d610-4966-8de0-ff36c636c12a.png)
### Kp = 1, Kd = 3

![Kp = 1, Kd = 3](https://user-images.githubusercontent.com/77116615/191517331-d85506ab-ef54-4ff5-8fa9-94b62bfbb22c.png)
### Kp = 1, Kd = 5

![Kp = 1, Kd = 5](https://user-images.githubusercontent.com/77116615/191517353-28c72aa5-8caa-4e8e-8994-62bdadc75c06.png)
### Kp = 1, Kd = 7

![Kp = 1, Kd = 7](https://user-images.githubusercontent.com/77116615/191517382-31db825a-3143-4105-bb7a-311fe91927dd.png)
### Kp = 1, Kd = 9

![Kp = 1, Kd = 9](https://user-images.githubusercontent.com/77116615/191517410-12f3293b-4029-49f5-b032-401fb0085691.png)

## Conclusion
Based on previous tests, we conclude that by adding Derivaitve constant :
* Rise time is **decreased**
* Settling time is **increased**
* Overshoot is **increased**
* SSE is **slighty decreased**

### 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)