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94 lines
3.1 KiB
Markdown
94 lines
3.1 KiB
Markdown
# Derivative Effect on Control System
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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!
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## Software
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This program ran in Matlab
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## Variables
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`s = tf('s');` defines `s` as 'frequency domain' for transfer function and will be used further.
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```
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J = 0.01;
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b = 0.1;
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K = 0.01;
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R = 1;
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L = 0.5;
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```
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Those variable comes from BLDC control system.
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```
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Kp = 1;
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Kd = 1;
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% Kd = 3;
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% Kd = 5;
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% Kd = 7;
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% Kd = 9;
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```
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Variable above is the constant from PD control, we're trying to varies the constant to analyze derivative effect on control system
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## Process
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The BLDC motor control system should be defined as transfer function by initialize its numerator-denumerator and *tf()* function.
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```
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num_motor = [K];
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den_motor = [J*L J*R+b*L R*b+K*K];
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motor = tf(num_motor,den_motor)
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```
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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);`
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That system will be test with step, ramp, and impulse input by call below lines
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```
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subplot(311), impulse(complete); % Impulse reponse
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subplot(312), step(complete); % Step Response
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subplot(313), step(complete / s); % Ramp response
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stepinfo(complete)
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```
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Since Matlab doesn't provide any steady-state error calculation, we process it by call below lines
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```
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[y,t] = step(complete); % Calculate Steady-State error
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sse = abs(1 - y(end))
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```
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Last line works to limit the graph
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```
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xlim([0 50])
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ylim([0 3])
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```
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## Testing
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For Kp = 1
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| Param | Kd = 1 | Kd = 3 | Kd = 5 | Kd = 7 | Kd = 9 |
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|--- |--- |--- |--- |--- |--- |
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| Rise Time | 0.0540 | 0.0140 | 0.0081 | 0.0057 | 0.0044 |
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| Settling Time | 2.1356 | 3.2085 | 3.9313 | 4.6494 | 5.3646 |
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| Overshoot | 50.9930 | 232.5791 | 359.4791 | 452.0385 | 522.2002 |
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| SSE | 0.9088 | 0.9077 | 0.9075 | 0.9075 | 0.9069 |
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### Kp = 1, Kd = 1
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### Kp = 1, Kd = 3
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### Kp = 1, Kd = 5
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### Kp = 1, Kd = 7
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### Kp = 1, Kd = 9
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## Conclusion
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Based on previous tests, we conclude that by adding Derivaitve constant :
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* Risie time is **increased**
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* Settling time is **increased**
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* Overshoot is **decreased**
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* SSE is **decreased**
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### Notes
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Contact nanda.r.d@mail.ugm.ac.id for more information
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### Links
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You can access the source code here
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[github.com/nandard/control-system.git](https://github.com/nandard/control-system.git)
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