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114 lines
3.8 KiB
Markdown
114 lines
3.8 KiB
Markdown
# Integral Effect on Control System
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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!
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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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% Ki = 1;
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% Ki = 3;
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% Ki = 5;
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Ki = 7;
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% Ki = 9;
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```
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Variable above is the constant from PI control, we're trying to varies the constant to analyze integral 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 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);`
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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 | Ki = 1 | Ki = 3 | Ki = 5 | Ki = 7 | Ki = 9 |
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|--- |--- |--- |--- |--- |--- |
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| Rise Time | 22.7723 | 6.7782 | 3.5914 | 2.3175 | 2.3175 |
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| Settling Time | 40.3716 | 12.1907 | 6.3158 | 3.6779 | 3.6779 |
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| Overshoot | 0 | 0 | 0 | 0.3523 | 0 |
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| SSE | 1.7396e-06 | 0.0034 | 0.0033 | 0.0034 | 6.6536e-05 |
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Kp = 1, Ki = 1
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Kp = 1, Ki = 3
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Kp = 1, Ki = 5
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Kp = 1, Ki = 7
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Kp = 1, Ki = 9
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Notes: In theory, SSE should decrease following the increased Ki, but i suspect Matlab just can't compute too much floating point. Hence, i add two additional test below with larger constant to show the effects.
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## Additional Testing
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For Kp = 50
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| Param | Ki = 0 | Ki = 5 |
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|--- |--- |--- |
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| Rise Time | 0.1201 | 0.1415 |
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| Settling Time | 0.6376 | 29.5503 |
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| Overshoot | 19.6150 | 6.1627 |
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| SSE | 0.1127 | 0.0082 |
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Kp = 50, Ki = 0
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Kp = 50, Ki = 5
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## Conclusion
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Based on previous tests, we conclude that by adding Integral 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/routh_table.git](https://github.com/nandard/routh_table.git)
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