Simulation and Comparison of P, PI, PID Controllers on MATLAB/ Simulink

It is to be noted that, when the gain is increased speed of response is increasing in the case of the P and PID controller but in the PI controller gain of response is decreases. In the PID controller, there is a minor decrease or no changes are shown in various parameters which can see from tables. Hence there is no change in steady-state error so the PID controller is better than the P and PID controller.

1. Simulation and Comparison of P, PI, PID Controllers on MATLAB/ Simulink HARSH DEO [ 2K19/EE/106 ] HARSH KUMAR [ 2K19/EE/108 ]

2. The controller (an analogue/digital circuit, and software), is trying to keep the controlled variable such as temperature, liquid level, motor velocity, robot joint angle, at a certain value called the set point (SP). Controllers improve steady state accuracy by decreasing the steady state errors. Maximum overshoot of the system can be controlled using these controllers

3. SOME DEFINITIONS The peak time is the time required for the response to reach the first peak of the overshoot. Overshoot is when a signal or function exceeds its target. The difference between the desired final output and the actual one" when the system reaches a steady state OVERSHOOT STEADY STATE ERROR PEAK TIME

4. CONTROLLERS A controller is one which compares controlled values with the desired values and has a function to correct the deviation produced. There are three basic types of controllers: Proportional Controller { P Controller } Derivative Controller { D Controller } Integral Controller { I Controller } CONTROLLERS

5. P CONTROLLER P controller stands for Proportional Control With proportional control, the actuator applies a corrective force that is proportional to the amount of error: Output p = K p x E Output p = system output due to proportional K p proportional constant for the system called gain E = error, the difference between where the controlled variable should be and where it is. E= SP - PV 5

6. P CONTROLLER In a proportional controller the output (also called the actuating signal) is directly proportional to the error signal. A(t)= K p x e(t) Where, KP is proportional constant also known as controller gain. KP should be kept greater than unity. If the value of KP is greater than unity, then it will amplify the error signal and thus the amplified error signal can be detected easily 6

7. PI CONTROLLER Pl controller stands for proportional integral controller. P-I controller is mainly used to eliminate the steady state error resulting from P controller. This controller is mostly used in areas where speed of the system is not an issue. It is a combination of proportional and an integral controller the output (also called the actuating signal) is equal to the summation of proportional and integral of the error signal. 8

8. PI CONTROLLER A proportional and integral controller output is directly proportional to the summation of proportional of error and integration of the error signal. Where, K p and K i are the proportional constant and integral constant.   9

9. EXPERIENCE 01

10. PID CONTROLLER PID stands for proportional integrated derivative A proportional-integral-derivative controller (PID controller) is a generic control loop feedback mechanism (controller) widely used in industrial control systems. A PID controller attempts to correct the error between a measured process variable and a desired setpoint by calculating and then outputting a corrective action that can adjust the process accordingly. 11

11. PID CONTROLLER It consists of three controllers : Integral control Proportional control Derivative control The foundation of the system is proportional control. Adding integral control provides a means to eliminate steady-state error, but increases overshoot. Derivative control increases stability by reducing the tendency to overshoot. 12

12. PID CONTROLLER A proportional and integral controller output is directly proportional to the summation of proportional of error and integration of the error signal. Output PID = output from PID controller K P = proportional control gain K I = integral control gain K D derivative control gain E = error (deviation from set point) ( ) = sum of all past errors (area under the error/time curve) = rate of change of error (slope of the error curve)   13

13. SIMULATION RESULT

14. SIMULATION RESULT

15. Comparison Of Gain Response Of P, PI & PID Controllers. PARAMETER SPEED OF RESPONSE STABILITY ACCURACY Increasing K Increase Deteriorates Improves Increasing K i Decrease Deteriorates Improves Increasing K d Increase Improves No Impact

16. APPLICATION PID controllers are applicable to many control problems, and often perform satisfactorily without any improvements or evev tuning. Proportional-Integral-Derivative (PID) controllers are used in most automatic process control applications in industry today to regulate flow, temperature, pressure, level, and many other industrial process variables. PID CONTROLLER

17. “ It is to be noted that, when gain is increasing speed of response is increasing in case of P and PID controller but in PI controller gain of response is decreasing. In PID controller there is a minor decrease or no changes are shown in various parameter which can see from tables. Hence there is no change in steady state error so PID controller is better than P and PID controller.” CONCLUSION