Lecture 10 PID and its Tuning (9) (1).pptx

Control

1. Lecture 10 PID and its Tuning 1 12:25 am

2. Main contents What’s PID? How to tune PID? 2 12:25 am

3. Why is Controller Necessary? Blue response resembles an un-controlled system. This response is oscillatory as well as it takes much longer to settle down. For a mechanical system, this could be due to Inertia effect, friction, backlash etc. The red response is of a controlled system. This response contains no oscillations, and it settles to equilibrium / steady state in lesser time. Job of a control system is to “ generate a control input / effort that can be used to drive the un-controlled system , albeit externally , to achieve the desired performance ”. 3 12:25 am

4. Analysis of Response: Transient Specifications Unit Step Response of Second Order System 4 12:25 am

5. Transient Response Specifications Percentage Overshoot (% O.S): It is the amount that the response overshoots the steady state, or final, value at the peak time, expressed as a percentage of the steady-state value. Rise Time (T r ): Time required for the step response to rise from 10% to 90% of its final value. Delay Time (T d ): Time required for the step response to reach 50% of final value. Settling Time (T s ): Time required for the step response to decrease and stay within ±5% of its final value. Steady State Error ( e ss ): It is the difference between the output and the reference input after the steady state has reached. 5 12:25 am

6. Feedback Controller Feedback controller generates a control signal / effort / external disturbance based on the input signal it receives. The input signal is error: difference between measured value and desired value or set point. Feedback counters disturbance as well as variation in process. Block Diagram of Feedback Controller 6 12:25 am

7. Proportional Integral Derivative Control PID stands for P roportional I ntegral D erivative Control. Being robust & easy to implement, it is one of the most widely used closed loop control for precise operation of industrial applications and processes. Input PID Plant Output ∑ + _ e u Block Diagram of PID Controller 7 12:25 am

8. Proportional Control In Proportional Control, the control signal, u , is directly proportional to the error, e. As the gain is increased the system responds faster to changes in set-point but becomes progressively under damped and eventually unstable. 8 12:25 am

9. Proportional Control Action P Control Signal 9 12:25 am

10. Proportional Control Advantages: Simple and easy to design and tune Rapid Response / Reduces Rise Time Reduces Steady State Error Disadvantages: Not possible to eliminate Steady State Error / Offset Could lead to instability / rise in overshoot/ oscillations Applications: Float Valve, Thermostat etc 10 12:25 am

11. Derivative Control Derivative control produces a control signal proportional to the rate at which the error is changing. Also known as rate controller. While sudden/rapid change in error leads to a control signal of larger magnitude, gradual change leads to small magnitude. Even if the error is huge, the derivative control will generate no signal if the error is constant Thus, not used alone; used with P control 11 12:25 am

12. Derivative Control Action D Control Signal 12 12:25 am

13. Derivative Control Advantages: Reduces Settling time ; Adds lead Reduces Overshoot ; Adds more stability Disadvantages: Not possible to eliminate Steady State Error / Offset Not possible to use alone Excessive use may make the system slow Amplifies Noise Applications: In conjunction with P Control 13 12:25 am

14. Integral Control Rate of change of integral control signal is proportional to error. Control signal proportional to integral of error. When the error is zero, the control signal is a constant value. When the error is constant, the control signal varies at constant rate. 14 12:25 am

15. Integral Control Action I Control Signal 15 12:25 am

16. Integral Control Advantages: Eliminates steady state error/offset Decreases Rise Time Disadvantages: Causes Integral Wind Up Leads to minor increase in overshoot Could make the system less stable Increases Settling time Applications: In conjunction with P Control 16 12:25 am

17. Integral Wind Up Caused by actuator saturation . What Happens? Feedback loop is broken, and the system runs in open loop because the actuator remains saturated. While the error is zero, the integral term will keep building and become very large over a period of time. This in turn would lead to saturation of control signal. The condition will prevail even when the error changes and it may take a long time before the integrator and the controller output comes inside the saturation range. The consequence is that there are large time delay. 17 12:25 am

18. PID: Series / Interacting Form Derivate Action interacts with Integral Action Modification in derivative time constant affects integral action Commercially used controller P D I e u + + + + 18 12:25 am

19. Transfer Function of Series Form 19 12:25 am

20. PID: Parallel / Non-Interacting Form Ideal Form Derivative Action does not Interact with Integral Action 20 12:25 am

21. Transfer Function of Parallel Form 21 12:25 am

22. Parallel Form: PI Control Proportional Integral (PI) Control helps minimize rise time, settling time as well as eliminate steady state error . 22 12:25 am

23. PI Control 23 12:25 am

24. Parallel Form: PD Control Proportional Derivative (PD) Control helps reduce rise time, settling time as well as minimize overshoot . 24 12:25 am

25. Proportional Derivative Control 25 12:25 am

26. Effect of P, I & D on Transient Specifications 26 12:25 am

27. P, I & D Control Action 27 12:25 am

28. Obtain an open-loop response and determine what needs to be improved. Add a proportional control to improve the rise time. Add a derivative control to improve the overshoot. Add an integral control to eliminate the steady-state error. Adjust each of P, I & D until you obtain a desired overall response referring to the table shown previously to find out which controller affects which characteristics. It is not necessary to implement all three controllers (P, I & D) into a single system. For example, if a PI controller gives a good enough response, then you don't need to add D control to the system. Simple is better . PID: Stepwise Procedure for Manual Tuning 28 12:25 am

29. 90% processes are controlled using PID. Regulation of Processes in Industry, for instance: Flow Temperature Pressure Servo / DC motor Control Linear Position Control Applications of PID Control 29 12:25 am

30. Summary What’s PID? How to tune PID? 30 12:25 am