1. ENTC 395 Lecture 7a

2. Today 4 PID control –Overview –Definitions –Open loop response 4 Example –SIMULINK implementation

3. Reading 4 Last time Laplace Transforms Appendix F.1-F.4 4 Today: Handout - Control Theory 4 Next time: Handout - Control Theory

4. Control Systems Plant: A system to be controlled Controller:Provides the excitation for the plant, controls the overall system behavior

5. Controller: Inputs and Outputs R: Desired operating point Y: Actual operating point e:Error signal = R-Y u:Correction signal

6. PID Controllers K P = Proportional gain K I = Integral gain K D = Derivative gain Controller response may be a function of three components of the error signal

7. PID Controller Transfer Function K P = Proportional gain K I = Integral gain K D = Derivative gain In s space the transfer function looks like this:

8. Parameter Effects The effect of the Ks on a system are summarized below. Actual relations are more complex. Ks are not independent.

9. Example Our old friend the spring mass damper system

10. Example Our old friend the spring mass damper system  M = 1kg  b = 10 N.s/m  k = 20 N/m  F(t) = 1 (Step input)

11. Example The goal of this example is to demonstrate how K P, K I and K D modifies the system response. Goals:  Fast rise time  Minimum overshoot  No steady-state error

12. Example -- Open loop response The open loop response is simply the response of the system with no controller in the loop.

13. Example -- Open loop response For a step input of 20 N the mass moves 1.0 m x=F/k x=20N/20(N/m) x=20m

14. Example -- Proportional Control Change problem add an active proportional controller

15. Example -- Proportional Control Change problem add an active proportional controller Response now changes also

16. Example -- PD Control Change active proportional controller add K D Response now changes also

17. Example -- PD Control- Response Change active proportional controller add K D Response now changes also

18. Example -- PID Control Change to active PID controller

19. Example -- PID Control Response Change to active PID controller