Overall controller design

1. Overall controller design • Draw R.L.for G(s) • Draw desired region for closed-loop poles based on specs • If R.L. goes through region, pick pd on R.L. and in region. Go to step 7.

2. Pick pd in region (leave some safety flex) • Compute angle deficiency: • a. PD control, choose zpd such that then

3. b. Lead control: choose zlead, plead such that You can select zlead & compute plead. Or you can use the “bisection” method to compute z and p. Then

4. Compute overall gain: • If there is no steady-state error requirement, go to 14. • With K from 7, evaluate error constant. You already have:

5. The 0, 1, 2 should matchp, v, a This is for lag control. For PI:

6. Compute desired error const. from specs: • For PI : set K*a = K*d & solve for ziFor lag : pick zlag & let

7. Re-compute K • Get closed-loop T.F. Do step response analysis. • If not satisfactory, go back to 3 and redesign.

8. If we have both PI and PD we have PID control:

9. Lead-lag design example Too much overshoot, too slow & ess to ramp is too large.

11. Draw R.L. for G(s) & the desired region

12. Clearly R.L. does not pass through desired region.need PD or lead. Let’s do lead.Pick pd in region

13. Now choose zlead & plead. Could use bisection. Let’s pick zlead to cancel plant pole s + 0.5

14. Use our formula to get plead Now compute K : Now evaluate error constant Kva

16. Should re-compute K, but let’s skip: do step response.

18. Op-amp controller circuit: • Proportional:

19. Integral:

20. Derivative control:

21. PD controller:

22. PI controller:

23. PID controller:

24. Lead or lag controller:

25. If R1C1 > R2C2then z < pThis is lead controller If R1C1 < R2C2then z > pThis is lag controller

26. Lead-lag controller: