1. Professor Walter W. Olson Department of Mechanical, Industrial and Manufacturing Engineering University of Toledo Lecture 27a: Problem Session

2. Exercise 1: 1 st Order ZN PID Design Design a PID controller for the system with a step response below: (lines on next slide)

3. Exercise 1: 1 st Order ZN PID Design Design a PID controller for the system with a step response below:

4. Exercise 1: 1 st Order ZN PID Design

5. Exercise 2: Oscillatory ZN PID Design Design a PI Controller for the following system (K cr =10):

6. Exercise 2: Oscillatory ZN PID Design Design a PI Controller for the following system (K cr =10): 9 complete cycles in 19 sec

7. Exercise 3: Lead Design (Root Locus) Design a lead controller for the open loop system below with unity feedback which will result in a damping ratio of 0.36 while reducing the 5% settling time by 50% Part 1: where would you like to see the closed loop poles?

8. Exercise 3: Lead Design (Root Locus) Part 1: where would you like to see the closed loop poles? Part 2: Placing a zero and a pole

9. Exercise 3: Lead Design (Root Locus) Part 2: Placing a zero and a pole Try a zero at -1 and a pole at -10: Need to bend the curve up more

10. Exercise 3: Lead Design (Root Locus) Part 2: Placing a zero and a pole Try a zero at -1 and a pole at -15: Closer…

11. Exercise 3: Lead Design (Root Locus) Part 2: Placing a zero and a pole Try a zero at -1 and a pole at -18: Very close: Could fine adjust more Accepting this controller:

12. Exercise 4: Lead Design (frequency) For the following system, increase the static velocity error 2.0/sec with a phase margin of 50 o :

13. Exercise 4: Lead Design (frequency) For the following system, increase the static velocity error 2.0/sec with a phase margin of 50 o :

14. Exercise 4: Lead Design (frequency) For the following system, increase the static velocity error 2.0/sec with a phase margin of 50 o :

15. Exercise 4: Lead Design (frequency) For the following system, increase the static velocity error 2.0/sec with a phase margin of 50 o :