# Lecture 27a: Problem Session

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Professor Walter W. OlsonDepartment of Mechanical, Industrial and Manufacturing EngineeringUniversity of ToledoLecture 27a: Problem Session

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

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

Exercise 1: 1st Order ZN PID Design

Exercise 2: Oscillatory ZN PID DesignDesign a PI Controller for the following system (Kcr=10):

Exercise 2: Oscillatory ZN PID DesignDesign a PI Controller for the following system (Kcr=10):

9 complete cycles in 19 sec

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?

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 poleExercise 3: Lead Design (Root Locus)

Part 2: Placing a zero and a poleTry a zero at -1 and a pole at -10:Need to bend the curve up more

Exercise 3: Lead Design (Root Locus)

Part 2: Placing a zero and a poleTry a zero at -1 and a pole at -15:Closer

Exercise 3: Lead Design (Root Locus)

Part 2: Placing a zero and a poleTry a zero at -1 and a pole at -18:Very close: Could fine adjust moreAccepting this controller:

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

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

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