Instructions
ELEN90055 Control Systems Worksheet 4
Semester 2
This worksheet covers step response transients. Solutions to starred problems will be provided after the practice class.
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1∗. A certain servo system has dynamics dominated by a pair of complex poles and no finite zeros. The time domain specifications are
Rise time: Overshoot: Settling time:
tr ≤ 0.6 sec. Mp ≤ 17% ts ≤ 9.2 sec.
(a) Sketch the region in the complex s-plane for which the poles could be placed such that all specifications are met.
(b) Indicate the specific locations that will have the smallest rise time, an overshoot of Mp ≤ 17% and also meet the settling time specification exactly (ts = 9.2sec).
2∗. (Question 9, Control system final exam 2017):
Suppose you want to achieve an overshoot of no more than 10% and a rise time of at most 2 sec. Assume that there are no finite zeros in the transfer function. Sketch the region of the complex plane where all the dominant poles of the closed-loop transfer function should be located.
3∗. (Question 9, Control system final exam 2016):
Suppose that you designed two controllers for a given plant and they both yield a stable closed-loop system. The first controller gives you rise time tr = 0.5sec and settling time ts = 10sec. The second controller gives you the rise time tr = 1sec and settling time ts = 4sec. Which controller gives you a faster response for the closed-loop system?
4. (Question 5, Control system final exam 2016):
Suppose that you have found that the characteristic polynomial of a closed-loop system takes the following form:
s3 +(kp +3)s2 +4kps+15
where kp > 0 is a controller parameter that you can tune. Explain how you can use the Routh-Hurwitz criterion to check if the settling time (5% of the final value) is smaller than 2 sec (you do not need to complete all calculations – just explain the steps you would use).
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