homework6_solutions.pdf

# homework6_solutions.pdf - ECE 460 Solutions to Homework 6...

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ECE 460: Solutions to Homework 6 Instructor: Stan Baek Due: Monday, March 7, at 2:10pm Note 1. Your solutions should be neat and legible; always show your work. Problem 1. (50 points) Sketch the root locus with respect to K for the following choices for G ( s ). Be sure to give the asymptotes, break-away and break-in points, and departure and arrival angles if applied. Discuss the transient response as you change K from zero to the infinity. Clearly specify Rule #1, #2, ... to show your work on this problem. After completing each hand sketch, use MATLAB rlocus to verify your sketch and submit the MATLAB plot. Hint: Make use of the MATLAB commands from Lab 2, such as poly , roots , conv , etc. if necessary. Solution: (a) The open-loop system is unstable, but the closed-loop system will be stable once K is larger than a certain value. As we keep increasing K , the overshoot and the settling time of the closed-loop system will decrease until the system becomes critically-damped. If we keep increasing K after that, the settling time will increase.

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