homework7_solutions.pdf

# homework7_solutions.pdf - ECE 460 Solutions to Homework 7...

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ECE 460: Solutions to Homework 7 Instructor: Stan Baek Due: Wednesday, March 16, at 2:10pm Note 1. Your solutions should be neat and legible; always show your work. Note 2. This homework set includes design problems. It is very important to show all of your work for full credit. Submit your Matlab code and plots. Problem 1. (20 points) Use MATLAB rlocus to determine the value of the gain K for which the system with the open-loop transfer function G ( s ) = K s ( s + 2)( s + 4) has closed-loop poles with a damping ratio ζ = 0.5. Solution: A sketch of the root-locus is shown in Figure 1. The desired value of K is determined at the point where the root-locus crosses the ζ = 0 . 5 line in the s-plane. The desired value of K is 8.3. Problem 2. For the dynamic system give by G ( s ) = 15( s 2 + 0 . 9 s + 0 . 8) ( s + 1)( s 2 + 1 . 1 s + 1) . (a) (20 points) Design a PID compensator (P, PI, PD, or PID as necessary) to meet the following specifications: %OS 5%, settling time 15 msec, peak time 10 msec, and zero steady-state error.

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