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HW7 - ENME462 Vibrations, Spring2010...

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ENME 462 Vibrations, Controls and Optimization II Spring 2010 Homework 7 Page 1 of 1 Dr. S Bergbreiter Homework 7: Design via Root Locus Due Wednesday, April 7 by 5pm in drop box outside 2170 Martin *Include your name, section and the date on each assignment and draw a box around your answer! Include your hours spent on this homework in the upper right hand corner 1. Problem 8.37 in Nise (Control Systems Engineering, 5 th Edition). 2. A feedback system to control the speed of a DC motor is provided below with the DC motor transfer function (voltage input, speed output). ( )( ) t e t K Js b Ls R K K c G K t = K e = 0.01 Nm/A, J = 0.01 kgm 2 /s 2 , b = 0.1 Nms, L = 0.5 H, R = 1 a. Roughly sketch the root locus for a simple proportional controller (G c = K p ). b. Find a gain K p resulting in a closed loop step response with an overshoot of 5%. c. Find a location for closed loop poles on the s plane that will satisfy the closed loop step response constraints of overshoot = 5% and settling time < 0.5s. Is this point on the root locus you drew in part a?
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