20095ee141_1_HW3 - sol

20095ee141_1_HW3 - sol - EE141 Principles of Feedback...

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Unformatted text preview: EE141 Principles of Feedback Control (Fall 2009) Solutions to Homework 3 ____________________________________________________________________________ 3.38) 2 sign changes in the first column => 2 roots in the RHP => unstable. 2 sign changes in the first column => 2 roots in the RHP => unstable. 3.39) 2 sign changes in the first column => 2 roots with positive real parts. 2 sign changes in the first column => 2 roots with positive real parts. 3.41) 4.6) a) 3) 5 11 4) 5 11.01 2.1 15.11 .2 10.6 1 10 15 10 Controller 3 has a rise time of 1.82 seconds compared to 1.61 seconds for controller 4 while the overshoot is 4.95% for controller 3 compared to 13.9% for controller 4. b) The steady state error for controller 3 is 1 compared to 0.1 for controller 4. c) Peak magnitude of the plant input equals 5 in both cases. d) Controller 3 results in a higher rise time but a much lower overshoot, much lower settling time (5.4 seconds compared to 15.9 seconds) and nearly the same peak time compared to that of controller 4. Both controllers result in a 0 steady state error for a step input but controller 4 results in a lower steady state error for a ramp input. Controller 3 is recommended. ...
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This note was uploaded on 04/04/2010 for the course EE 141 taught by Professor Balakrishnan during the Fall '07 term at UCLA.

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