hw5 - 2. How about for a proportional controller K...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F09 Homework 5 Due Friday, October 30th, 2009 Explain all answers! Problem 1 Text problem 5.6(d)(e) Problem 2 Text problem 5.7(b) Problem 3 Text problem 5.8(a) Problem 4 Text problem 5.13 (In this problem they say “the root locus . .. is a circle . ..” where they mean to say “the root locus . .. includes a circle . ..”). Problem 5 Consider a unity negative feedback conFguration with a stable plant that has one (and only one) zero with positive real part and has P (0) > 0. 1. To determine the closed-loop pole locations when using a proportional controller K > 0, should you use the - 180 degree root locus or the 0 degree root locus? Think carefully, and explain fully. You may want to give an example to help explain your answer, but make sure your answer explains the general case.
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Unformatted text preview: 2. How about for a proportional controller K < 0? 3. Will the closed-loop be stable for K s that are large in magnitude? Problem 6 Consider the unity negative feedback conFguration with P ( s ) = 5 s ( s + 5) and C ( s ) given by a PI controller. 1. Draw the root locus diagram and calculate centroids, collision locations, etc. for the cases where the zero of the PI controller is at-. 5,-3,-5 and-7. 2. Compute the zero location for the PI controller for which the root locus plot transitions from no collisions on the real axis to two collisions on the real axis. or this critical value of the zero, at what angles do the branches collide and at what angles do they depart from the collision? Draw the root locus diagram for this value of the zero....
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