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hw-421-s06-13

# hw-421-s06-13 - ECE 421 Spring 2006 HW Assignment#13 Bode...

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ECE 421, Spring 2006, HW Assignment #13 Bode Compensator Design Problems Due 4:00 p.m., Friday, May 5, 2006 For each problem, design a compensator G c ( s ) such that all of the speci fi cations are satis fi ed. Use MATLAB to draw the uncompensated and compensated Bode magnitude and phase plots. All problems have unity feedback. 1. A certain plant is described by G p 1 ( s ) = 2(0 . 25 s + 1) s (0 . 6 s + 1)(0 . 025 s + 1)(0 . 015 s + 1) The following speci fi cations must be satis fi ed by the closed-loop system: (a) the steady-state error for a unit ramp input must be 0 . 02 ; (b) the compensated phase margin must be at least 55 ; (c) the settling time for the step response of the compensated system must be longer than the settling time for the uncompensated system (with e ss speci fi cation sat- is fi ed). 2. A certain plant is described by G p 2 ( s ) = 1 s 2 (0 . 3 s + 1) The following speci fi cations must be satis fi ed by the closed-loop system: (a) the compensated gain crossover frequency ω x compensated must be between 0.1 and 1.0 rad/sec;

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