homework4 - 5. Find if any roots of the polynomial 12 28 23...

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EE 3657 Homework # 4 – Assigned Wed Mar 16 - Due Wed Mar 23 Covers Routh and Steady-State Errors. Your notes and the textbook should be ample material to solve these problems. 1. The polynomial 4 4 2 3 4 ) ( 2 3 4 5 6 s s s s s s s a satisfies the necessary condition for stability since all the {a i } are positive and non-zero. Determine how many, if any, roots of the system are in the RHP. 2. Consider a unity feedback system with feed-forward transfer function given as follows:   6 1 1 ) ( s s s s K s G . Is the system open-loop stable? For what values of K? Is the system closed-loop stable? For what values of K? 3. Find the range of values of controller gains ( K , K I ) so that the unity feedback system with controller given by s K K I and plant given by ) 1 )( 2 ( 1 ) ( s s s G is stable. 4. Find if any roots of the polynomial 9 6 6 2 3 ) ( 2 3 4 5 s s s s s s a are in the RHP.
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Unformatted text preview: 5. Find if any roots of the polynomial 12 28 23 11 5 ) ( 2 3 4 5 s s s s s s a are on the imaginary axis or in the RHP. 6. Consider a unity-feedback system with the closed-loop transfer function given by b as s b Ks s R s C 2 ) ( . Determine the open-loop transfer function ) ( s G . Show that the steady-state error in the unit-ramp response is given by b K a K e v ss 1 . 7. Consider a unity-feedback system with open-loop transfer function given by B Js s K s G ) ( . Discuss the effects that varying the values of K and B has on the steady-state error in the unit-ramp response. Sketch typical unit-ramp response curves for a small, medium, and large value of K, assuming constant B ....
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This note was uploaded on 07/30/2011 for the course EEL 3657 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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