Assignment 9-Questions

# Assignment 9-Questions - = 1 s 2 2 s 2 s 2 2 s 5(a What is...

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ECE3085 - Homework #7 Due: Apr. 1, 2009 Problem 1. (8 pts) Recall the simplified version of a satellite orientation control system from the last homework set. The plant and controller were P ( s ) = 1 Js 2 C ( s ) = K (1 + s T ) . where T = 3 sec and K/J = 2 / 3 . Pretend instead that J = 3 / 2 and K is unknown. The closed loop system can be modified to be H ( s ) = P ( s ) C ( s ) 1 + P ( s ) C ( s ) = KG ( s ) 1 + KG ( s ) . (a) What is G ( s ) ? (b) What is the root locus of G ( s ) ? (c) For what values of K > 0 is the system stable? Problem 2. (8 pts) Consider the plant P ( s ) = s - 2 s 2 + 5 s . (a) What is the root locus of P ( s ) ? (b) For what values of K > 0 is the system stable? Problem 3. (10 pts) Consider the plant P ( s
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Unformatted text preview: ) = 1 ( s 2 + 2 s + 2)( s 2 + 2 s + 5) . (a) What is the root locus of P ( s ) ? (b) For what values of K > is the system stable? Problem 4. (12 pts) Consider the plant P ( s ) = s + 15 ( s 2 + 10 s )( s 2 + 8 s + 15) . (a) What is the root locus of P ( s ) ? (b) For what values of K > is the system stable? Problem 5. (12 pts) Consider the plant P ( s ) = s 2-2 s-15 ( s 2 + s + 5)( s 2 + 4 s + 4) . (a) What is the root locus of P ( s ) ? (b) For what values of K > is the system stable?...
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