HW5 - K for stability. 3. Consider a unity feedback system...

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ECE 313 – Fall 2008 Homework # 5 Due Friday, October 3, 2008 1. For each of the following transfer functions, use the Routh-Hurwitz Criterion to find how many poles are in the right-half plane, in the left-half plane, and on the imaginary axis. In each case state whether or not the system is stable. (a) 24 22 7 4 1 ) ( 2 3 4 + + = s s s s s G (b) 24 50 35 10 ) 2 ( ) ( 2 3 4 + + + + = s s s s s s G (c) 2 3 3 3 ) 2 ( ) ( 2 3 4 + + + + + = s s s s s s G (d) 1 1 ) ( 2 3 4 + + + + = s s s s s G 2. Consider a unity feedback system with the transfer function ) 4 )( 3 )( 2 )( 1 ( ) ( + + + + = s s s s K s G in the forward path, where K is positive. Find the range of
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Unformatted text preview: K for stability. 3. Consider a unity feedback system with the transfer function ) 2 )( 1 ( ) ( + + = s s s K s G in the forward path, where K is positive. (a) State the system type. (b) Find , , and . p K v K a K (c) Find the steady state error for an input of , , and . ) ( 10 t u ) ( 10 t tu ) ( 10 2 t u t (d) Can you choose K such that the steady state error is less than in each of the three cases of part (c)? 1 ....
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