ECE3085-ControlSystems-Exam2_Spring08_solution

ECE3085-ControlSystems-Exam2_Spring08_solution - ECE 3085...

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Unformatted text preview: ECE 3085 Spring 2008 Exam 2 Closed-Book, Closed-Notes, 4 Problems. Name: All 4 problems relate to the following control system architecture: C P y r +- e + + d 1. Assuming the plant transfer function and input signals are P ( s ) = 1 s ( s + 2) , r ( t ) = 0 , d ( t ) = 1( t ) identify the zero-state responses associated with the following compensator transfer functions: C ( s ) response # explanation- . 05 6 one unstable pole 2 4 stable with y ss = 1 / 2 10 3 stable with y ss = 1 / 10 1 + 2 s- 1 1 pair of poles on stability boundary 1 + 3 s- 1 5 pair of unstable poles 7 + 7 s- 1 2 stable with y ss = 0 From the block diagram C ( s ) = k p Y ( s ) = 1 s 2 + 2 s + k p D ( s ) , C ( s ) = k p + k i 1 s Y ( s ) = s s 3 + 2 s 2 + k p s + k i D ( s ) P-control is characterized by stability condition k p > 0 and steady-state output y ss = 1 /k p , whereas PI- control is characterized by stability conditions k p > 0, k i > 0, 2 k p > k i and steady-state output y ss = 0....
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ECE3085-ControlSystems-Exam2_Spring08_solution - ECE 3085...

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