ex2 - r ( t ) = 3 cos(2 t ) u ( t ) when K = 1 . 2 3....

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ME 451 Examination #2 March 28, 2008
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1. Consider the control system shown below with C ( s ) = K and G ( s ) = 6 ( s + 1)( s + 2)( s + 3) . r ( t ) y ( t ) e ( t ) C ( s ) G ( s ) + - (a) [15 pts] Find the range of K for which the closed-loop system is stable. (b) [15 pts] Find the steady-state error for a unit step input when K = 1 and K = 12 . 1
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2. Consider the control system shown below with C ( s ) = K and G ( s ) = 1 s + 1 . r ( t ) y ( t ) e ( t ) C ( s ) G ( s ) + - (a) [15 pts] Find the sensitivity of T ( s ) = Y ( s ) /R ( s ) to K and the type of the system. (b) [15 pts] Find the steady-state error for the input
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Unformatted text preview: r ( t ) = 3 cos(2 t ) u ( t ) when K = 1 . 2 3. Consider the control system shown below with C ( s ) = K and G ( s ) = s + 4 s ( s + 2) . r ( t ) y ( t ) C ( s ) G ( s ) +-(a) [30 pts] Accurately sketch the root locus of the system. (b) [10 pts] Find the value of K so that s =-1 is a pole of the closed-loop system. 3...
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ex2 - r ( t ) = 3 cos(2 t ) u ( t ) when K = 1 . 2 3....

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