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me375_sp11_hwk04

me375_sp11_hwk04 - ME 375 Spring 2011 Homework No 4 Due...

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ME 375 – Spring 2011 Homework No. 4 Due: Friday, February 11 Problem No. 1 Part A: (20%) For each of the following systems, determine the transfer function G s ( ) = Y s ( ) / U s ( ) and calculate the poles of this transfer function. a) 5 y + 7 y = 15 u t ( ) b)  y + 10 y + 21 y = 4 u t ( ) c)  y + 14 y + 58 y = 6 u t ( ) + 4 u t ( ) d) x + 6 x 8 y = u t ( ) and y + 6 y + 8 x = u t ( ) Part B: (10%) A third-order system has an input of u t ( ) and an output of y t ( ) . The forced response portion of Y s ( ) = L y t ( ) corresponding to a unit step input u t ( ) is known to be: Y forced s ( ) = 1 s s 3 + 3 s 2 + 4 s + 5 ( ) a) Determine the input-output differential equation for the system. b) From your result in a), determine the transformed free response Y free s ( ) corresponding to initial conditions of: y 0 ( ) =  y 0 ( ) = 0 and y 0 ( ) = 6 .
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Problem No. 2 (30%) The transfer function G s ( ) for a system with input U s ( ) and output Y s ( ) has a static gain of 8, has one zero z 1 and has three poles p 1 , p 2 and p 3 . The zero and poles are shown in the complex plane below.
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