Transcription of Homework 4 - Solutions
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EE C128 / ME C134 Spring 2014 HW4 - SolutionsUC BerkeleyHomework 4 - SolutionsNote:Each part of each problem is worth 3 points and the Homework is worth a total of 42 Space Representation To Transfer FunctionFind the transfer function and poles of the system represented in state space below. x= 8 41 32057 9 x+ 4 34 u(t)y=[2 8 3]x;x(0) = 000 Solution:G(s) =C(sI A) 1B(sI A) 1=1s3 s2 91s+ 67 (s 2)(s+ 9) (4s+ 29)(s 2) 3s 27(s2+s 77) 35s 317s 76(s2 10s+ 4) C(sI A) 1B=1s3 s2 91s+ 67[2 8 3] (s 2)(s+ 9) (4s+ 29)(s 2) 3s 27(s2+s 77) 35s 317s 76(s2 10s+ 4) 4 34 G(s) = 44s2+ 291s+ 1814s3 s2 91s+ Function Analysis For Mechanical SystemsFor the system shown below, do the following:(a) Find the transfer functionG(s) =X(s)/F(s).(b) Find , n, % OS,Ts, :(a) Writing the equation of motion yields, (5s2+5s+28)X(s) =F(s).
Homework 4 - Solutions Note: Each part of each problem is worth 3 points and the homework is worth a total of 42 points. 1. State Space Representation To Transfer Function Find the transfer function and poles of the system represented in state space below. x_ = 2 6 4 8 4 1 3 2 0 5 7 9 3 7 5x+ 2 6 4 4 3 4 3 7
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