HW03_solutions - Winter 2009 EECS 460 Homework #3 Solutions...

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Winter 2009 EECS 460 Homework #3 Solutions 1. (a) 4 yy yu −+ =   4 _ (b) 4 69 yy y u u + Let us start off with 4 . We know that 2 32 () 9 6 4 Ys s Us s s + = −+ and 1 4 = . Therefore, ( ) 22 () 9 6 9 () 6 () Ys Ys s sYs = += or 96 yyy = + . Knowing this, we can construct the diagram as follows: 4 _ 6 9
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Winter 2009 2. (a) We can write the state space notation for the system as follows. Our states for this model are 1 23 ,, x y x yx y = =  . [ ] 11 22 33 1 2 3 0 10 0 0 01 0 401 1 100 xx x xu x yx x   = +    =  (b) We note that 96 yyy = + , and choose our states to be 1 = = . Therefore, our state space model for this system is given below. [ ] 1 2 3 0 0 1 609 x x x = + =
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Winter 2009 3. The signal flow graph is shown below: We need to calculate ) ( ) ( s R s Y . First look at the direct paths from ) ( s R to ) ( s Y . For this we assume that the input 0 ) ( = s N . Direct Paths 1 23 P GG = 2 13 P GG = Next, calculate the loop gains.
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This note was uploaded on 04/13/2010 for the course CS 235 taught by Professor Sabnis during the Spring '10 term at Punjab Engineering College.

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HW03_solutions - Winter 2009 EECS 460 Homework #3 Solutions...

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