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Express the system in state space form

  1. May 5, 2017 #1
    1. The problem statement, all variables and given/known data
    The question asks me to express the system shown in the image in state-space form, firstly by using the transfer function which was fine but the second part asks to express in state-space form by using the components A,B,C,D as the states x1,x2,x3,x4

    2. Relevant equations
    U(s) = input

    3. The attempt at a solution
    So looking at each branch i got the following:
    (U(s) - x4)*(4/s+6) = x1
    (x1)*(6/s+3) = x3
    (x1)*(2/s+2) = x2
    these were all correct looking at the mark scheme but for the last branch i did: (x2+x3)*(1/S+1) = x4 whereas the mark scheme says it should be (X1+x2) *(1/S+1) = x4. I dont know why its x1 instead of x3 because looking at the block diagram x2 and x3 are added just before the x4 branch. Can anyone see where i am going wrong?
     

    Attached Files:

  2. jcsd
  3. May 5, 2017 #2

    FactChecker

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    Science Advisor
    Gold Member

    You are correct.

    PS. Put parentheses around your denominators. 4/s+6 should be 4/(s+6)
     
  4. May 5, 2017 #3
    Thanks for clearing it up!
     
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