Homework Help: Express the system in state space form

1. May 5, 2017

MattH150197

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?

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2. May 5, 2017

FactChecker

You are correct.

PS. Put parentheses around your denominators. 4/s+6 should be 4/(s+6)

3. May 5, 2017

MattH150197

Thanks for clearing it up!