Tree state space equation

I am trying to model state space of the system whose equations shown at the picture,i could not figure out to how to use the command ss to model system hence ss(A,B1,B2,C1,C2,D1,D2...) is not working.is there anyway to develop state space model of such systems with matlab?

Answer 1

[John BG]

hawk

your system is

xdot=A*x+B1*x+B2*u

y=C2*x+D11*w+D12*u

z=C1*x+D11*w+D12*u

when you apply A, B1, .. you get the following:

xdot=A*x+B2*u

y=C2*x+D21*u

z=C1*x

note that the 3rd equation is just telling that z is proportional to x. If you ignore z, build your SS model, with

xdot=A*x+B2*u

y=C2*x+D21*u

and then calculate z out of x with z=C1*x.

Rewording, include z inside x, or as mentioned, ignore the 3rd equation, build the model, and calculate z afterwards.

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thanks in advance

John

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