control system toolbox - state space model containing constant vectors
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I am trying to create a state space model using ss. My system has the following format:
dx/dt = Ax + Bu + f
y = Cx + Du
(x,y and u are states, outputs and inputs resp)
f is a constant real valued vector.
How can I create such models in control toolbox?
After this, I would like to obtain the discrete time equivalent.
Please help.
Abhishek
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Rajiv Singh
2011-8-11
One way is to add a new state to the system whose derivative is zero.
Let X = [x; x2] where x2 is a single variable if f is a scalar.
dX/dt = [A 1; 0 0] X + [B; 0] u
y = [C 0] X + Du
X(0) = [x(0); f]
Fangjun Jiang
2011-8-12
That means your input has an offset. For example Define New_u=u+Offset, so u=New_u-Offset and put it in your equation.
dx/dt=Ax+B(New_u-Offset)+f;
y=Cx+D(New_u-Offset)
And solve: B*Offset=f for the value of Offset. All shall be proper size matrix.
And you don't need to worry about the constant term at y=Cx+D*New_u-D*Offset because it is just a constant term at your output.
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Fangjun Jiang
2011-8-12
Yes. That's what I remembered. After using ss() to solve your problem, your original input and output are just off by a constant term.
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