Conversion from multivariable ARX model to multivariable State-Space model using MATLAB

If I understand your needs right, you have a model of a MIMO system in the format

D(d)y(k)=N(d)u(k)

and you would like to find an equivalent state-space model

xdot(k) = Ax(k)+Bu(k) y(k) = Cx(k)+Du(k)

what you need is a routine for conversion between polynomial matrix fraction D^-1N and state-space format. As far as I know, there is none in Control System Toolbox for Matlab. This routine is included in a commercial Polynomial Toolbox distributed by

In Polynomial Toolbox, the typical session looks like this:

A = -0.64 - 0.56d + 0.44d^2 -0.95 + 0.78d + 0.57d^2 -0.82 - 0.27d - 1.2d^2 -2.2 + 0.99d - 0.52d^2 B = 0.23 + 0.021d -1 - 0.95d

a = x1 x2 x3 x4 x1 -1.583 1 1.266 0 x2 3.401 0 2.82 0 x3 0.4702 0 -0.02444 1 x4 -1.808 0 -1.288 0 b = u1 x1 3.926 x2 -4.29 x3 -0.1479 x4 2.565 c = x1 x2 x3 x4 y1 1 0 0 0 y2 -0 0 1 0 d = u1 y1 -2.374 y2 1.341 Sampling time: 1 Discrete-time model.

Best regards, Zdenek

Hi Zdenek,

Thanks a lot for your help!!!!! I really appreciate it ^__^

Regards,

Richard

Zdenek Hur=E1k wrote: