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

Hi Richard,

Richard wrote:


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 http://www.polyx.com . You can also check
if it is included in the Slicot library at http://www.slicot.de . Some
functionality for polynomial matrices is also covered in Scilab, as far as
I know.

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 Hurák wrote: