functiontoZerosAndPolesMIMO

Information

Syntax

zp = StateSpace.Conversion.toZerosAndPolesMIMO(ss)

Description

Computes a matrix of ZerosAndPoles records

          product(s + n1[i]) * product(s^2 + n2[i,1]*s + n2[i,2])
zp = k * ---------------------------------------------------------
          product(s + d1[i]) * product(s^2 + d2[i,1]*s + d2[i,2])

of a system from state space representation, i.e. isolating the uncontrollable and unobservable parts and the eigenvalues and invariant zeros of the controllable and observable sub systems are calculated. The algorithm applies the method described in [1] for each input-output pair.

Example

  Modelica_LinearSystems2.StateSpace ss=Modelica_LinearSystems2.StateSpace(
    A = [-1.0, 0.0, 0.0;
          0.0,-2.0, 0.0;
          0.0, 0.0,-3.0],
    B = [0.0, 1.0;
         1.0, 1.0;
        -1.0, 0.0],
    C = [0.0, 1.0, 1.0;
         1.0, 1.0, 1.0],
    D = [1.0, 0.0;
         0.0, 1.0]);

algorithm
  zp:=Modelica_LinearSystems2.StateSpace.Conversion.toZerosAndPoles(ss);

// zp = [(s^2 + 5*s + 7)/( (s + 2)*(s + 3) ), 1/(s + 2);
         1/( (s + 2)*(s + 3) ), 1*(s + 1.38197)*(s + 3.61803)/( (s + 1)*(s + 2) )]

i.e.

         |                                                   |
         |    (s^2+5*s+7)                    1               |
         | -----------------               -----             |
         |  (s + 2)*(s + 3)                (s+2)             |
  tf  =  |                                                   |
         |        1             (s + 1.38197)*(s + 3.61803)  |
         | -------------       ----------------------------- |
         | (s + 2)*(s + 3)            (s + 1)*(s + 2)        |
         |                                                   |

References

 [1] Varga, A and Sima, V. (1981):

Numerically stable algorithm for transfer function matrix evaluation. Int. J. Control, Vol. 33, No. 6, pp. 1123-1133.
 

Inputs

Outputs

Revisions