.Modelica_LinearSystems2.StateSpace.Conversion.toZerosAndPolesMIMO

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.
 

Interface

encapsulated function toZerosAndPolesMIMO
  import Modelica.Utilities.Streams.print;
  import Modelica;
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.Math.Complex;
  import Modelica_LinearSystems2.ZerosAndPoles;
  import Modelica_LinearSystems2.StateSpace;
  input StateSpace ss "State space system";
  input Real tol = 1e-10 "Tolerance of reduction procedure, default tol = 1e-10";
  output ZerosAndPoles zp[size(ss.C, 1), size(ss.B, 2)];
end toZerosAndPolesMIMO;

Revisions