.Modelica_LinearSystems2.StateSpace.Transformation.toIrreducibleForm

Information

Syntax

tss = StateSpace.Transformation.toIrreducibleForm(ss)

Description

This function calculates a minimal controllable and observable block Hessenberg realization for a given state-space representation. Therefore, all uncontrollable and unobservable modes are removed by performing orthogonal similarity transformations as described in [1].

This function is called to compute transfer functions of state space representations as described in [1]. Look at [1] for further details

Example

  Modelica_LinearSystems2.StateSpace ss=Modelica_LinearSystems2.StateSpace(
    A = [-4.5,  1.5,   4.0;
         -4.0,  1.0,   4.0;
         -1.5, -0.5,   1.0],
    B = [  1; 0; 1 ],
    C = [1,  0,  0],
    D = [0]);

algorithm
  tss:=Modelica_LinearSystems2.StateSpace.Transformation.toIrreducibleForm(ss);
//  tss=StateSpace(
      A=[-0.5],
      B=[-sqrt(0.5)],
      C=[-1/sqrt(0.5)1],
      D=[0])

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 toIrreducibleForm
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.StateSpace;
  import Modelica_LinearSystems2.Math.Complex;
  import Modelica;
  input StateSpace ss "State space system";
  input Real tol = 1e-10 "Tolerance of reduction procedure, default tol = 1e-10";
  output StateSpace ssm3(redeclare Real A[rankQ2, rankQ2], redeclare Real B[rankQ2, size(ss.B, 2)], redeclare Real C[size(ss.C, 1), rankQ2], redeclare Real D[size(ss.D, 1), size(ss.D, 2)]);
end toIrreducibleForm;

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