.Modelica_LinearSystems2.Internal.frequencyResponseGain

Information

Syntax

zp = StateSpace.Conversion.toZerosAndPoles(ss)

Description

Computes a ZerosAndPoles record

          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 using the transformation algorithm described in [1]. The uncontrollable and unobservable parts are isolated and the eigenvalues and invariant zeros of the controllable and observable sub system are calculated.

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 = [1.0;
         1.0;
         0.0],
    C = [1.0,1.0,1.0],
    D = [0.0]);

algorithm
  zp:=Modelica_LinearSystems2.StateSpace.Conversion.toZerosAndPoles(ss);
//                s + 1.5
//   zp = 2 -----------------
             (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 frequencyResponseGain
  import Modelica;
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.StateSpace;
  import Modelica_LinearSystems2.Internal;
  import Modelica.Utilities.Streams.print;
  input Real A[:, size(A, 1)] "A-matrix of linear state space system";
  input Real B[size(A, 1), :] "B-matrix of linear state space system";
  input Real C[:, size(A, 1)] "C-matrix of linear state space system";
  input Real D[size(C, 1), size(B, 2)] "D-matrix of linear state space system";
  input Real Zeros[:, 2] "Zeros of state space system as Real matrix (first column: real, second column imaginary values)";
  input Real Poles[:, 2] "Poles of state space system as Real matrix (first column: real, second column imaginary values)";
  output Real gain "y(s) = gain*(s-z1)*(s-z2)*...*(s-zm)/((s-p1)*(s-p2)*...(s-pn))";
end frequencyResponseGain;

Revisions