.Modelica_LinearSystems2.StateSpace.Conversion.toTransferFunctionMIMO

Information

Syntax

tf = StateSpace.Conversion.toTransferFunctionMIMO(ss)

Description

Computes a matrix of TransferFunction records

        n_i(s)     b0_i + b1_i*s + ... + bn_i*s^n
tf_i = -------- = --------------------------------
        d_i(s)     a0_i + a1_i*s + ... + an_i*s^n

with repetitive application of Conversion.toTransferFunction.

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 + 5*s + 6), 1/(s + 2);
         1/(s^2 + 5*s + 6), (1*s^2 + 5*s + 5)/(s^2 + 3*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)        |
         |                                                   |

Interface

function toTransferFunctionMIMO
  import Modelica;
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.TransferFunction;
  import Modelica_LinearSystems2.StateSpace;
  import Modelica_LinearSystems2.ZerosAndPoles;
  input StateSpace ss "State space system";
  input Real tol = 1e-10 "Tolerance of reduction procedure, default tol = 1e-10";
  output TransferFunction tf[size(ss.C, 1), size(ss.B, 2)] "Matrix of transfer function objects";
end toTransferFunctionMIMO;

Revisions