.Modelica_LinearSystems2.DiscreteTransferFunction.Analysis.initialResponse

Information

Syntax

(y, t, x) = DiscreteTransferFunction.Analysis.initialResponse(x0, dtf, tSpan)

Description

First, the discrete transfer function representation is transformed into discrete state space representation which is given to DiscreteStateSpace.Analysis.timeResponse and the initial response of the discrete state space system for initial state x0 is calculated. The type of the time response is defined by the input responseType, i.e. in this case

Initial "Initial response",

The outputs y and x of the discrete state space systrem are calculated for each time step t=k*dt.

Example

  DiscreteTransferFunction z = Modelica_LinearSystems2.DiscreteTransferFunction.z();
  Modelica_LinearSystems2.DiscreteTransferFunction dtf=(0.0023753*z^2 + 0.00475059*z + 0.0023753)/(z^2 - 1.89549*z + 0.904988);

  Real tSpan= 0.4;
  Real x0[1]={1,2};

  Real y[5,1,1];
  Real t[5];
  Real x[5,1,1]

algorithm
  dtf.Ts:=0.1;
  (y,t,x):=Modelica_LinearSystems2.DiscreteTransferFunction.Analysis.initialResponse(x0,dtf,tSpan,response,x0);
//  y[:,1,1] = {0.0187315575967189, 0.0271552102903869, 0.0345205091861731, 0.0408580313775029, 0.0462052138701078}
//         t = {0, 0.1, 0.2, 0.3, 0.4}
//  x[:,1,1] = {1.0, 2.0, 2.88598574821853, 3.66037203581564, 4.3264045475288}

Interface

encapsulated function initialResponse
  import Modelica;
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.DiscreteTransferFunction;
  import Modelica_LinearSystems2.DiscreteStateSpace;
  input Real x0[:] = fill(0, 0) "Initial state vector";
  extends Modelica_LinearSystems2.Internal.timeResponseMask_tf_discrete;
end initialResponse;