.Modelica_LinearSystems2.DiscreteStateSpace.Analysis.stepResponse

Information

Syntax

      (y) = DiscreteStateSpace.Analysis.stepResponse(dss)
(y, t, x) = DiscreteStateSpace.Analysis.stepResponse(dss, tSpan)

Description

Function stepResponse calculates the step response of a discrete state space system. Starting at x(t=0)=0 and y(t=0)=C*x0 + D*u0, the outputs y and the states x are calculated for each time step t=k*dss.Ts. The function call

DiscreteStateSpace.Analysis.stepResponse(dss, tSpan)

gives the same result as

DiscreteStateSpace.Analysis.timeResponse(response=Types.TimeResponse.Step, dss, tSpan, x0=fill(0,size(ss.A,1))).

Note that an appropriate step response of a discrete system that is comparable to the step response of the corresponding continuous system requires the "StepExact" conversion from continuous system to discrete system.

Example

  Modelica_LinearSystems2.DiscreteStateSpace dss=Modelica_LinearSystems2.DiscreteStateSpace(
    A=[0.904837418036 ],
    B=[0.095162581964],
    C=[2],
    D=[0],
    B2=[0],
    Ts=0.1,
    method = Modelica_LinearSystems2Types.Method.StepExact);

  Real tSpan= 0.4;

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

algorithm
  (y,t,x) := Modelica_LinearSystems2.DiscreteStateSpace.Analysis.stepResponse(dss,tSpan);
//  y[:,1,1]={0, 0.19, 0.3625, 0.518, 0.659}
//         t={0, 0.1, 0.2, 0.3, 0.4}
//  x[:,1,1]={0, 0.0952, 0.1813, 0.2592, 0.33}

Interface

encapsulated function stepResponse
  import Modelica;
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.DiscreteStateSpace;
  extends Modelica_LinearSystems2.Internal.timeResponseMask_discrete;
end stepResponse;