.Modelica_LinearSystems2.DiscreteStateSpace.Analysis.initialResponse

Information

Syntax

      (y) = DiscreteStateSpace.Analysis.initialResponse(x0, dss)
(y, t, x) = DiscreteStateSpace.Analysis.initialResponse(x0, dss, tSpan)

Description

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

DiscreteStateSpace.Analysis.initialResponse(x0,dss, dt, tSpan)

gives the same result as

DiscreteStateSpace.Analysis.timeResponse(dss, tSpan, response=Types.TimeResponse.Initial, x0=x0).

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_LinearSystems2.Types.Method.StepExact);

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

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

algorithm
  (y,t,x):=Modelica_LinearSystems2.DiscreteStateSpace.Analysis.initialResponse(x0,dss,tSpan);
//  y[:,1,1]={2, 1.809, 1.637, 1.4812, 1.3402}
//         t={0, 0.1, 0.2, 0.3, 0.4}
//  x[:,1,1]={1, 0.9048, 0.8186, 0.7406, 0.6701}

See also

DiscreteStateSpace.Analysis.timeResponse, StateSpace.Analysis.initialResponse

Interface

encapsulated function initialResponse
  import Modelica;
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.DiscreteStateSpace;
  input Real x0[:] = fill(0, 0) "Initial state vector";
  extends Modelica_LinearSystems2.Internal.timeResponseMask_discrete(redeclare Real y[:, size(dss.C, 1), 1], redeclare Real x_discrete[:, size(dss.A, 1), 1]);
end initialResponse;