functioninitialResponse

Calculate the time response of a state space system for given initial condition and zero inputs

Extends from Modelica_LinearSystems2.Internal.timeResponseMask2 (Declares the common structure for the set of response functions).

Information

Syntax

(y, t, x) = StateSpace.Analysis.initialResponse(ss, dt, tSpan, x0)

Description

Function initialResponse calculates the time response of a state space system for given initial condition and zero inputs. The state space system is transformed to a appropriate discrete state space system and, 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*dt.

StateSpace.Analysis.initialResponse(x0,ss, dt, tSpan)

gives the same result as

StateSpace.Analysis.timeResponse(ss, dt, tSpan, response=Types.TimeResponse.Initial, x0=x0).

Example

   Modelica_LinearSystems2.StateSpace ss=Modelica_LinearSystems2.StateSpace(
      A=[-1],
      B=[1],
      C=[2],
      D=[0]);
  Real Ts=0.1;
  Real tSpan= 0.4;
  Real x0[2] = {1};

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

algorithm
  (y,t,x):=StateSpace.Analysis.initialResponse(x0,ss,Ts,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}

Inputs

Type	Name	Default	Description
Real[:]	x0	fill(0, 0)	Initial state vector
StateSpace	sc (from timeResponseMask2)		State space system
Real	dt (from timeResponseMask2)	0	Sample time [s]
Real	tSpan (from timeResponseMask2)	0	Simulation time span [s]

Outputs

Type	Name	Description
Real[:,size(sc.C, 1),size(sc.B, 2)]	y (from timeResponseMask2)	Output response: (number of samples) x (number of outputs) x (number of inputs)
Real[:]	t (from timeResponseMask2)	Time vector: (number of samples)
Real[:,size(sc.A, 1),size(sc.B, 2)]	x_continuous (from timeResponseMask2)	State trajectories: (number of samples) x (number of states) x (number of inputs)

Revisions

Date	Author	Comment
2010-05-31	Marcus Baur, DLR-RM	Realization