Modelica_LinearSystems2.Utilities.Import

Functions to import data in a Modelica environment

Package Content

NameDescription
Modelica_LinearSystems2.Utilities.Import.Examples Examples Demonstrate the usage of the Import functions
Modelica_LinearSystems2.Utilities.Import.linearize linearize Linearize a model after simulation up to a given time

Modelica_LinearSystems2.Utilities.Import.linearize

Linearize a model after simulation up to a given time

Information


This function initializes a Modelica model and then simulates the model with its default experiment options until time instant "t_linearize". If t_linearize=0, no simulation takes place (only initialization). At the simulation stop time, the model is linearized in such a form that

Formally, the non-linear hybrid differential-algebraic equation system is therefore treated as the following ordinary equation system at time instant t_linearize:

    der(x) = f(x,u)
         y = g(x,u) 

Taylor series expansion (linearization) of this model around the simulation stop time t_linearize:

   u0 = u(t_linearize)
   y0 = y(t_linearize)
   x0 = x(t_linearize) 

and neglecting higher order terms results in the following system:

   der(x0+dx) = f(x0,u0) + der(f,x)*dx + der(f,u)*du
      y0 + dy = g(x0,u0) + der(g,x)*dx + der(g,u)*du

where der(f,x) is the partial derivative of f with respect to x, and the partial derivatives are computed at the linearization point t_linearize. Re-ordering of terms gives (note der(x0) = 0):

   der(dx) = der(f,x)*dx + der(f,u)*du + f(x0,u0)
        dy = der(g,x)*dx + der(g,u)*du + (g(x0,u0) - y0)

or

   der(dx) = A*dx + B*du + f0
        dy = C*dx + D*du

This function returns the matrices A, B, C, D and assumes that the linearization point is a steady-state point of the simulation (i.e., f(x0,u0) = 0). Additionally, the full Modelica names of all inputs, outputs and states shall be returned if possible (default is to return empty name strings).

Inputs

NameDescription
modelNameName of the Modelica model
t_linearizeSimulate until T_linearize and then linearize [s]

Outputs

NameDescription
A[nx, nx]A-matrix
B[nx, nu]B-matrix
C[ny, nx]C-matrix
D[ny, nu]D-matrix
inputNames[nu]Modelica names of inputs
outputNames[ny]Modelica names of outputs
stateNames[nx]Modelica names of states

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