WSMLinearize

WSMLinearize["mmodel"]
gives a linearized state-space to the model "mmodel" at an equilibrium.

WSMLinearize["mmodel",{{{x1,x10},},{{u1,u10},}}]
linearizes at state values {x10,} and input values {u10,}.

DetailsDetails

  • WSMLinearize linearizes a continuous-time system designed in Wolfram SystemModeler.
  • WSMLinearize returns a StateSpaceModel object.
  • WSMLinearize["mmodel",spec] allows the following symbolic values for spec:
  • "EquilibriumValues"uses WSMFindEquilibrium["mmodel"]
    "InitialValues"uses WSMModelData["mmodel","GroupedInitialValues"]
  • WSMLinearize["mmodel",vals,spec] uses spec to add missing values in vals.
  • The default spec is taken to be "EquilibriumValues".
  • The resulting StateSpaceModel has states xi, inputs uj, and outputs yk as defined in "mmodel".
  • The list of states, inputs, and outputs can be found from WSMModelData["mmodel",spec]:
  • "StateVariables"state variables xi
    "InputVariables"input variables uj
    "OutputVariables"output variables yk
  • WSMLinearize reduces a system of DAEs to a system of ODEs and linearizes the resulting ODEs.
  • A system of ODEs with state equations and output equations is linearized at a point and .
  • The linearized system has state , input , and output , with state equations and output equation . The matrices are given by , , , and , all evaluated at and .
  • The returned StateSpaceModel corresponds to the system , .
  • The shortest unique model name mmodel can be used where WSMNames["*.mmodel"] gives a unique match.
  • The following options can be given:
  • Method"NumericDerivative"methods for linearization algorithm
    WSMProgressMonitorAutomaticcontrol display of progress
  • The option Method has the following possible settings:
  • "NumericDerivative"uses SystemModeler linearization
    "SymbolicDerivative"uses StateSpaceModel linearization

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Load Wolfram SystemModeler Link:

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Linearize a DC-motor model around an equilibrium:

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Linearize a mixing tank model around equilibrium with given state and input constraints:

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Use the diagram representation of a model as input:

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Copy and paste the output above:

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