SystemModelLinearize

SystemModelLinearize[model]

gives a linearized StateSpaceModel for model at an equilibrium.

SystemModelLinearize[model,op]

linearizes at the operating point op.

Details and Options

  • SystemModelLinearize gives a linear approximation of model near an operating point.
  • A linear model is typically used for control design, optimization and frequency analysis.
  • A system with equations and output equations is linearized at an operating point and that should satisfy f(0,x0,u0)0.
  • The returned linear StateSpaceModel has state , input and output , with state equations and output equation . The matrices are given by , , , and , all evaluated at , and .
  • SystemModelLinearize[model] is equivalent to SystemModelLinearize[model,"EquilibriumValues"].
  • Specifications for op use the following values for the operating point:
  • "InitialValues"initial values from model
    "EquilibriumValues"FindSystemModelEquilibrium[model]
    sim or {sim,"StopTime"}final values from SystemModelSimulationData sim
    {sim,"StartTime"}initial values of sim
    {sim,time}values at time from sim
    {{{x1,x10},},{{u1,u10},}}state values xi0 and input values ui0
  • The simulation sim can be obtained using SystemModelSimulate[model,All,].
  • SystemModelLinearize linearizes a system of DAEs symbolically, or first reduces it to a system of ODEs and linearizes the resulting ODEs numerically.
  • The following options can be given:
  • MethodAutomaticmethods for linearization algorithm
    SystemModelProgressReportingAutomaticcontrol display of progress
  • The option Method has the following possible settings:
  • "NumericDerivative"reduces to ODEs and then linearizes numerically
    "SymbolicDerivative"linearizes symbolically from a system of DAEs

Examples

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Basic Examples  (3)

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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Linearize one of the included introductory hierarchical examples:

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Scope  (19)

Generalizations & Extensions  (1)

Options  (3)

Applications  (10)

Properties & Relations  (8)

Possible Issues  (1)

Introduced in 2018
(11.3)
|
Updated in 2019
(12.0)