# 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:
•  Method Automatic methods for linearization algorithm SystemModelProgressReporting Automatic control 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:

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

 In:= Out= Linearize one of the included introductory hierarchical examples:

 In:= Out= In:= Out= ## Possible Issues(1)

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