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linearizeInput

Specify inputs to linearized model

Since R2021b

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Syntax

linearizeInput(model,labeltext)
input = linearizeInput(model,labeltext)

Description

example

linearizeInput(model,labeltext)adds inputs for the boundary condition, constraint, load, or source with the labellabeltext. In the linearized model, the input valueu= 1 corresponds to a unit boundary condition acting on the entire region specified bylabeltext. In other words, simulating the linearized model with the input valueu(t) = 25 is equivalent to setting the boundary condition value to 25 in the thermal or structural model in Partial Differential Equation Toolbox™. For more information, seeAlgorithms.

For a structural analysis model, the following boundary conditions, constraints, and loads can become inputs of the linearized model:

  • A structural boundary constraint. Use thestructuralBCfunction with theConstraintargument.

  • A displacement or a displacement component on the boundary. Use thestructuralBCfunction with theDisplacement,XDisplacement,YDisplacement, orZDisplacementargument.

  • A structural boundary load. Use thestructuralBoundaryLoadfunction with thePressure,Force, orSurfaceTractionargument.

  • A structural body load. Use thestructuralBodyLoadfunction with theGravitationalAccelerationargument.

The boundary conditions, loads, or constraints withx-,y-, andz- components produce one input channel per component.

For a thermal analysis model, the following boundary conditions and sources can become inputs of the linearized model:

  • A temperature or heat flux on the boundary. Use thethermalBCfunction with theTemperatureorHeatFluxargument.

  • An internal heat source. Use theinternalHeatSourcefunction.

Each selected condition or source produces a single scalar input in the linearized model.

To make a condition, constraint, load, or source available as a linearization input, always label it upon creation. For example, specify an internal heat source for a thermal model as follows:

internalHeatSource(thermalmodel,25,"Label","HeatSource");

The remaining boundary conditions are set to zero for linearization purposes, regardless of their value in the structural or thermal model. Ensure that you label all nonzero boundary conditions and pass them as inputs usinglinearizeInput.

UselinearizeInputandlinearizeOutputtogether with thelinearizefunction to extract sparse linear models from structural and thermal models.

input= linearizeInput(model,labeltext)returns a structure arrayinputwith the linearization input description.

Examples

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Open Live Script

Use labels to pass the parameters of a 2-D thermal analysis model to thelinearizefunction. This function extracts sparse linear models for use with Control System Toolbox™.

Create a transient thermal model.

thermalmodel = createpde("thermal","transient");

Add the block geometry to the thermal model by using thegeometryFromEdgesfunction. The geometry description file for this problem is calledcrackg.m.

geometryFromEdges(thermalmodel,@crackg);

Plot the geometry, displaying edge labels.

pdegplot(thermalmodel,"EdgeLabels","on") ylim([-1,1]) axisequal

图包含一个坐标轴对象。The axes object contains 9 objects of type line, text.

Generate a mesh.

generateMesh(thermalmodel);

Specify the thermal conductivity, mass density, and specific heat of the material.

thermalProperties(thermalmodel,"ThermalConductivity",1,..."MassDensity",1,..."SpecificHeat",1);

Specify the temperature on the left edge as100, and constant heat flow to the exterior through the right edge as-10. Add a unique label to each boundary condition.

thermalBC(thermalmodel,"Edge",6,"Temperature",100,"Label","TempBC"); thermalBC(thermalmodel,"Edge",1,"HeatFlux",-10,"Label","FluxBC");

Specify that the entire geometry generates heat and add a unique label to this assignment.

internalHeatSource(thermalmodel,25,"Label","HeatSource");

Set an initial value of0for the temperature.

thermalIC(thermalmodel,0);

Call thelinearizeInputfunction with the previously defined labels for the boundary conditions and the internal heat source to set the inputs for thelinearizefunction. Add one label per function call.

linearizeInput(thermalmodel,"HeatSource"); linearizeInput(thermalmodel,"TempBC"); linearizeInput(thermalmodel,"FluxBC");

TheLinearizeInputsproperty ofthermalmodelstores the inputs.

thermalmodel.LinearizeInputs
ans=1×3 struct array with fields:RegionType RegionID Label
Open Live Script

Create inputs for gravity and a short pressure pulse on tuning fork.

Create a structural transient analysis model.

structuralmodel = createpde("structural","transient-solid");

Import and plot the tuning fork geometry.

importGeometry(structuralmodel,"TuningFork.stl"); pdegplot(structuralmodel)

图包含一个坐标轴对象。The axes object contains 3 objects of type quiver, patch, line.

Generate a mesh.

generateMesh(structuralmodel,"Hmax",0.005);

Specify Young's modulus, Poisson's ratio, and the mass density to model linear elastic material behavior. Specify all physical properties in consistent units.

structuralProperties(structuralmodel,"YoungsModulus",210E9,..."PoissonsRatio",0.3,..."MassDensity",8000);

Identify faces for applying boundary constraints and loads by plotting the geometry with the face labels.

figure("units","normalized","outerposition",[0 0 1 1]) pdegplot(structuralmodel,"FaceLabels","on") view(-50,15) title("Geometry with Face Labels")

图包含一个坐标轴对象。坐标轴对象with title Geometry with Face Labels contains 3 objects of type quiver, patch, line.

Impose sufficient boundary constraints to prevent rigid body motion under applied loading. Typically, you hold a tuning fork by hand or mount it on a table. As a simplified approximation of this boundary condition, fix a region near the intersection of the tines and the handle (faces 21 and 22).

structuralBC(structuralmodel,"Face",[21,22],"Constraint","fixed");

Specify the pressure loading on a tine as a short rectangular pressure pulse.

structuralBoundaryLoad(structuralmodel,"Face",11,..."Pressure",5E6,..."EndTime",1e-3,..."Label","Pressure");

Specify the acceleration due to gravity as a body load.

structuralBodyLoad(structuralmodel,..."GravitationalAcceleration",[0 0 -1],..."Label","Gravity");

Create inputs for gravity and the pressure pulse on the tuning fork.

linearizeInput(structuralmodel,"Gravity"); linearizeInput(structuralmodel,"Pressure");

TheLinearizeInputsproperty ofstructuralmodelstores the inputs.

structuralmodel.LinearizeInputs
ans=1×2 struct array with fields:RegionType RegionID Label

Input Arguments

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Structural or linear thermal model, specified as aStructuralModelobject or aThermalModelobject. Thelinearizefunction does not support nonlinear thermal analysis.

Label for boundary condition, specified as a character vector or a string.

Data Types:char|string

Output Arguments

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Linearization input description, returned as a structure array.

Algorithms

Thelinearizefunction constructs a linear model whose inputs are a subset of the boundary conditions, loads, or sources applied to the thermal or structural model in Partial Differential Equation Toolbox and whose outputs are the resulting values at the selected DoFs. For example, if you designate the heat source

internalHeatSource(model,25,"Face",2,"Label","heatSource")

as a linearization input

linearizeInput(model,"heatSource")

and designate the temperatures on faceXas linearization outputs

linearizeOutput(model,"Face",X)
then the response of the linearized model to the constant inputu(t) = 25(the heat source value in the thermal model) matches the Partial Differential Equation Toolbox simulation results for faceX.

tlist = 1:10;u = repmat(25、大小(tlist));ysp = lsim(linsys,uLoad,tlist);

Note that loads and boundary conditions not included as linearization inputs are assumed to be zero in the linearized model regardless of their values in the structural or thermal model in Partial Differential Equation Toolbox. Simulation results can differ in this case.

Version History

Introduced in R2021b

See Also

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