linearize

(To be removed) Linearize structural or thermal model

Since R2021b

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linearize will be removed.

Syntax

sys = linearize(model)
mx = linearize(model,"OutputType","matrices")

Description

sys = linearize(model) extracts a sparse linear model for use with Control System Toolbox™. For a structural analysis model, linearize extracts a mechss (Control System Toolbox) model. For a thermal analysis model, it extracts a sparss (Control System Toolbox) model. For transient models, linearize uses time 0.

Use linearizeInput to specify the inputs of the linear model that correspond to external forcing, such as loads or internal heat sources. The toolbox treats the value of each selected constraint, load, or source as a constant, and the value becomes one input channel in the linearized model. 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 using linearizeInput.

Use linearizeOutput to specify the outputs of the linear model in terms of regions of the geometry, such as cells (for 3-D geometries only), faces, edges, or vertices. This includes all degrees of freedom (DoFs) in the specified region as output values. For structural models, you can also specify which of the x, y, and z degrees of freedom to include as outputs.

Use sys.InputName and sys.OutputGroup to locate the inputs and outputs of sys that correspond to a particular boundary condition or to a selected region.

example

mx = linearize(model,"OutputType","matrices") returns the finite element matrices A, B, C, D, E or M, K, B, F used to construct the mechss and sparss models in the previous syntax.

Examples

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Open Live Script

Linearize a model for thermal analysis and return finite element matrices.

Create a transient thermal model.

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

Add the block geometry to the thermal model by using the geometryFromEdges function. The geometry description file for this problem is called crackg.m.

geometryFromEdges(thermalmodel,@crackg);

Plot the geometry with the edge labels.

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

Figure contains an axes object. 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 as 100, 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 of 0 for the temperature.

thermalIC(thermalmodel,0);

Specify the inputs of the linearized model by calling the linearizeInput function with the previously defined labels for the boundary conditions and the internal heat source. Add one label per function call.

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

Specify the outputs of the linearized model by calling the linearizeOutput function to set the regions of interest for measuring temperature. Specify one region per function call. For example, specify that the output is the temperature value at all nodes on edge 2.

linearizeOutput(thermalmodel,"Edge",2);

Measure the temperature on edge 2.

sys = linearize(thermalmodel)
Sparse continuous-time state-space model with 27 outputs, 3 inputs, and 1351 states.
Model Properties

Use "spy" and "showStateInfo" to inspect model structure. 
Type "help sparssOptions" for available solver options for this model.

In the linearized model, use sys.InputName to check that the inputs to sys are the heat source, the temperature on edge 6, and the heat flux on edge 1.

sys.InputName
ans = 3×1 cell
    {'HeatSource'}
    {'TempBC'    }
    {'FluxBC'    }

In the linearized model, use sys.OutputGroup to locate the sections associated with each coordinate.

sys.OutputGroup
ans = struct with fields:
    Edge2: [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27]

If you do not have Control System Toolbox™, you can access the finite element matrices A, B, C, and E as follows.

mx = linearize(thermalmodel,"OutputType","matrices")
mx = struct with fields:
    A: [1351×1351 double]
    B: [1351×3 double]
    C: [27×1351 double]
    E: [1351×1351 double]

Input Arguments

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Structural or thermal model, specified as a StructuralModel object or a ThermalModel object. The linearize function does not support nonlinear thermal analysis.

Example: thermalmodel = createpde("thermal","steadystate")

Example: structuralmodel = createpde("structural","static-solid")

Output Arguments

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Sparse linear models for use with Control System Toolbox, returned as a mechss or sparss model object.

Finite element matrices A, B, C, D, and E or M, K, B, and F, returned as a structure array.

Version History

Introduced in R2021b

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See Also

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