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Specify inputs to linearized model

`linearizeInput(`

adds inputs for the boundary condition, constraint, load, or source with the label
`model`

,`labeltext`

)`labeltext`

. In the linearized model, the input value
*u* = 1 corresponds to a unit boundary condition acting on the entire
region specified by `labeltext`

. In other words, simulating the
linearized model with the input value *u*(*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, see Algorithms.

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

A structural boundary constraint. Use the

`structuralBC`

function with the`Constraint`

argument.A displacement or a displacement component on the boundary. Use the

`structuralBC`

function with the`Displacement`

,`XDisplacement`

,`YDisplacement`

, or`ZDisplacement`

argument.A structural boundary load. Use the

`structuralBoundaryLoad`

function with the`Pressure`

,`Force`

, or`SurfaceTraction`

argument.A structural body load. Use the

`structuralBodyLoad`

function with the`GravitationalAcceleration`

argument.

The boundary conditions, loads, or constraints with *x*-,
*y*-, and *z*- 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 the

`thermalBC`

function with the`Temperature`

or`HeatFlux`

argument.An internal heat source. Use the

`internalHeatSource`

function.

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 using `linearizeInput`

.

Use `linearizeInput`

and `linearizeOutput`

together with the `linearize`

function
to extract sparse linear models from structural and thermal models.

The `linearize`

function 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 face `X`

as linearization
outputs

linearizeOutput(model,’Face’,X)

`X`

.tlist = 1:10; u = repmat(25,size(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.

`linearize`

| `linearizeOutput`

| `structuralBodyLoad`

| `structuralBoundaryLoad`

| `structuralBC`

| `internalHeatSource`

| `thermalBC`