# Parameters: Linear Solver

Command ElementModifies a linear parameter element.

## Format

```
<Param_Linear
[ anim_scale = "
```*real*" ]
[ balancing = { "TRUE" | "FALSE" | "AUTO"} ]
[ disable_damping = { "TRUE" | "FALSE" } ]
[ eigen_analysis = { "TRUE" | "FALSE" } ]
[ gyroscopic = { "NONE" | "PARTIAL" | "FULL" } ]
[ pinput_id = "integer" ]
[ poutput_id = "integer" ]
[ write_simulinkmdl = { "YES" | "NO" } ]
[ write_matlabfiles = { "YES" | "NO" } ]
[ write_eig_info = { "YES" | "NO" } ]
[ write_energy_dist = { "YES" | "NO" } ]
/>

## Attributes

`anim_scale`- Modifies a scale factor for magnifying the mode shapes during
animation. The default is
`anim_scale`= 1.0 `balancing`- Modifies whether the A matrix should be pre-conditioned using diagonal
scaling to improve robustness of the eigenvalue solution. Choose
from:
TRUE: MotionSolve will always balance the A matrix using diagonal scaling.

FALSE: MotionSolve will not balance the A matrix.

AUTO: MotionSolve determines when to balance the A matrix based on the condition number of the eigenvector matrix. See Parameters: Linear Solver model documentation for more details.

The default for

`balancing`is AUTO. `disable_damping`- Modifies whether the linearization solver should disable damping from all force elements for the eigenvalue solution.
`eigen_analysis`- Modifies whether linear analysis should perform or skip the eigen
analysis. This can be used in cases when only the A, B, C, and D
matrix are needed. If NO is selected, then eigen
information and energy distribution information won’t be written.
Select from TRUE or FALSE.
The default is

`eigen_analysis`= TRUE. `gyroscopic`- Specifies how MotionSolve should compute gyroscopic effects when linearizing a rotating system.
`pinput_id`- Modifies the plant input ID used for the B and D state matrices. Can be
optionally used with the
`write_matlabfile`and/or`write_simulinkmdl`option. `poutput_id`- Modifies the plant output ID used for the C and D state matrices. Can
be optionally used with the
`write_matlabfile`and/or`write_simulinkmdl`option. `write_simulinkmdl`- Modifies whether the A, B, C,and D matrices that are calculated are to
be written out in Simulink MDL format or not. Select from
"YES" and "NO". The default is
`write_simulinkmdl`= "YES". `write_matlabfiles`- Modifies whether the A,B,C,and D matrices that are calculated are to be
written out into a file that can be read in by MATLAB. Select from
"YES" and "NO". The default is
`write_matlabfiles`= "YES". `write_eig_info`- Modifies whether the eigenvalue and eigenvector data is written to a
.eig file. Select from
"YES" and "NO". The default is
`write_eig_info`= "YES". `write_energy_dist`- Modifies whether the modal kinetic energy distribution is written out to the solver log file and the *_linz.mrf output file. Select from "YES" and "NO".

## Example

```
<Param_Linear
anim_scale = "1."
write_simulinkmdl = "NO"
write_matlabfiles = "NO"
write_eig_info = "YES"
write_energy_dist = "YES"
/>
```

## Comments

- Param_Linear element
controls settings for Linearization simulation type. This simulation
provides the following information about the model:
- Matrices A, B, C and D are written in MATLAB format in four separate files with extensions .a, .b, .c and .d respectively.
- The state space form linear system is written in Simulink format in an MDL file
- States selected for linearization are written out to MotionSolve .log file.
- Eigenvalues are written to the .eig file
- One MRF file is written per eigenvector. It is used for mode shape animation in conjunction with the MotionView model MDL file. Note that this is a different file than the Simulink MDL file.
- If inputs and outputs are defined using
Control_PlantInput and
Control_PlantOutput elements,
respectively, then the state space description of the plant is
computed as follows:
(1) $$\begin{array}{l}\dot{x}=Ax+Bu\\ y=Cx+Du\end{array}$$ - Otherwise, only the eigensolution is performed.

- Retrieving gyroscopic effects when performing a linear analysis becomes
important when analyzing rotating systems. MotionSolve can
compute “partial” or “full” gyroscopic effects when linearizing a rotating
system:
- Partial: This implies that the angular momentum term $L=I\omega $ is held constant when computing the solution. Here, $I$ is the 3x3 inertia matrix of the body in a body-fixed frame and $\omega $ is the angular velocity of the body in that frame. The results from using this approach will typically match reference results OptiStruct for the same system. This is the default used by the solver.
- Full: This implies that the angular momentum term described above is not treated as constant when computing the solution.
- None: No gyroscopic effects are included in the linear solution.