# 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.
The default is "FALSE"; damping will be considered 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.
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".
The default is write_energy_dist = "NO".

## Example

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

1. 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)
$\begin{array}{l}\stackrel{˙}{x}=Ax+Bu\\ y=Cx+Du\end{array}$
• Otherwise, only the eigensolution is performed.
2. 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.