## Specify Options for Modal Truncation in Model Reducer

The Model Reducer app provides several options to configure model order
reduction using Modal Truncation method for LTI and sparse LTI models. The following
sections describe the available options on the **Options**
dialog.

### Modal Truncation Configuration

Use this dialog to specify modal truncation options for LTI models. These options control the numerical aspects of modal decomposition.

**Preserve DC gain**— Preserve the DC gain (steady-state value of step response) to match the time response better.**Compute modes only**— Flag to only compute modes for the original system.When you enable this option, the software computes only the pole locations, damping, and natural frequency of the poles

When you disable this option, the software computes a full modal decomposition.

**Input Scaling**— Input scaling factors.Input scaling factors, specified as a vector of length

*Nu*, where*Nu*is the number of inputs in the original model.Use this option to emphasize specific input channels in the model. The software evaluates the modal contributions for the scaled system.

This affects only the normalized DC contribution. For the input scaling factor

*D*and output scaling factor_{u}*D*, the normalized DC contribution of_{y}*G*(_{k}*s*) in continuous time is obtained as$$\frac{\Vert {D}_{y}{G}_{k}(0){D}_{u}\Vert}{\Vert {D}_{y}G(0){D}_{u}\Vert}$$

In discrete time, the software uses the first time samples

*G*(1) and_{k}*G*(1).**Output Scaling**— Output scaling factors.Output scaling factors, specified as a vector of length

*Ny*, where*Ny*is the number of outputs in the original model.Use this option to emphasize specific output channels in the model. The software evaluates the modal contributions for the scaled system.

This affects only the normalized DC contribution. For the input scaling factor

*D*and output scaling factor_{u}*D*, the normalized DC contribution of_{y}*G*(_{k}*s*) in continuous time is obtained as$$\frac{\Vert {D}_{y}{G}_{k}(0){D}_{u}\Vert}{\Vert {D}_{y}G(0){D}_{u}\Vert}$$

In discrete time, the software uses the first time samples

*G*(1) and_{k}*G*(1).**DC Frequency**— Frequency for evaluating and matching DC contributions, specified as a nonnegative scalar. For models with integrators, you cannot evaluate modal contributions at DC since the DC gain is infinite. To evaluate modal contributions and match gains at a different frequency, set the property to a positive value. The default value of this property corresponds to the DC contributions.**SepTol**— Relative accuracy of modal contribution, specified as a scalar between 0 and 1. This option limits the condition number of the block diagonalizing transformation to roughly`SepTol`

/`eps`

. Increasing`SepTol`

helps yield smaller modal components at the expense of accuracy.

### Sparse Modal Truncation Configuration

For sparse models, the app requires you to specify some options before you can perform model order reduction. Use this dialog to specify modal truncation options for sparse models.

**Frequency vector (rad/s)**— Frequencies at which to compute and plot frequency response, specified as a vector.**Preserve DC gain**— Preserve the DC gain (steady-state value of step response) to match the time response better.**Frequency focus**— Frequency range of interest, specified as a vector of form`[fmin,fmax]`

. When you specify a value for this property, the algorithm computes only modes in this frequency range.By default, the focus is unspecified (

`[0 inf]`

) and the algorithm computes the`MaxOrder`

modes with smallest magnitude.**Maximum order**— Maximum order of the modal approximation, specified as a positive integer. This value limits the number of eigenvalues computed by the Krylov-Schur iterations and the order of the modal approximation of the original sparse model.**Compute modes only**— Flag to only compute modes for the original system.When you enable this option, the software computes only the pole locations, damping, and natural frequency of the poles

When you disable this option, the software computes a full modal decomposition.

**Input Scaling**— Input scaling factors.Input scaling factors, specified as a vector of length

*Nu*, where*Nu*is the number of inputs in the original model.Use this option to emphasize specific input channels in the model. The software evaluates the modal contributions for the scaled system.

This affects only the normalized DC contribution. For the input scaling factor

*D*and output scaling factor_{u}*D*, the normalized DC contribution of_{y}*G*(_{k}*s*) in continuous time is obtained as$$\frac{\Vert {D}_{y}{G}_{k}(0){D}_{u}\Vert}{\Vert {D}_{y}G(0){D}_{u}\Vert}$$

In discrete time, the software uses the first time samples

*G*(1) and_{k}*G*(1).**Output Scaling**— Output scaling factors.Output scaling factors, specified as a vector of length

*Ny*, where*Ny*is the number of outputs in the original model.Use this option to emphasize specific output channels in the model. The software evaluates the modal contributions for the scaled system.

*D*and output scaling factor_{u}*D*, the normalized DC contribution of_{y}*G*(_{k}*s*) in continuous time is obtained as$$\frac{\Vert {D}_{y}{G}_{k}(0){D}_{u}\Vert}{\Vert {D}_{y}G(0){D}_{u}\Vert}$$

In discrete time, the software uses the first time samples

*G*(1) and_{k}*G*(1).**DC Frequency**— Frequency for evaluating and matching DC contributions, specified as a nonnegative scalar. For models with integrators, you cannot evaluate modal contributions at DC since the DC gain is infinite. To evaluate modal contributions and match gains at a different frequency, set the property to a positive value. The default value of this property corresponds to the DC contributions.**SepTol**— Relative accuracy of modal contribution, specified as a scalar between 0 and 1. This option limits the condition number of the block diagonalizing transformation to roughly`SepTol`

/`eps`

. Increasing`SepTol`

helps yield smaller modal components at the expense of accuracy.**ModeTol**— Tolerance for identifying converged eigenvalues in Krylov-Schur iterations, specified as a positive scalar.

For more information about the sparse modal truncation algorithm, see Algorithms.