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## Frequency-Domain Validation of Linearization

### Validate Linearization in Frequency Domain using Linear Analysis Tool

This example shows how to validate linearization results using an estimated linear model.

In this example, you linearize a Simulink® model using the model initial conditions. You then estimate the frequency response of the model using the same operating point (model initial condition). Finally, you compare the estimated response to the exact linearization result.

```sys = 'scdDCMotor';
open_system(sys);```
• Open the Linear Analysis Tool for the model.

In the Simulink model window, select Analysis > Control Design > Linear Analysis.

• Select a visualization for the linearized model.

In the Plot Result list, choose New Bode.

• Linearize the model.

Click .

A new linearized model, linsys1, appears in the Linear Analysis Workspace.

The software used the model initial conditions as the operating point to generate linsys1.

Step 2. Create sinestream input signal.

• Click the Frequency Response Estimation tab.

In this tab, you estimate the frequency response of the model.

• Open the Create sinestream input dialog box.

Select Sinestream from the Input Signal list.

• Initialize the input signal frequencies and parameters based on the linearized model.

Click Initialize frequencies and parameters.

The Frequency content viewer is populated with frequency points. The software chooses the frequencies and input signal parameters automatically based on the dynamics of linsys1.

• In the Frequency content viewer of the Create sinestream input dialog box, select all the frequency points.

• Modify the amplitude of the input signal.

Enter 1 in the Amplitude box.

• Click OK.

The input signal in_sine1 appears in the Linear Analysis Workspace.

Step 3. Select the plot to display the estimation result.

In the Plot Result list, choose Bode Plot 1 to add the next computed linear system to Bode Plot 1.

Step 4. Estimate frequency response.

Click .

The estimated system, estsys1, appears in the Linear Analysis Workspace.

Step 5. Examine estimation results.

Bode Plot 1 now shows the Bode responses for the estimated model and the linearized model.

The frequency response for the estimated model matches that of the linearized model.

### Choosing Frequency-Domain Validation Input Signal

For frequency-domain validation of linearization, create a sinestream signal. By analyzing one sinusoidal frequency at a time, the software can ignore some of the impact of nonlinear effects.

SinestreamAll linearization inputs and outputs are on continuous signals.frest.Sinestream
Sinestream with fixed sample timeOne or more of the linearization inputs and outputs is on a discrete signalfrest.createFixedTsSinestream

You can easily create a sinestream signal based on your linearized model. The software uses the linearized model characteristics to accurately predict the number of sinusoid cycles at each frequency to reach steady state.

When diagnosing the frequency response estimation, you can use the sinestream signal to determine whether the time series at each frequency reaches steady state.