## Effects of Time-Varying Source Blocks on Frequency Response Estimation

Time-varying source blocks in a Simulink^{®} model can interfere with frequency response estimation by driving the model away
from the steady-state operating point of the system. To facilitate frequency response
estimation, you can disable time-varying source blocks by setting them to constant values for
estimation.

You can identify time-varying sources when estimating frequency responses at the command
line and when using the **Model Linearizer** app.

To find source blocks, the software traces every signal path that can affect the signal value at each linearization output point in the model. The traced signal paths:

Signal paths inside virtual and nonvirtual subsystems.

Signal paths inside normal-mode referenced models. To ensure that the algorithm identifies source blocks within referenced models, set all referenced models to normal simulation mode before finding time-varying sources.

Signals routed through From and Goto blocks, or through Data Store Read and Data Store Write blocks.

Signals routed through switches. The software algorithm assumes that any pole of a switch can be active during frequency response estimation. The algorithm therefore follows the signal back through all switch inputs.

Some time-varying source blocks might not be found by the algorithm. If the internal
signal path of a block does not contain a block with no input port, that block is not reported
by the `frest.findSources`

function or in the app. To
bring the model to steady state, replace the source block with a Constant block, or a different source block.

### Set Time-Varying Sources to Constant for Estimation Using **Model Linearizer**

This example also shows how to improve estimation results by setting time-varying sources to
be constant when estimating frequency responses using the **Model Linearizer**
app.

Open the Simulink model.

`sys = "scdspeed_ctrlloop"; open_system(sys)`

Linearize the model.

Set the

`Engine Model`

block to normal mode for accurate linearization.set_param("scdspeed_ctrlloop/Engine Model","SimulationMode","Normal")

Open the

**Model Linearizer**for the model.In the Simulink model window, in the

**Apps**gallery, click**Model Linearizer**.Click

**Bode**to linearize the model and generate a Bode plot of the result.The linearized model,

`linsys1`

, appears in the**Linear Analysis Workspace**.

Create an input sinestream signal for the estimation.

Open the Create sinestream input dialog box.

On the

**Estimation**tab, in the**Input Signal**drop-down list, select**Sinestream**.Open the Add frequencies dialog box.

Click

**Add Frequencies**.Specify the input sinestream frequency range and number of frequency points.

Enter

`10`

in the**Min**box.Enter

`100`

in the**Max**box.Enter

`10`

in the box for the number of frequency points.Click

**OK**.The added points are visible in the frequency content viewer of the Create sinestream input dialog box.

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

Specify input sinestream parameters.

Change the

**Number of periods**and**Settling periods**to ensure that the model reaches steady-state for each frequency point in the input sinestream.Enter

`30`

in the**Number of periods**box.Enter

`25`

in the**Settling periods**box.Create the input sinestream.

Click

**OK**. The new input signal,`in_sine1`

, appears in the**Linear Analysis Workspace**.

Set the Diagnostic Viewer to open when estimation is performed.

On the

**Estimation**tab, select**Diagnostic Viewer**.Estimate the frequency response for the model.

Click

**Bode Plot 1**to estimate the frequency response. The Diagnostic Viewer appears in the document area and the estimated system`estsys1`

appears in the**Linear Analysis Workspace**.Compare the estimated model and the linearized model.

In

**Bode Plot 1**, there is one frequency point where the estimation and linearization do not matchClick on the

**Diagnostic Viewer**tab in the plot area of the**Model Linearizer**.Configure the

**Diagnostic Viewer**to show only the frequency point where the estimation and linearization results do not match.On the

**Diagnostic Viewer**tab, in the**Frequency Selector**section, enter`9`

in the**From**box and`11`

in the**To**box to set the frequency range that is analyzed in the**Diagnostic Viewer**.The

**Filtered Steady State Time Response**plot shows a signal that is not sinusoidal.View the unfiltered time response.

Right-click the

**Filtered Steady State Time Response**plot and clear the**Show filtered steady state output only**option.The step input and external disturbances drive the model away from the operating point used to linearize the model, which prevents the response from reaching steady-state. To correct this problem, find and disable the time-varying source blocks that interfere with the estimation. Then, estimate the frequency response of the model again.

Find and disable the time-varying sources within the model.

Open the Options for frequency response estimation dialog box.

On the

**Estimation**tab, in the**Options**section, click**More Options**.In the Options for frequency response estimation dialog box, on the

**Time Varying Sources**tab, click**Find and add time varying source blocks automatically**.This action populates the time varying sources list with the block paths of the time varying sources in the model. These sources will be held constant during estimation.

Close the dialog box.

Estimate the frequency response for the model.

On the estimation tab, click

**Bode Plot 1**to estimate the frequency response. The estimated system`estsys2`

, appears in the**Linear Analysis Workspace**.Compare the newly estimated model and the linearized model.

In

**Bode Plot 1**, the magnitude response of`estsys1`

matches the exact linearization.

### Set Time-Varying Sources to Constant for Estimation at the Command Line

This example also shows how to improve estimation results by setting time-varying
sources to be constant when estimating frequency responses using the
`frestimate`

function.

Open the Simulink model.

```
sys = "scdspeed_ctrlloop";
open_system(sys)
```

Obtain the linear analysis points from the model.

io = getlinio(mdl);

Set the Engine Model subsystem to normal mode for accurate simulation results.

set_param("scdspeed_ctrlloop/Engine Model","SimulationMode","Normal")

Linearize the model.

sys = linearize(mdl,io);

Estimate the frequency response between 10 and 100 rad/s.

in = frest.Sinestream(... "Frequency",logspace(1,2,10),... "NumPeriods",30, "SettlingPeriods",25); [sysest,simout] = frestimate(mdl,io,in);

Compare the estimation results `sysest`

with the exact linearization
`sys`

.

frest.simView(simout,in,sysest,sys)

To view the unfiltered time response for the first frequency point, in the Simulation Results Viewer:

In the

**Bode Diagram**section, adjust the shaded frequency range to contain only the first frequency point, which does not match the exact linearization at that frequency.In the

**Time Response**section, right click the plot and clear the**Show filtered steady state output only**parameter.

The step input and external disturbances drive the model away from the operating point, preventing the response from reaching steady-state. To correct this problem, find and disable the time-varying source blocks that interfere with the estimation.

Identify the time-varying source blocks using `frest.findSources`

.

srcblks = frest.findSources(mdl,io);

Create a frequency response estimation option set to disable the blocks.

opts = frestimateOptions; opts.BlocksToHoldConstant = srcblks;

Repeat the frequency response estimation using the specified options.

[sysest2,simout2] = frestimate(mdl,io,in,opts); frest.simView(simout2,in,sysest2,sys)

In the **Bode Diagram** section, the estimated frequency response matches the
exact linearization.

View the unfiltered time response for the first frequency point. In the Simulation Results Viewer:

In the

**Bode Diagram**section, adjust the shaded frequency range to contain only the first frequency point.In the

**Time Response**section, right click the plot and clear the**Show filtered steady state output only**parameter.

As shown in the **Time Response** plot, the system remains near the
initial operating point.