Learn more about System Identification Toolbox

Estimating a Transfer Function with a Noise Model

On this page…
Estimating a Second-Order Transfer Function with Complex Poles and Noise Validating the Models

Estimating a Second-Order Transfer Function with Complex Poles and Noise

In this portion of the tutorial, you estimate a second-order transfer function and include a noise model. By including a noise model, you optimize the estimation results for prediction application.

You must have already estimated the model, as described in Estimating a Second-Order Transfer Function Using Default Settings.

If you have not performed this step, click here to complete it.

To estimate a second-order transfer function with noise:

1. If the Process Models dialog box is not open, select Estimate > Process models in the System Identification Tool GUI. This action opens the Process Models dialog box.

2. In the Model Transfer Function area, specify the following options:

   • Under Poles, select 2 and Underdamped.

     This selection updates the Model Transfer Function to a second-order model structure that can contain complex poles.

     

   • Make sure that the Zero and Integrator check boxes are cleared to exclude a zero and an integrator (self-regulating ) from the model.

   • Disturbance Model — Set to Order 1 to estimate a noise model H as a continuous-time, first-order ARMA model:

     

     where and D are first-order polynomials, and e is white noise.

     This action specifies the Focus as Prediction, which improves accuracy in the frequency range where the noise level is low. For example, if there is more noise at high frequencies, the algorithm assigns less importance to accurately fitting the high-frequency portions of the data.

   • Name — Edit the model name to P2DUe1 to generate a model with a unique name in the System Identification Tool GUI.

3. Click Estimate.

4. In the Process Models dialog box, set the Disturbance Model to Order 2 to estimate a second-order noise model.

5. Edit the Name field to P2DUe2 to generate a model with a unique name in the System Identification Tool GUI.

6. Click Estimate.

Back to Top

Validating the Models

In this portion of the tutorial, you evaluate model performance using the Model Output and the Residual Analysis plots.

You must have already estimated the models, as described in Estimating a Second-Order Transfer Function Using Default Settings and Estimating a Second-Order Transfer Function with Complex Poles and Noise.

If you have not performed these steps, click here to complete them.

Comparing the Model Output Plots

To generate the Model Output plot:

• Select the Model output check box in the System Identification Tool GUI.

  If the plot is empty, click the model icons in the System Identification Tool window to display these models on the plot.

The following Model Output plot shows the simulated model output, by default. The simulated response of the models is approximately the same for models with and without noise. Thus, including the noise model does not affect the simulated output.

To view the predicted model output:

• In the Model Output plot window, select Options > 5 step ahead predicted output.

The following Model Output plot shows that the predicted model output of P2DUe2 (with a second-order noise model) is better than the predicted output of the other two models (without noise and with a first-order noise model, respectively).

Comparing the Residual Analysis Plots

To generate the Residual Analysis plot:

• Select the Model resids check box in the System Identification Tool GUI.

  If the plot is empty, click the model icons in the System Identification Tool window to display these models on the plot.

P2DUe2 falls well within the confidence bounds on the Residual Analysis plot.

To view residuals for P2DUe2 only, remove models P2DU and P2DUe1 from the Residual Analysis plot by clicking the corresponding icons in the System Identification Tool GUI.

The Residual Analysis plot updates, as shown in the following figure.

The whiteness test for P2DUe2 shows that the residuals are uncorrelated, and the independence test shows no correlation between the residuals and the inputs. These tests indicate that P2DUe2 is a good model.

Back to Top

Estimating a Second-Order Transfer Function (Process Model) with Complex Poles

Viewing Model Parameters

© 1984-2009- The MathWorks, Inc.    -   Site Help   -   Patents   -   Trademarks   -   Privacy Policy   -   Preventing Piracy   -   RSS