10. Validating the ARX Model

You can use the LabVIEW System Identification Assistant to perform a k-step-ahead prediction using sample stimulus and response signals. You can validate a model using the data from the k-step-ahead prediction. Model validation applies data from the original stimulus signal to the model to produce a response and compares this predicted response with the original response signal. The closer the predicted response is to the original response, the more accurate the model is.

Complete the following steps to validate the ARX model for the motor.

1. In the Project View, right-click the Pole-Zero Analysis step and select Insert After»System Identification»Model Analysis»Model Validation from the shortcut menu to add a Model Validation step after the Pole-Zero Analysis step.
2. On the Input Signals tab in the Configuration View, verify that ARX Model is selected in the Model pull-down menu.
3. Select Test Stimulus from the Stimulus Signal pull-down menu to specify Test Stimulus as the stimulus signal to use to perform the k-step-ahead prediction.
4. Select Test Response from the Response Signal pull-down menu to specify Test Response as the response signal to use to perform the k-step-ahead prediction.
   
   Recall that Normalized Stimulus and Normalized Response are the signals you used to estimate the ARX model. Now you use Test Stimulus and Test Response, which are smaller sets of data samples from the same motor, to validate the accuracy of the model.
5. Notice that the mean square error (MSE) is 0.00075. On the Settings tab, notice that Prediction Step is set to 1. This model therefore has a very small error with a small prediction step.
6. Set Prediction Step to 10. Notice that MSE is now 0.00634. The MSE is larger with a larger prediction step. However, the error is less than 1% so you can conclude that the estimated model is a close approximation of the system.
7. In the Project View, rename the SysID Model Prediction output to ARX Model Prediction. This output signal is the predicted response from the ARX model to the Test Stimulus stimulus signal.
   
   Notice the two graphs in the Configuration View. Both illustrate the accuracy of the ARX model. The Response Signals graph displays Test Response and ARX Model Prediction. Recall that Test Response is the original response to Test Stimulus, whereas ARX Model Prediction is the estimated response of the configured ARX model to the Test Stimulus signal. The more the two signals in the Response Signals graph overlap, the more accurate the model is. In this example, the signals overlap very closely, which means the model is a close approximation of the system.
   
   Similarly, the Error Signal graph displays the difference between the two signals shown in the Response Signals graph. The closer the values of the Error Signal graph are to 0, the more accurate the model is.
8. Select File»Save Project to save the project.