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Analyze Batch Linearization Results in Linear Analysis Tool

This example shows how to use response plots to analyze batch linearization results in Linear Analysis Tool. The term batch linearization results refers to linearizations for varying parameter values, such as illustrated in Batch Linearize Model for Parameter Value Variations Using Linear Analysis Tool. You can use the techniques illustrated in this example to analyze the frequency response, stability, and other system characteristics for batch linearization results.

View Parameters of a Response

For this example, suppose that you have batch linearized a model as described in Batch Linearize Model for Parameter Value Variations Using Linear Analysis Tool. You have generated a step response plot of an array of linear models computed for a 2-D parameter grid, with variations of outer-loop controller gains Ki1 and Kp1.

When you perform batch linearization, Linear Analysis Tool generates a plot showing the responses of all linear models resulting from the linearization. You choose the response plot type, such as Step, Bode, or Nyquist, when you linearize. You can create additional plots at any time as described in Analyze Results Using Linear Analysis Tool Response Plots.

To view the parameters associated with a particular response, click the response on the plot.

A data tip appears on the plot, providing information about the selected response and the related model. The last lines of the data tip show the parameter combination that yielded this response. For example, in this plot, the selected response corresponds to the model obtained by setting Kp1 to 0.07875 and Ki1 to 0.061.

View Step Response of Subset of Results

Suppose you want to view the responses for only the models linearized at a specific Ki1 value, the middle value Ki1 = 0.0410. Right-click the plot and select Array Selector. The Model Selector for LTI Arrays dialog box opens.

The Selection Criterion Setup panel contains two columns, one for each model array dimension of linsys1. Linear Analysis Tool flattens the 2-D parameter grid into a one-dimensional array, so that variations in both Kp1 and Ki1 are represented along the indices shown in column 1. To determine which entries in this array correspond to Ki1 = 0.0410, examine the Parameter Variations table.

The Ki1 = 0.0410 values are the seventh to twelfth entries in this table. Therefore, you want to select array indices 7–12.

In the Model Selector for LTI Arrays dialog box, enter [7:12] in the field below column 1. The selection in the column changes to reflect this subset of the array.

Click OK. The step plot displays responses only for the models with Ki1 = 0.0410.

Export Array to MATLAB Workspace

You can export the model array to the MATLAB® workspace to perform further analysis or control design. To do so, in the Linear Analysis Tool, in the Data Browser, drag the array from Linear Analysis Workspace to the MATLAB workspace.

You can then use Control System Toolbox™ control design tools, such as the Linear System Analyzer (Control System Toolbox) app, to analyze linearization results. Or, use Control System Toolbox control design tools, such as pidtune or Control System Designer, to design controllers for the linearized systems.

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