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Estimating Step- and Frequency-Response Models

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Why Estimate Step- and Frequency-Response Models? Estimating the Frequency Response Estimating the Step Response

Why Estimate Step- and Frequency-Response Models?

Frequency-response and step-response are nonparametric models that can help you understand the dynamic characteristics of your system. These models are not represented by a compact mathematical formula with adjustable parameters. Instead, they consist of data tables.

In this portion of the tutorial, you estimate these models using the data set ze. You must have already created ze, as described in Creating iddata Objects.

The response plots from these models show the following characteristics of the system:

• The response from the first input to the output might be a second-order function.

• The response from the second input to the output might be a first-order or an overdamped function.

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Estimating the Frequency Response

The System Identification Toolbox product provides three functions for estimating the frequency response:

• etfe computes the empirical transfer function using Fourier analysis.

• spa estimates the transfer function using spectral analysis for a fixed frequency resolution.

• spafdr lets you specify a variable frequency resolution for estimating the frequency response.

Use the spa command to estimate the frequency response:

Ge=spa(ze);

To plot the frequency response as a Bode plot, type the following command in the MATLAB Command Window:

bode(Ge)

This command produces the following plot.

Frequency Response for the First Input-Output Path

The amplitude peaks at the frequency of about 0.7 rad/s, which suggests a possible resonant behavior (complex poles) for the first input-to-output combination—ConsumptionRate to ProductionRate.

To view the second input Current, select the MATLAB Figure window, and press Enter. The input/output pair is displayed, as shown in the following figure.

Frequency Response for the Second Input-Output Path

In both plots, the phase rolls off rapidly, which suggests a time delay for both input/output combinations.

Tip   When your data contains multiple inputs and outputs, press Enter to view the next input/output pair.

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Estimating the Step Response

To estimate the step response from the data, use the step command with the following arguments:

step(ze,30)

The first step argument is the name of the data object. The second argument is the duration of the step input in the time units you specified (minutes).

This calculation produces the following plot.

Step Response from Both Inputs to the Output

The step response for the first input/output combination suggests an overshoot, which indicates the presence of an underdamped mode (complex poles) in the physical system.

The step response from the second input to the output shows no overshoot, which indicates either a first-order response or a higher-order response with real poles (overdamped response).

The step-response plot indicates a nonzero delay in the system, which is consistent with the rapid phase roll-off you got in the Bode plot you created in Estimating the Step Response.

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Preparing Data

Estimating Delays in the Multiple-Input System

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