System Identification Toolbox™

BJ Estimator - Estimate parameters of Box-Jenkins model from SISO data in Simulink software returning idpoly object

Library

System Identification Toolbox

Description

The BJ Estimator block estimates the parameters of a Box-Jenkins model, and returns the estimated model as an idpoly object.

For information about the default algorithm settings used for model estimation, see the Algorithm Properties reference page.

Each estimation generates a figure with the following plots:

• Actual (measured) output versus the simulated or predicted model output.

• Error in simulated model, which is the difference between the measured output and the model output.

Model Definition

The Box-Jenkins model is defined, as follows:

where the coefficients of

are the parameters being estimated, and is the backward shift operator defined by .

The following block diagram shows the Box-Jenkins model structure.

Input

The block accepts two inputs, corresponding to the measured input-output data for estimating the model.

First input: Input signal.

Second input: Output signal.

Output

The BJ Estimator block outputs a sequence of multiple models (idpoly), estimated at regular intervals during the simulation.

The Data window field in the block parameter dialog box specifies the number of data samples to use for estimation, as the simulation progresses.

The output format depends on whether you specify the Model Name in the block parameter dialog box.

Dialog Box

Orders of model [nb nc nd nf nk]

Integers n_b, n_c, n_d, and n_f specify the number of B, C, D, and F model parameters, respectively.

Integer n_k specifies the input-output delay.

Calculate after how many points

Number of input data samples that specify the interval after which to estimate a new model.

Default: 25

Sample time

Sampling time for the model.

Note   If you use a fixed step-size solver, the fixed step size must be consistent with this sample time.

Length of data window

Number of past data samples used to estimate each model. A longer data window should be used for higher-order models. Too small a value might cause poor estimation results, and too large a value leads to slower computation.

Default: 200.

Model name

Name of the model.

Whether you specify the model name determines the output format of the resulting models, as follows:

• If you do not specify a model name, the estimated models display in the MATLAB Command Window in a transfer-function format.

• If you specify a model name, the resulting models are output to the MATLAB workspace as a cell array.

Simulation/Prediction

Simulation: The algorithm uses only measured input data to simulate the response of the model.

Prediction: Specifies the forward-prediction horizon for computing the response K steps in the future, where K is 1, 5, or 10.

Examples

This example shows how you can use the BJ Estimator block in a Simulink model.

1. Specify the data in iddata1.mat for estimation:

   load iddata1;
   IODATA = z1; 

2. Create a new Simulink model, as follows:

   • Add the IDDATA Source block and specify IODATA in the Iddata object field of the IDDATA Source block parameters dialog box.

   • Add the BJ Estimator block to the model. Set the sample time in the block to 0.1 seconds and the simulation end time to 30 seconds.

   • Connect the Input and Output ports of the IDDATA Source block to the u and y ports of the BJ Estimator block, respectively.

     

3. Run the simulation.

   The estimated models appear in the MATLAB Command Window every 25 samples.

See Also

Related Commands

Topics in the System Identification Toolbox User's Guide

ARX Estimator

IDDATA Sink