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# PEM Estimator

Estimate generic input-output polynomial model parameters from SISO data using iterative prediction-error minimization method

## Library

System Identification Toolbox

## Description

The PEM Estimator block estimates linear input-output polynomial models in Simulink® software.

 Note:   The PEM Estimator block will be removed in a future release. There is no replacement for this block.

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 input-output polynomial structure is defined, as follows:

where

• y(t) is the output at time t.

• A, B, F, C, and D are the parameters , , , and to be estimated.

• is a white-noise disturbance.

## 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 PEM Estimator block outputs a sequence of multiple models (idpoly objects), 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 [na nb nc nd nf nk]

Integers na, nb, nc, nd, nf, and nk, specify the number of A, B, C, D, and F model parameters nk is the input-output delay, respectively.

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 PEM Estimator block in a Simulink model.

1. Specify 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 PEM 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 PEM Estimator block, respectively.

3. Run the simulation.

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