# Estimate Process Model

Estimate continuous-time process model for single-input, single-output (SISO) system in either time or frequency domain in the Live Editor

## Open the Task

To add the **Estimate Process Model** task to a live script
in the MATLAB Editor:

On the

**Live Editor**tab, select**Task > Estimate Process Model**.In a code block in your script, type a relevant keyword, such as

`process`

or`estimate`

. Select`Estimate Process Model`

from the suggested command completions.

## Examples

## Parameters

**Select Data**

`Data Type`

— Data type for input and output data

`Time`

(default) | `Frequency`

| `Data Object`

The task accepts single-channel numeric measurement values that are uniformly
sampled in time. Data can be packaged as numeric arrays (`Time`

or
`Frequency`

type) or in a data object, such as an `iddata`

or `idfrd`

object.

The data type you choose determines the additional parameters you must specify.

`Time`

— Specify**Sample Time**and**Start Time**in the time units that you select.`Frequency`

— Specify**Frequency**by selecting the variable name of a frequency vector in your MATLAB workspace. Specify the units for this frequency vector. Specify**Sample Time**in seconds.`Data Object`

— Specify no additional parameters, because the data object already contains information on time or frequency sampling.

`Estimation Input and Estimation Output`

— Variable names of input and output data for estimation

valid variable names

Select the input and output variable names from the MATLAB workspace choices. Use these parameters when **Data
Type** is `Time`

or
`Frequency`

.

`Estimation Object`

— Variable name of data object containing input and output data to be used for estimation

valid variable name

Select the data object variable name from the MATLAB workspace choices. Use this parameter when **Data Type**
is `Data Object`

.

`Validation Input (u) and Validation Output (y)`

— Variable names of input and output data to be used for validation

valid variable names

Select the input and output variable names, or the data object name, from the
workspace choices. Use these parameters when **Data Type** is
`Time`

or `Frequency`

. Specifying
validation data is optional but recommended.

`Validation Object`

— Variable name of data object containing input and output data for validation

valid variable name

Select the data object variable name from the MATLAB workspace choices. Use this parameter when **Data Type**
is `Data Object`

. Specifying validation data is optional but
recommended.

**Specify Model Structure**

`Structure`

— Zeros and poles in model

`One Pole`

(default) | `Two Real Poles`

| `Underdamped Pair`

| `Underdamped Pair + Real Pole`

The task allows you to specify one of four basic structures. These structures range from a simple first-order process to a more dynamic second-order or third-order process with complex conjugate (underdamped) poles.

`One Pole`

`Two Real Poles`

`Underdamped Pair`

`Underdamped Pair + Real Pole`

`Delay`

— Include transport delay

off (default) | on

Include transport delay, or input-to-output delay, of one sample. The transport delay is also known as dead time.

`Zero`

— Include process zero

off (default) | on

Include a process zero in the numerator.

`Integrator`

— Include integrator

off (default) | on

Include an integrator, represented by an additional 1/ *s* term.
Including an integrator creates a self-regulating process.

**Specify Estimation Initialization**

`Initial Values`

— Initial values of structure parameters

0 | parameter values

Specify initial values for the estimation and whether these values are to be fixed
or estimated. The values to specify depend on the model structure and your
specifications for **Delay** and **Zero**. Below
**Specify model structure**, the task displays the equation that
represents the specified system. This equation contains all of the parameters that can
be estimated, and that you can initialize or fix. The possible parameters are:

*Kp*— Static gain*T*— Time constant for first real pole_{p1}*T*— Time constant for second real pole_{p2}*Tω*— Time constant for complex poles, equal to the inverse of the natural frequency*ζ*— Damping coefficient for complex poles*T*— Transport delay_{d}*T*— Time constant for the process zero_{z}

All time-based parameters are in the time units you select for
**Sample Time**.

**Specify Optional Parameters**

`Fit Focus`

— Minimize prediction error or simulation error

`Prediction`

(default) | `Simulation`

Fit focus specifies what error to minimize in the loss function during estimation.

`Prediction`

— Minimize the one-step-ahead prediction error between measured and predicted outputs. This estimation approach focuses on producing a good predictor model for the estimation inputs and outputs. Prediction focus generally produces the best estimation results because it uses both input and output measurements, thus accounting for disturbances.`Simulation`

— Minimize the error between measured and simulation outputs. This estimation approach focuses on producing a simulated model response that has a good fit with the estimation inputs and outputs. Simulation focus is generally best for validation, especially with data sets not used for the original estimation.

`Initial Conditions`

— Handling of initial conditions

`Auto`

(default) | `Zero`

| `Estimate`

| `Backcast`

Set this option when you want to choose a specific method for initializing the
model. With the default setting of `Auto`

, the software chooses
the method based on the estimation data. Choices are:

`Zero`

— The initial state is set to zero.`Estimate`

— The initial state is treated as an independent estimation parameter.`Backcast`

— The initial state is estimated using the best least squares fit.

`Input Intersampling`

— Intersampling behavior for input signal

`Zero-order hold`

(default) | `Triangle approximation`

| `Band-limited`

Input intersampling is a property of the input data. The task uses this property
when estimating process models. Specify **Input Intersampling** when
your data type is `Time`

or
`Frequency`

. If you are using an `iddata`

object, the object already contains the intersampling information. Choices for this
property are:

`Zero-order hold`

— Piecewise-constant input signal between samples`Triangle approximation`

— Piecewise-linear input signal between samples, also known as first-order hold`Band-limited`

— Input signal has zero power above the Nyquist frequency

`Search Method`

— Numerical search mode for iterative parameter estimation

`Auto`

(default) | `Gauss-Newton`

| `Adaptive Gauss-Newton`

| `Levenberg-Marquardt`

| `Gradient Search`

`Auto`

— For each iteration, the software cycles through the methods until it finds the first direction descent that leads to a reduction in estimation cost.`Gauss-Newton`

— Subspace Gauss-Newton least-squares search.`Levenberg-Marquardt`

— Levenberg-Marquardt least-squares search.`Adaptive Gauss-Newton`

—Adaptive subspace Gauss-Newton search.`Gradient Search`

— Steepest descent least-squares search.

`Max. Iterations`

— Maximum number of iterations during error minimization

20 (default) | positive integer

Set the maximum number of iterations during error minimization. The iterations stop
when **Max. Iterations** is reached or another stopping criterion is
satisfied, such as **Tolerance**.

`Tolerance`

— Minimum percentage of expected improvement in error

0.01 (default) | positive integer

When the percentage of expected improvement is less than
**Tolerance**, the iterations stop.

`Weighting Prefilter`

— Weighting prefilter for loss function

`No filter`

(default) | `Passband(s)`

| `LTI Filter`

| `Frequency weights vector`

Set this option when you want to apply a weighting prefilter to the loss function that the task minimizes when you estimate the model. When you select an option, you must also select the associated variable in your workspace that contains the filter information. The available options depend on the domain of the data.

Weighting Prefilter | Data Domain | Filter Information |
---|---|---|

`No Filter` | Time and frequency | |

`Passbands` | Time and frequency | Passband ranges, specified as a 1-by-2 row vector or an
n-by-2 matrix, where n is the number
of passbands |

`LTI Filter` | Time and frequency | SISO LTI model |

`Frequency Weights Vector` | Frequency | Frequency weights, specified as a column vector with the same length as the frequency vector |

For instance, suppose that you are performing estimation with SISO
frequency-domain data and that in your MATLAB workspace, you have a column vector `W`

that contains
frequency weights for the prefilter. In the task, select ** Weighting
prefilter > Frequency weights vector** and the variable
`W`

.

**Visualize Results**

`Output Plot`

— Plot comparison of model and measured outputs

on (default) | off

Plot a comparison of the model output and the original measured data, along with the fit percentage. If you have separate validation data, a second plot compares the model response to the validation input data with the measured output from the validation data set.

## Version History

**Introduced in R2019b**