# Process Models

Low-order transfer function models with static gain, time constant, and input-output delay

Process models are popular for describing system dynamics in many industries and apply to various production environments. The advantages of these models are that they are simple, support transport delay estimation, and the model coefficients have an easy interpretation as poles and zeros.

A simple SISO process model has a gain, a time constant, and a gain.

`$sys=\frac{{K}_{p}}{1+{T}_{p1}s}{e}^{-{T}_{d}s}.$`

Here, Kp is the proportional gain. Tp1 is the time constant of the real pole, and Td is the transport delay (dead time).

In System Identification Toolbox™, the `idproc` model provides the process model structure and can represent process models with up to three poles and a zero.

## Apps

 System Identification Identify models of dynamic systems from measured data

 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

## Functions

expand all

 `idproc` Continuous-time process model with identifiable parameters `procest` Estimate process model using time or frequency data
 `pem` Prediction error minimization for refining linear and nonlinear models `idpar` Create parameter for initial states and input level estimation `delayest` Estimate time delay (dead time) from data `init` Set or randomize initial parameter values
 `getpvec` Obtain model parameters and associated uncertainty data `setpvec` Modify values of model parameters `getpar` Obtain attributes such as values and bounds of linear model parameters `setpar` Set attributes such as values and bounds of linear model parameters
 `procestOptions` Options set for `procest`

## Topics

### Process Model Basics

What Is a Process Model?

A process model is a simple continuous-time transfer function that describes linear system dynamics in terms of static gain, time constants, and input-output delay.

Data Supported by Process Models

Use regularly sampled time-domain and frequency-domain data, and continuous-time frequency-domain data.

### Estimate Process Models

Estimate Process Models Using the App

Specify model parameters and estimation options to use for estimating a process model.

Identify Low-Order Transfer Functions (Process Models) Using System Identification App

Identify continuous-time transfer functions from single-input/single-output (SISO) data using the app.

Estimate Process Models at the Command Line

Estimate first-order process models with fully free parameters and with a combination of fixed and free parameters.

Estimating Multiple-Input, Multi-Output Process Models

Specify whether to estimate the same transfer function for all input-output pairs, or a different transfer function for each pair.

### Set Process Model Options

Process Model Structure Specification

Configure the model structure by specifying the number of real or complex poles, and whether to include a zero, delay, and integrator.

Disturbance Model Structure for Process Models

Specify a noise model.

Specifying Initial Conditions for Iterative Estimation Algorithms

Specify how the algorithm treats initial conditions for estimation of model parameters.

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