# 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, they support transport delay estimation, and the model coefficients have easy interpretations as poles and zeros.

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

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

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

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 `idproc` Continuous-time process model with identifiable parameters `procest` Estimate process model using time-domain or frequency-domain 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.