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# Transfer Function Models

Transfer function models

Transfer function models describe the relationship between the inputs and outputs of a system using a ratio of polynomials. The model order is equal to the order of the denominator polynomial. The roots of the denominator polynomial are referred to as the model poles. The roots of the numerator polynomial are referred to as the model zeros.

The parameters of a transfer function model are its poles, zeros and transport delays.

In continuous-time, a transfer function model has the form:

`$Y\left(s\right)=\frac{num\left(s\right)}{den\left(s\right)}U\left(s\right)+E\left(s\right)$`

Here, Y(s), U(s) and E(s) represent the Laplace transforms of the output, input and noise, respectively. num(s) and den(s) represent the numerator and denominator polynomials that define the relationship between the input and the output.

For more information, see What are Transfer Function Models?

## Apps

 System Identification Identify models of dynamic systems from measured data

## Functions

expand all

 `idtf` Transfer function model with identifiable parameters `tfest` Estimate transfer function `pem` Prediction error minimization for refining linear and nonlinear models
 `delayest` Estimate time delay (dead time) from data `init` Set or randomize initial parameter values
 `tfdata` Access transfer function data `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
 `tfestOptions` Option set for `tfest`

## Topics

### Transfer Function Model Basics

What are Transfer Function Models?

Transfer function models describe the relationship between the inputs and outputs of a system using a ratio of polynomials.

Estimate Transfer Function Models in the System Identification App

This topic shows how to estimate transfer function models in the System Identification app.

Estimate Transfer Function Models at the Command Line

This topic shows how to estimate transfer function models at the command line.

Data Supported by Transfer Function Models

Characteristics of estimation data for transfer function identification.

### Estimate Transfer Function Models

Estimate Transfer Function Models by Specifying Number of Poles

This example shows how to identify a transfer function containing a specified number of poles for given data.

Estimate Transfer Function Models with Transport Delay to Fit Given Frequency-Response Data

This example shows how to identify a transfer function to fit a given frequency response data (FRD) containing additional phase roll off induced by input delay.

Estimate Transfer Function Models With Prior Knowledge of Model Structure and Constraints

This example shows how to estimate a transfer function model when the structure of the expected model is known and apply constraints to the numerator and denominator coefficients.

Estimate Transfer Functions with Delays

This example shows how to estimate transfer function models with I/O delays.

Estimate Transfer Function Models with Unknown Transport Delays

This example shows how to estimate a transfer function model with unknown transport delays and apply an upper bound on the unknown transport delays.

### Frequency Domain Troubleshooting

Troubleshoot Frequency-Domain Identification of Transfer Function Models

Improve frequency-domain model estimation by preprocessing data and applying frequency-dependent weighting filters.

### Model Initialization and Structure Parameters

Transfer Function Structure Specification

Specify the values and constraints for the numerator, denominator and transport delays.

Specifying Initial Conditions for Iterative Estimation of Transfer Functions

Specify how initial conditions are handled during model estimation in the app and at the command line.

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