# Varying Transfer Function

Transfer function with varying coefficients

Libraries:
Control System Toolbox / Linear Parameter Varying

## Description

This block implements a continuous-time transfer function with varying coefficients. The instantaneous transfer function is given by:

`$H\left(s\right)=\frac{{b}_{0}+{b}_{1}{s}^{-1}+\cdots +{b}_{N}{s}^{-N}}{1+{a}_{1}{s}^{-1}+\cdots +{a}_{N}{s}^{-N}}=\frac{{b}_{0}{s}^{N}+{b}_{1}{s}^{N-1}+\cdots +{b}_{N}}{{s}^{N}+{a}_{1}{s}^{N-1}+\cdots +{a}^{N}}.$`

N is number of poles, specified with the Transfer function order parameter. Feed the values of the coefficients b0, b1,…, bN and a1, a2,…, aN to the corresponding block input ports.

Note

The above expression for H(s) applies only to Varying Transfer Function blocks added to a model in R2023a or later. For information about Varying Transfer Function blocks created in R2022b or earlier, see Varying Transfer Function block formula changed.

Use this block and the other blocks in the Linear Parameter Varying library to implement common control elements with variable parameters or coefficients. For more information, see Model Gain-Scheduled Control Systems in Simulink.

## Ports

### Input

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Transfer function input signal.

Transfer function numerator coefficients. The number of coefficient ports is determined by the Transfer function order parameter.

For a zero-feedthrough transfer function, clear the Enable feedthrough checkbox. Clearing this checkbox disables the b0 input port. (since R2023a)

Transfer function denominator coefficients. The number of coefficient ports is determined by the Transfer function order parameter. The coefficient of the lowest-order term (a0) is fixed to 1.

Before R2023a: The denominator coefficients are `a0`, `a1`,…. The coefficient aN is fixed to 1. For more information, see Varying Transfer Function block formula changed.

### Output

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Transfer function output signal.

## Parameters

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Transfer function order N, specified as a positive integer. This parameter determines the number of coefficient input ports on the block.

Since R2023a

Enable the b0 input port for a transfer function with direct feedthrough. For a zero-feedthrough transfer function, clear this checkbox. Disabling the port for zero-feedthrough models is numerically more reliable than feeding a zero-constant into the port.

## Version History

Introduced in R2017b

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