# Tustin Pilot Model

Represent Tustin pilot model

Pilot Models

## Description

The Tustin Pilot Model block represents the pilot model that A. Tustin describes in The Nature of the Operator’s Response in Manual Control, and its Implications for Controller Design. (For more information, see [1].) When modeling human pilot models, use this block for the least accuracy, compared to that provided by the Crossover Pilot Model and Precision Pilot Model blocks. This block requires less input than those blocks, and provides better performance. However, the results might be less accurate.

This pilot model is a single input, single output (SISO) model that represents human behavior, based on the transfer function:

`$\frac{u\left(s\right)}{e\left(s\right)}=\frac{{K}_{p}\left(1+Ts\right)}{s}{e}^{-\tau s}.$`

In this equation:

VariableDescription
KpPilot gain.
τTransport delay time caused by the pilot neuromuscular system.
u(s)Input to the aircraft model and output to the pilot model.
e(s)Error between the desired pilot value and the actual value.

This block has non-linear behavior. If you want to linearize the block (for example, with one of the Simulink® `linmod` functions), you might need to change the Pade approximation order. The Tustin Pilot Model block implementation incorporates the Simulink Transport Delay block with the Pade order (for linearization) parameter set to `2` by default. To change this value, use the `set_param` function, for example:

`set_param(gcb,'pade','3')`

## Parameters

Pilot gain

Specifies the pilot gain.

Pilot time delay (s)

Specifies the total pilot time delay, in seconds. This value typically ranges from 0.1 s to 0.2 s.

Specifies the pilot lead constant.

## Inputs and Outputs

InputDimension TypeDescription

First

1-by-1 Contains the command for the signal that the pilot model controls.

Second

1-by-1 Contains the signal that the pilot model controls.
OutputDimension TypeDescription

First

1-by-1 Contains the command for the aircraft.

## References

[1] Tustin, A., The Nature of the Operator’s Response in Manual Control, and its Implications for Controller Design. Convention on Automatic Regulators and Servo Mechanisms. May, 1947.