Represent precision pilot model

Pilot Models

The Precision Pilot Model block represents the pilot model described
in *Mathematical Models of Human Pilot Behavior*.
(For more information, see [1]). This pilot model
is a single input, single output (SISO) model that represents some
aspects of human behavior when controlling aircraft. When modeling
human pilot models, use this block for the most accuracy, compared
to that provided by the Tustin Pilot Model and Crossover Pilot Model blocks.

This block is an extension of the Crossover Pilot Model block. When calculating the model, this block also takes into account the neuromuscular dynamics of the pilot. This block implements the following equation:

$${Y}_{p}={K}_{p}{e}^{-\tau s}\left(\frac{{T}_{L}s+1}{{T}_{I}s+1})\right)\left[\frac{1}{\left({T}_{N1}s+1\right)\left(\frac{{s}^{2}}{{\omega}_{N}{}^{2}}+\frac{2{\zeta}_{N}}{{\omega}_{N}}s+1\right)}\right].$$

In this equation:

Variable | Description |
---|---|

K_{p} | Pilot gain. |

τ | Pilot delay time. |

T_{L} | Time lead constant for the equalizer term. |

T_{I} | Time lag constant. |

T_{N1} | Time constant for the neuromuscular system. |

ω_{N} | Undamped frequency for the neuromuscular system. |

ζ_{N} | Damping ratio for the neuromuscular system. |

A sample value for the natural frequency and the damping ratio of a human is 20 rad/s and 0.7, respectively. The term containing the lead-lag term is the equalizer form. This form changes depending on the characteristics of the controlled system. A consistent behavior of the model can occur at different frequency ranges other than the crossover frequency.

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 Precision 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')

**Type of control**From the list, select one of the following options to specify the type of aircraft dynamics that you want to control. The equalizer form changes according to these values. For more information, see [2].

Option (Controlled Element Transfer Function) Transfer Function of Controlled Element ( *Y*)_{c}Transfer Function of Pilot ( *Y*)_{p}Proportional $${K}_{c}$$

Lag-lead, T _{I}>> T_{L}Rate or velocity $$\frac{{K}_{c}}{s}$$

1 Acceleration $$\frac{{K}_{c}}{{s}^{2}}$$

Lead-lag, T _{L}>> T_{I}Second order $$\frac{{K}_{c}{\omega}_{n}{}^{2}}{{s}^{2}+2\zeta {\omega}_{n}s+{\omega}_{n}^{2}}$$

Lead-lag if ω

_{m}<< 2/τ.Lag-lead if ω

_{m}>> 2/τ.**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.

**Equalizer lead constant**Specifies the equalizer lead constant.

**Equalizer lag constant**Specifies the equalizer lag constant.

**Lag constant for neuromuscular system**Specifies the neuromuscular system lag constant.

**Undamped natural frequency neuromuscular system (rad/s)**Specifies the undamped natural frequency neuromuscular system in rad/s.

**Damping neuromuscular system**Specifies the damping neuromuscular system.

**Controlled element undamped natural frequency (rad/s)**Specifies the controlled element undamped natural frequency in rad/s.

Input | Dimension Type | Description |
---|---|---|

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. |

Output | Dimension Type | Description |
---|---|---|

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

[1] McRuer, D. T., Krendel, E., *Mathematical
Models of Human Pilot Behavior*. Advisory Group on Aerospace
Research and Development AGARDograph 188, Jan. 1974.

[2] McRuer, D. T., Graham, D., Krendel, E.,
and Reisener, W., *Human Pilot Dynamics in Compensatory
Systems*. Air Force Flight Dynamics Lab. AFFDL-65-15. 1965.

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