Precision Pilot Model

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:


In this equation:

KpPilot gain.
τPilot delay time.
TLTime lead constant for the equalizer term.
TITime lag constant.
TN1Time constant for the neuromuscular system.
ωNUndamped frequency for the neuromuscular system.
ζNDamping 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:



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 (Yc)Transfer Function of Pilot (Yp)


Lag-lead, TI >> TL
Rate or velocity




Lead-lag, TL >> TI
Second order


Lead-lag if ωm << 2/τ.

Lag-lead if ωm >> 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.

Inputs and Outputs

InputDimension TypeDescription


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


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


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.

Introduced in R2012b