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Represent crossover pilot model
The Crossover 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 more accuracy than that provided by the Tustin Pilot Model block. This block is also less accurate than the Precision Pilot Model block.
The Crossover Model takes into account the combined dynamics of the human pilot and the aircraft, using the following form around the crossover frequency:
In this equation:
Variable  Description 

Y_{p}  Pilot transfer function. 
Y_{c}  Aircraft transfer function. 
ω_{c}  Crossover frequency. 
τ  Transport delay time caused by the pilot neuromuscular system. 
If the dynamics of the aircraft (Y_{c}) change, Y_{p} changes correspondingly. From the options provided in the Type of control parameter, specify the dynamics of the aircraft. The preceding table lists the possible types of control that you can select for the aircraft.
Note: This block is valid only around the crossover frequency. It is not valid for discrete inputs such as a step. 
This block has nonlinear 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 Crossover 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')
From the list, select one of the following options to specify the type of dynamics control that you want the pilot to have over for the aircraft.
Option (Controlled Element Transfer Function)  Transfer Function of Controlled Element (Y_{c})  Transfer Function of Pilot (Y_{p})  Y_{c}Y_{p}  Notes 

Proportional 


 
Rate or velocity 


 
Spiral divergence 


 
Second order  Short period 


 Short period, with 
Acceleration (*) 


 
Roll attitude (*) 


 With T_{L} ≈ T_{I} 
Unstable short period(*) 


 With T_{L}≈ T_{I1} 
Second order  Phugoid(*) 


 Phugoid, with 
* Indicates that the pilot model includes a Derivative block, which produces a numerical derivative. For this reason, do not send discontinuous (such as a step) or noisy input to the Crossover Pilot Model block. Such inputs can cause large outputs that might render the system unstable.
Variable  Description 

K_{c}  Aircraft gain. 
K_{p}  Pilot gain. 
τ  Pilot time delay. 
T_{I}  Lag constant. 
T_{L}  Lead constant. 
ζ  Damping ratio for the aircraft. 
ω_{n}  Natural frequency of the aircraft. 
From the list, select one of the following options to specify which value the block is to calculate:
Crossover frequency — The block calculates the crossover frequency value. Selecting this option disables the Crossover frequency (rad/s) parameter.
Pilot gain — The block calculates the pilot gain value. Selecting this option disables the Pilot gain parameter.
Specifies the gain of the aircraft controlled dynamics.
Specifies the pilot gain.
Specifies a crossover frequency value, rad/s. This value ranges from 1 to 10 rad/s.
Specifies the total pilot time delay, in seconds. This value typically ranges from 0.1 s to 0.2 s.
Input  Dimension Type  Description 

First  1by1  Contains the command for the signal that the pilot model controls. 
Second  1by1  Contains the signal that the pilot model controls. 
Output  Dimension Type  Description 

First  1by1  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 180, Jan. 1974.