Crossover Pilot Model
A cross-sectional dynamic model of pilot behaviour.
Description
The Crossover Pilot Model block implements a cross-over dynamic model of pilot behaviour according to [1]. The model takes into account the effect of cross-over dynamics of pilot and aircraft behaviour near the cut-off frequency:
where
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- is the transfer function of the pilot;
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- is the transfer function of the aircraft;
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- shear frequency, rad/s;
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- pilot’s lag constant characterising his neuromuscular system, s.
When the dynamics of the aircraft changes. the dynamics of the pilot’s behaviour changes .
The table shows the variants of pilot behaviour dynamics:
| Type of pilot behaviour dynamics | Transfer function of the aircraft | Pilot transfer function | Product of transfer functions | Notes |
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`Second order - Short period |
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The condition of short-periodic motion: |
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Provided that |
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Provided that |
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Fugoidal motion condition: at |
The following notations are used in the table:
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- gain factor of the transfer function of the aircraft;
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- gain of the pilot’s transfer function;
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- pilot lag constant, s.
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- time constant of the denominator of the pilot transfer function, s;
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- time constant of the numerator of the pilot transfer function, s;
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- damping coefficient of the aircraft;
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- natural frequency of the aircraft, rad/s.
The symbol * marks variants of pilot behaviour dynamics, which require the block Derivative, which performs numerical differentiation. This means that the block can generate an output signal of high amplitude when a discrete signal, such as a step function, is applied to its input. This in turn can lead to the transition of the whole system to an unstable state.
| The block adequately describes the dynamics of the pilot’s behaviour only near the cut-off frequency. If a discrete signal, e.g. a step function, is input to the block, the block may not work correctly. |
This model better describes the pilot behaviour compared to the block Tustin Pilot Model.
Parameters
Type of control - type of dynamics of pilot behaviour
Proportional (by default) | Rate or velocity | Spiral divergence | Second order - Short period | Acceleration() | Roll attitude() | Unstable short period() | Second order - Phugoid()
Type of pilot behaviour dynamics.
Dependencies
The available block parameters depend on the selected value for the Type of control parameter. The parameters Calculated value, Controlled element gain, Pilot gain, Crossover frequency (rad/s), and Pilot time delay(s) are always available.
Calculated value - calculated parameters
Crossover frequency (by default) | Pilot gain.
Parameters that the block calculates: crossover frequency or pilot gain. If one of the parameters is selected, the other parameter is not available.
Controlled element gain - pilot gain factor
1.0(By default) | scalar.
The gain of the aircraft transfer function.
Pilot gain - pilot gain factor
3.0 (by default) | scalar
Pilot transfer function gain.
Dependencies
To use this parameter, set the Calculated value parameter to Pilot gain.
Crossover frequency (rad/s) - cut-off frequency
3.0(By default) | scalar.
Crossover frequency, rad/s. The value should lie in the range from 1.0 to 10.0.
Dependencies
To use this parameter, set the Calculated value parameter to Crossover frequency.
Pilot time delay(s) - Pilot time delay constant
0.1 (By default) | scalar.
Pilot time delay constant, s. Usually the value ranges from 0.1 s to 0.2 s.
Pilot lead constant - time constant of the numerator of the pilot transfer function
1.0(By default) | scalar
Time constant of the numerator of the pilot transfer function, s.
Dependencies
To use this parameter, set the Type of control parameters to one of the values: Roll attitude(), Unstable short period(), Second order - Phygoid(*).
Pilot lag constant - time constant of the denominator of the pilot transfer function
5.0(By default) | scalar.
Pilot transfer function denominator time constant, s.
Dependencies
To use this parameter, set the Type of control parameters to Second order - Short period.