Crossover Pilot Model

Represent crossover pilot model

Libraries:
Aerospace Blockset / Pilot Models

Description

The Crossover Pilot Model block represents the pilot model described in Mathematical Models of Human Pilot Behavior [1]). This pilot model is a single input, single output (SISO) model that represents some aspects of human behavior when controlling aircraft.

The Crossover Pilot Model takes into account the combined dynamics of the human pilot and the aircraft, using the form described in Algorithms around the crossover frequency.

This block has nonlinear behavior. If you want to linearize the block (for example, with linearize (Simulink Control Design) or one of the linmod functions), you might need to change the Pade approximation order. The Crossover Pilot Model block implementation incorporates the 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')

Note

The linmod function provides only basic linearization capabilities. For full linearization functionality, use Simulink^® Control Design™ software. For more information, see Choose Linearization Tools (Simulink Control Design).

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.

Ports

Input

expand all

x com — Signal command
scalar

Signal command that the pilot model controls, specified as a scalar.

Data Types: double

x — Signal
scalar

Signal that the pilot model controls, specified as a scalar.

Data Types: double

Output

expand all

u — Aircraft command
scalar

Aircraft command, returned as a scalar.

Data Types: double

Parameters

expand all

Type of control — Dynamics control
`Proportional` (default) | `Rate or velocity` | `Spiral divergence` | `Second order - Short period` | `Acceleration()` | `Roll attitude()` | `Unstable short period()` | `Second order - Phugoid()`

Dynamics control that you want the pilot to have over the aircraft. This table lists the options and associated dynamics.

Option (Controlled Element Transfer Function)	Transfer Function of Controlled Element ( Y _c )	Transfer Function of Pilot ( Y _p )	Y _c Y _p	Notes
`Proportion al`	$K_{c}$	$\frac{K_{p} e^{- τ s}}{s}$	$\frac{K_{c} K_{p} e^{- τ s}}{s}$
`Rate or velocity`	$\frac{K_{c}}{s}$	$K_{p} e^{- τ s}$	$\frac{K_{c} K_{p} e^{- τ s}}{s}$
`Spiral divergence`	$\frac{K_{c}}{T_{I} s - 1}$	$K_{p} e^{- τ s}$	$\frac{K_{c} K_{p} e^{- τ s}}{(T_{I} s - 1)}$
`Second order - Short period`	$\frac{K_{c} ω_{n}^{2}}{s^{2} + 2 ζ ω_{n} s + ω_{n}^{2}}$	$\frac{K_{p} e^{- τ s}}{T_{I} s + 1}$	$\begin{array}{l} \frac{K_{c} ω_{n}^{2}}{s^{2} + 2 ζ ω_{n} s + ω_{n}^{2}} \times \\ \frac{K_{p} e^{- τ s}}{T_{I} s + 1} \end{array}$	Short period, with $ω_{n} > 1 / τ$
`Acceleration (*)`	$\frac{K_{c}}{s^{2}}$	$K_{p} s e^{- τ s}$	$\frac{K_{c} K_{p} e^{- τ s}}{s}$
`Roll attitude (*)`	$\frac{K_{c}}{s (T_{I} s + 1)}$	$K_{p} (T_{L} s + 1) e^{- τ s}$	$\frac{K_{c} K_{p} e^{- τ s}}{s}$	With T _L ≈ T _I
`Unstable short period(*)`	$\frac{K_{c}}{(T_{I 1} s + 1) (T_{I 2} s - 1)}$	$K_{p} (T_{L} s + 1) e^{- τ s}$	$\frac{K_{c} K_{p} e^{- τ s}}{(T_{I 2} s - 1)}$	With T _L ≈ T _I1
`Second order - Phugoid(*)`	$\frac{K_{c} ω_{n}^{2}}{s^{2} + 2 ζ ω_{n} s + ω_{n}^{2}}$	$K_{p} (T_{L} s + 1) e^{- τ s}$	$\frac{K_{c} K_{p} ω_{n}^{2} e^{- τ s}}{s}$	Phugoid, with $\begin{array}{l} ω_{n} ≪ 1 / τ, \\ 1 / T_{L} \approx ζ ω_{n} \end{array}$

Option (Controlled Element Transfer Function)

Transfer Function of Controlled Element ( Y _c )

Transfer Function of Pilot ( Y _p )

Y _c Y _p

Notes

Proportion
											al

$K_{c}$

$\frac{K_{p} e^{- τ s}}{s}$

$\frac{K_{c} K_{p} e^{- τ s}}{s}$

Rate or velocity

$\frac{K_{c}}{s}$

$K_{p} e^{- τ s}$

$\frac{K_{c} K_{p} e^{- τ s}}{s}$

Spiral divergence

$\frac{K_{c}}{T_{I} s - 1}$

$K_{p} e^{- τ s}$

$\frac{K_{c} K_{p} e^{- τ s}}{(T_{I} s - 1)}$

Second order - Short period

$\frac{K_{c} ω_{n}^{2}}{s^{2} + 2 ζ ω_{n} s + ω_{n}^{2}}$

$\frac{K_{p} e^{- τ s}}{T_{I} s + 1}$

$\begin{array}{l} \frac{K_{c} ω_{n}^{2}}{s^{2} + 2 ζ ω_{n} s + ω_{n}^{2}} \times \\ \frac{K_{p} e^{- τ s}}{T_{I} s + 1} \end{array}$

Short
period,
with

ω_{n} > 1 / τ

Acceleration (*)

$\frac{K_{c}}{s^{2}}$

$K_{p} s e^{- τ s}$

$\frac{K_{c} K_{p} e^{- τ s}}{s}$

Roll attitude (*)

$\frac{K_{c}}{s (T_{I} s + 1)}$

$K_{p} (T_{L} s + 1) e^{- τ s}$

$\frac{K_{c} K_{p} e^{- τ s}}{s}$

With
T _L ≈ T _I

Unstable short period(*)

$\frac{K_{c}}{(T_{I 1} s + 1) (T_{I 2} s - 1)}$

$K_{p} (T_{L} s + 1) e^{- τ s}$

$\frac{K_{c} K_{p} e^{- τ s}}{(T_{I 2} s - 1)}$

With
T _L ≈ T _I1

Second order - Phugoid(*)

$\frac{K_{c} ω_{n}^{2}}{s^{2} + 2 ζ ω_{n} s + ω_{n}^{2}}$

$K_{p} (T_{L} s + 1) e^{- τ s}$

$\frac{K_{c} K_{p} ω_{n}^{2} e^{- τ s}}{s}$

Phugoid,
with

\begin{array}{l} ω_{n} ≪ 1 / τ, \\ 1 / T_{L} \approx ζ ω_{n} \end{array}

* 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.

This table defines the variables used in the list of control options.

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.

Dependencies

The Crossover Pilot Model parameters are enabled and disabled according to the Type of control options. The Calculated value, Controlled element gain, Pilot gain, Crossover frequency (rad/s), and Pilot time delay(s) parameters are always enabled.

Programmatic Use

Block Parameter: sw_popup

Type: character vector

Values: 'Proportion' |

'Rate or
									velocity'

|'Spiral divergence' | 'Second order - Short period' | 'Acceleration(*)' |

'Roll
									attitude(*)'

'Unstable short
									period(*)'

'Second order -
									Phugoid(*)'

Default: 'Proportion'

Calculated value — Crossover frequency or pilot gain
`Crossover frequency` (default) | `Pilot gain`

Crossover frequency or pilot gain value you want the block to calculate:

Crossover frequency — The block calculates the crossover frequency value. The parameter value is disabled.
Pilot gain — The block calculates the pilot gain value. The parameter value is disabled.

Programmatic Use

Block Parameter: freq_gain_popup

Type: character vector

Values:

'Crossover
									frequency'

| 'Pilot gain'

Default:

'Crossover
									frequency'

Controlled element gain — Controlled element gain
`1` (default) | scalar

Controlled element gain, specified as a double scalar.

Programmatic Use

Block Parameter: Kc

Type: character vector

Values: double scalar

Default: '1'

Pilot gain — Pilot gain
`3` (default) | scalar

Pilot gain, specified as a double scalar.

Dependencies

To enable this parameter, set Calculated value to Pilot gain.

Programmatic Use

Block Parameter: Kp

Type: character vector

Values: double scalar

Default: '3'

Crossover frequency (rad/s) — Crossover frequency
`3` (default) | scalar in the range of 1 and 10

Crossover frequency value, specified as double scalar, in rad/s. The value must be in the range between 1 and 10.

Dependencies

To enable this parameter, set Calculated value to Crossover frequency.

Programmatic Use

Block Parameter: omega_c

Type: character vector

Values: double scalar

Default: '3'

Pilot time delay(s) — Pilot time delay
`0.1` (default) | scalar

Total pilot time delay, specified as a double scalar, in seconds. This value typically ranges from 0.1 s to 0.2 s.

Programmatic Use

Block Parameter: time_delay

Type: character vector

Values: double scalar

Default: '0.1'

Pilot lead constant — Pilot lead constant
`1` (default) | scalar

Pilot lead constant, specified as a double scalar.

Dependencies

To enable this parameter, set Type of control to one of the following options:

Roll attitude (*)
Unstable short period (*)
Second order - Phygoid(*)

Programmatic Use

Block Parameter: T

Type: character vector

Values: double scalar

Default: '1'

Pilot lag constant — Pilot lag constant
`5` (default) | scalar

Pilot lag constant, specified as a double scalar.

Dependencies

To enable this parameter, set Type of control to Second order - Short period.

Programmatic Use

Block Parameter: Ti

Type: character vector

Values: double scalar

Default: '5'

Algorithms

The Crossover Model takes into account the combined dynamics of the human pilot and the aircraft, using the following form around the crossover frequency:

$Y_{p} Y_{c} = \frac{ω_{c} e^{- τ s}}{s},$

Where:

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.

Note

This block is valid only around the crossover frequency. It is not valid for discrete inputs such as a step.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2012b

Crossover Pilot Model

Description

Ports

Input

x com — Signal command
scalar

x — Signal
scalar

Output

u — Aircraft command
scalar

Parameters

Type of control — Dynamics control
`Proportional` (default) | `Rate or velocity` | `Spiral divergence` | `Second order - Short period` | `Acceleration()` | `Roll attitude()` | `Unstable short period()` | `Second order - Phugoid()`

Dependencies

Programmatic Use

Calculated value — Crossover frequency or pilot gain
`Crossover frequency` (default) | `Pilot gain`

Programmatic Use

Controlled element gain — Controlled element gain
`1` (default) | scalar

Programmatic Use

Pilot gain — Pilot gain
`3` (default) | scalar

Dependencies

Programmatic Use

Crossover frequency (rad/s) — Crossover frequency
`3` (default) | scalar in the range of 1 and 10

Dependencies

Programmatic Use

Pilot time delay(s) — Pilot time delay
`0.1` (default) | scalar

Programmatic Use

Pilot lead constant — Pilot lead constant
`1` (default) | scalar

Dependencies

Programmatic Use

Pilot lag constant — Pilot lag constant
`5` (default) | scalar

Dependencies

Programmatic Use

Algorithms

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

Functions

Crossover Pilot Model

Description

Ports

Input

x com — Signal command scalar

x — Signal scalar

Output

u — Aircraft command scalar

Parameters

Type of control — Dynamics control Proportional (default) | Rate or velocity | Spiral divergence | Second order - Short period | Acceleration(*) | Roll attitude(*) | Unstable short period(*) | Second order - Phugoid(*)

Dependencies

Programmatic Use

Calculated value — Crossover frequency or pilot gain Crossover frequency (default) | Pilot gain

Programmatic Use

Controlled element gain — Controlled element gain 1 (default) | scalar

Programmatic Use

Pilot gain — Pilot gain 3 (default) | scalar

Dependencies

Programmatic Use

Crossover frequency (rad/s) — Crossover frequency 3 (default) | scalar in the range of 1 and 10

Dependencies

Programmatic Use

Pilot time delay(s) — Pilot time delay 0.1 (default) | scalar

Programmatic Use

Pilot lead constant — Pilot lead constant 1 (default) | scalar

Dependencies

Programmatic Use

Pilot lag constant — Pilot lag constant 5 (default) | scalar

Dependencies

Programmatic Use

Algorithms

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

Functions

x com — Signal command
scalar

x — Signal
scalar

u — Aircraft command
scalar

Type of control — Dynamics control
`Proportional` (default) | `Rate or velocity` | `Spiral divergence` | `Second order - Short period` | `Acceleration()` | `Roll attitude()` | `Unstable short period()` | `Second order - Phugoid()`

Calculated value — Crossover frequency or pilot gain
`Crossover frequency` (default) | `Pilot gain`

Controlled element gain — Controlled element gain
`1` (default) | scalar

Pilot gain — Pilot gain
`3` (default) | scalar

Crossover frequency (rad/s) — Crossover frequency
`3` (default) | scalar in the range of 1 and 10

Pilot time delay(s) — Pilot time delay
`0.1` (default) | scalar

Pilot lead constant — Pilot lead constant
`1` (default) | scalar

Pilot lag constant — Pilot lag constant
`5` (default) | scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.