Custom Variable Mass 6DOF Wind (Wind Angles)
Implement wind angle representation of six-degrees-of-freedom equations of motion of custom variable mass
- Library:
Aerospace Blockset / Equations of Motion / 6DOF
Description
The Custom Variable Mass 6DOF Wind (Wind Angles) block implements a wind angle representation of six-degrees-of-freedom equations of motion of custom variable mass. For a description of the coordinate system employed and the translational dynamics, see the block description for the Custom Variable Mass 6DOF Wind (Quaternion) block.
For more information of the relationship between the wind angles, see Algorithms
Limitations
The block assumes that the applied forces act at the center of gravity of the body.
Ports
Input
Fxyz — Applied forces
three-element vector
Applied forces, specified as a three-element vector.
Data Types: double
Mxyz — Applied moments
three-element vector
Applied moments, specified as a three-element vector.
Data Types: double
dm/dt — Rates of change of mass
three-element vector
One or more rates of change of mass (positive if accreted, negative if ablated), specified as a three-element vector.
Data Types: double
m — Mass
scalar
Mass, specified as a scalar.
Dependencies
To enable this port, set Mass type to Custom
Variable.
Data Types: double
dI/dt — Rate of change of inertia tensor matrix
3-by-3 matrix
Rate of change of inertia tensor matrix, specified as a 3-by-3 matrix.
Dependencies
To enable this port, set Mass type to Custom
Variable.
Data Types: double
I — Inertia tensor matrix
3-by-3 matrix
Inertia tensor matrix, specified as a 3-by-3 matrix.
Dependencies
To enable this port, set Mass type to Custom
Variable.
Data Types: double
Vre — Relative velocities
three-element vector
One or more relative velocities at which the mass is accreted to or ablated from the body in body-fixed axes, specified as a three-element vector.
Dependencies
To enable this port, select Include mass flow relative velocity.
Data Types: double
Output
Ve — Velocity in flat Earth reference frame
three-element vector
Velocity in the flat Earth reference frame, returned as a three-element vector.
Data Types: double
Xe — Position in flat Earth reference frame
three-element vector
Position in the flat Earth reference frame, returned as a three-element vector.
Data Types: double
μ γ x (rad) — Wind rotation angles
three-element vector
Wind rotation angles [bank, flight path, heading], returned as a three-element vector, in radians.
Data Types: double
DCMwe — Coordinate transformation
3-by-3 matrix
Coordinate transformation from flat Earth axes to wind-fixed axes, returned as a 3-by-3 matrix.
Data Types: double
Vw — Velocity in wind-fixed frame
three-element vector
Velocity in wind-fixed frame, returned as a three-element vector.
Data Types: double
α β (rad) — Angle of attack and sideslip angle
two-element vector
Angle of attack and sideslip angle, returned as a two-element vector, in radians.
Data Types: double
dα/dt dβ/dt — Rate of change of angle of attack and rate of change of sideslip angle
two-element vector
Rate of change of angle of attack and rate of change of sideslip angle, returned as a two-element vector, in radians per second.
Data Types: double
ωb (rad/s) — Angular rates in body-fixed axes
three-element vector
Angular rates in body-fixed axes, returned as a three-element vector, in radians per second.
Data Types: double
dωb/dt — Angular accelerations
three-element vector
Angular accelerations in body-fixed axes, returned as a three-element vector, in radians per second squared.
Data Types: double
Abb — Accelerations in body-fixed axes
three-element vector
Accelerations of the body with respect to the body-fixed axes with the body-fixed coordinate frame, returned as a three-element vector.
Data Types: double
Abe — Accelerations with respect to inertial frame
three-element vector
Accelerations in body-fixed axes with respect to inertial frame (flat Earth), returned as a three-element vector. You typically connect this signal to the accelerometer.
Dependencies
To enable this point, select Include inertial acceleration.
Data Types: double
Parameters
Main
Units — Input and output units
Metric (MKS) (default) | English (Velocity in ft/s) | English (Velocity in kts)
Input and output units, specified as Metric (MKS), English (Velocity in ft/s), or English (Velocity in kts).
| Units | Forces | Moment | Acceleration | Velocity | Position | Mass | Inertia |
|---|---|---|---|---|---|---|---|
Metric (MKS) | Newton | Newton-meter | Meters per second squared | Meters per second | Meters | Kilogram | Kilogram meter squared |
English (Velocity in ft/s) | Pound | Foot-pound | Feet per second squared | Feet per second | Feet | Slug | Slug foot squared |
English (Velocity in kts) | Pound | Foot-pound | Feet per second squared | Knots | Feet | Slug | Slug foot squared |
Programmatic Use
Block Parameter:
units |
| Type: character vector |
Values: Metric (MKS) | English (Velocity in ft/s) | English (Velocity in kts) |
Default: Metric (MKS) |
Mass type — Mass type
Custom Variable (default) | Simple Variable | Fixed
Mass type, specified according to the following table.
| Mass Type | Description | Default for |
|---|---|---|
Fixed | Mass is constant throughout the simulation. | |
Simple Variable | Mass and inertia vary linearly as a function of mass rate. | |
Custom Variable | Mass and inertia variations are customizable. |
The Custom Variable selection conforms to the previously described
equations of motion.
Programmatic Use
Block Parameter:
mtype |
| Type: character vector |
Values:
Fixed | Simple Variable | Custom
Variable |
Default:
'Custom Variable' |
Representation — Equations of motion representation
Wind Angles (default) | Quaternion
Equations of motion representation, specified according to the following table.
| Representation | Description |
|---|---|
| Use Wind angles within equations of motion. |
| Use quaternions within equations of motion. |
The Quaternion selection conforms to the equations of motion in Algorithms.
Programmatic Use
Block Parameter:
rep |
| Type: character vector |
Values:
Wind Angles |
Quaternion |
Default:
'Wind Angles' |
Initial position in inertial axes [Xe,Ye,Ze] — Position in inertial axes
[0 0 0] (default) | three-element vector
Initial location of the body in the flat Earth reference frame, specified as a three-element vector.
Programmatic Use
Block Parameter: xme_0 |
| Type: character vector |
Values:
'[0 0 0]' | three-element vector |
Default:
'[0 0 0]' |
Initial airspeed, angle of attack, and sideslip angle [V,alpha,beta] — Initial airspeed, angle of attack, and sideslip angle
[0 0 0] (default) | three-element vector
Initial airspeed, angle of attack, and sideslip angle, specified as a three-element vector.
Programmatic Use
Block Parameter: Vm_0 |
| Type: character vector |
Values:
'[0 0 0]' | three-element vector |
Default:
'[0 0 0]' |
Initial wind orientation [bank angle,flight path angle,heading angle] — Initial wind orientation
[0 0 0] (default) | three-element vector
Initial wind angles [bank, flight path, and heading], specified as a three-element vector in radians.
Programmatic Use
Block Parameter: wind_0 |
| Type: character vector |
Values:
'[0 0 0]' | three-element vector |
Default:
'[0 0 0]' |
Initial body rotation rates [p,q,r] — Initial body rotation
[0 0 0] (default) | three-element vector
Initial body-fixed angular rates with respect to the NED frame, specified as a three-element vector, in radians per second.
Programmatic Use
Block Parameter: pm_0 |
| Type: character vector |
Values:
'[0 0 0]' | three-element
vector |
Default:
'[0 0 0]' |
Include mass flow relative velocity — Mass flow relative velocity port
off (default) | on
Select this check box to add a mass flow relative velocity port. This is the relative velocity at which the mass is accreted or ablated.
Programmatic Use
Block Parameter: vre_flag |
| Type: character vector |
Values: off | on |
Default: off |
Include inertial acceleration — Include inertial acceleration port
off (default) | on
Select this check box to add an inertial acceleration port.
Dependencies
To enable the Abe port, select this parameter.
Programmatic Use
Block Parameter: abi_flag |
| Type: character vector |
Values:
'off' | 'on' |
Default: off |
State Attributes
Assign a unique name to each state. Use state names instead of block paths throughout the linearization process.
To assign a name to a single state, enter a unique name between quotes, for example,
'velocity'.To assign names to multiple states, enter a comma-separated list surrounded by braces, for example,
{'a', 'b', 'c'}. Each name must be unique.If a parameter is empty (
' '), no name is assigned.The state names apply only to the selected block with the name parameter.
The number of states must divide evenly among the number of state names.
You can specify fewer names than states, but you cannot specify more names than states.
For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.
To assign state names with a variable in the MATLAB® workspace, enter the variable without quotes. A variable can be a character vector, cell array, or structure.
Position: e.g., {'Xe', 'Ye', 'Ze'} — Position state name
'' (default) | comma-separated list surrounded by braces
Position state names, specified as a comma-separated list surrounded by braces.
Programmatic Use
Block Parameter: xme_statename |
| Type: character vector |
Values:
'' | comma-separated list surrounded by braces |
Default: '' |
Velocity: e.g., 'V' — Velocity state name
'' (default) | character vector
Velocity state names, specified as a character vector.
Programmatic Use
Block Parameter: Vm_statename |
| Type: character vector |
Values:
'' | character vector |
Default: '' |
Incidence angle e.g., 'alpha' — Incidence angle state name
'' (default) | character vector
Incidence angle state name, specified as a character vector.
Programmatic Use
Block Parameter:
alpha_statename |
| Type: character vector |
Values:
'' |
Default:
'' |
Sideslip angle e.g., 'beta' — Sideslip angle state name
'' (default) | character vector
Sideslip angle state name, specified as a character vector.
Programmatic Use
Block Parameter:
beta_statename |
| Type: character vector |
Values:
'' |
Default:
'' |
Wind orientation e.g., {'mu', 'gamma', 'chi'} — Wind orientation state names
'' (default) | comma-separated list surrounded by braces
Wind orientation state names, specified as a comma-separated list surrounded by braces.
Programmatic Use
Block Parameter:
wind_statename |
| Type: character vector |
Values:
'' |
Default:
'' |
Body rotation rates: e.g., {'p', 'q', 'r'} — Body rotation state names
'' (default) | comma-separated list surrounded by braces
Body rotation rate state names, specified comma-separated list surrounded by braces.
Programmatic Use
Block Parameter:
pm_statename |
| Type: character vector |
Values:
'' | comma-separated list surrounded by braces |
Default:
'' |
Algorithms
The relationship between the wind angles, [μ γ χ]T, can be determined by resolving the wind rates into the wind-fixed coordinate frame.
Inverting J then gives the required relationship to determine the wind rate vector.
The body-fixed angular rates are related to the wind-fixed angular rate by the following equation.
Using this relationship in the wind rate vector equations, gives the relationship between the wind rate vector and the body-fixed angular rates.
References
[1] Stevens, Brian, and Frank Lewis. Aircraft Control and Simulation, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2003.
[2] Zipfel, Peter H. Modeling and Simulation of Aerospace Vehicle Dynamics. 2nd ed: Reston, VA: AIAA Education Series, 2007.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
See Also
6DOF (Euler Angles) | 6DOF (Quaternion) | 6DOF ECEF (Quaternion) | 6DOF Wind (Quaternion) | 6DOF Wind (Wind Angles) | Custom Variable Mass 6DOF (Euler Angles) | Custom Variable Mass 6DOF (Quaternion) | Custom Variable Mass 6DOF ECEF (Quaternion) | Custom Variable Mass 6DOF Wind (Quaternion) | Simple Variable Mass 6DOF (Euler Angles) | Simple Variable Mass 6DOF (Quaternion) | Simple Variable Mass 6DOF ECEF (Quaternion) | Simple Variable Mass 6DOF Wind (Wind Angles)