Simple Variable Mass 6DOF Wind (Wind Angles)

Description

For a description of the coordinate system employed and the translational dynamics, see the block description for the Simple Variable Mass 6DOF (Quaternion) block.

The relationship between the wind angles, [ $μ γ χ$ ]^T, can be determined by resolving the wind rates into the wind-fixed coordinate frame.

$[\begin{array}{l} p_{w} \\ q_{w} \\ r_{w} \end{array}] = [\begin{array}{l} \dot{μ} \\ 0 \\ 0 \end{array}] + [\begin{array}{l} 1 & 0 & 0 \\ 0 & \cos μ & \sin μ \\ 0 & - \sin μ & \cos μ \end{array}] [\begin{array}{l} 0 \\ \dot{γ} \\ 0 \end{array}] + [\begin{array}{l} 1 & 0 & 0 \\ 0 & \cos μ & \sin μ \\ 0 & - \sin μ & \cos μ \end{array}] [\begin{array}{l} \cos γ & 0 & - \sin γ \\ 0 & 1 & 0 \\ \sin γ & 0 & \cos γ \end{array}] [\begin{array}{l} 0 \\ 0 \\ \dot{χ} \end{array}] \equiv J^{- 1} [\begin{array}{l} \dot{μ} \\ \dot{γ} \\ \dot{χ} \end{array}]$

Inverting J then gives the required relationship to determine the wind rate vector.

$[\begin{array}{l} \dot{μ} \\ \dot{γ} \\ \dot{χ} \end{array}] = J [\begin{array}{l} p_{w} \\ q_{w} \\ r_{w} \end{array}] = [\begin{array}{l} 1 & (\sin μ \tan γ) & (\cos μ \tan γ) \\ 0 & \cos μ & - \sin μ \\ 0 & \frac{\sin μ}{\cos γ} & \frac{\cos μ}{\cos γ} \end{array}] [\begin{array}{l} p_{w} \\ q_{w} \\ r_{w} \end{array}]$

The body-fixed angular rates are related to the wind-fixed angular rate by the following equation.

$[\begin{array}{l} p_{w} \\ q_{w} \\ r_{w} \end{array}] = D M C_{w b} [\begin{matrix} p_{b} - \dot{β} \sin α \\ q_{b} - \dot{α} \\ r_{b} + \dot{β} \cos α \end{matrix}]$

Using this relationship in the wind rate vector equations, gives the relationship between the wind rate vector and the body-fixed angular rates.

$[\begin{array}{l} \dot{μ} \\ \dot{γ} \\ \dot{χ} \end{array}] = J [\begin{array}{l} p_{w} \\ q_{w} \\ r_{w} \end{array}] = [\begin{array}{l} 1 & (\sin μ \tan γ) & (\cos μ \tan γ) \\ 0 & \cos μ & - \sin μ \\ 0 & \frac{\sin μ}{\cos γ} & \frac{\cos μ}{\cos γ} \end{array}] D M C_{w b} [\begin{matrix} p_{b} - \dot{β} \sin α \\ q_{b} - \dot{α} \\ r_{b} + \dot{β} \cos α \end{matrix}]$

Parameters

Main

Units

Specifies the input and output units:

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

Mass Type

Select the type of mass to use:

`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 Simple Variable selection conforms to the previously described equations of motion.

Representation

Select the representation to use:

`Wind Angles`	Use wind angles within equations of motion.
`Quaternion`	Use quaternions within equations of motion.

The Wind Angles selection conforms to the previously described equations of motion.

Initial position in inertial axes

The three-element vector for the initial location of the body in the flat Earth reference frame.

Initial airspeed, sideslip angle, and angle of attack

The three-element vector containing the initial airspeed, initial sideslip angle and initial angle of attack.

Initial wind orientation

The three-element vector containing the initial wind angles [bank, flight path, and heading], in radians.

Initial body rotation rates

The three-element vector for the initial body-fixed angular rates, in radians per second.

Initial mass

The initial mass of the rigid body.

Empty mass

A scalar value for the empty mass of the body.

Full mass

A scalar value for the full mass of the body.

Empty inertia matrix

A 3-by-3 inertia tensor matrix for the empty inertia of the body, in body-fixed axes.

Full inertia matrix

A 3-by-3 inertia tensor matrix for the full inertia of the body, in body-fixed axes.

Include mass flow relative velocity

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.

Include inertial acceleration

Select this check box to enable an additional output port for the accelerations in body-fixed axes with respect to the inertial frame. You typically connect this signal to the accelerometer.

State Attributes

Assign unique name to each state. You can use state names instead of block paths during linearization.

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-delimited list surrounded by braces, for example, {'a', 'b', 'c'}. Each name must be unique.
If a parameter is empty (' '), no name assignment occurs.
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'}

Specify position state names.

Default value is ''.

Velocity: e.g., 'V'

Specify velocity state name.

Default value is ''.

Incidence angle: e.g., 'alpha'

Specify incidence angle state name.

Default value is ''.

Sideslip angle: e.g., 'beta'

Specify sideslip angle state name.

Default value is ''.

Wind orientation: e.g., {'mu', 'gamma', 'chi'}

Specify wind orientation state names. This parameter appears if the Representation parameter is set to Wind Angles.

Default value is ''.

Body rotation rates: e.g., {'p', 'q', 'r'}

Specify body rotation rates state names.

Default value is ''.

Mass: e.g., 'mass'

Specify mass state name.

Default value is ''.

Inputs and Outputs

Input	Dimension Type	Description
First	Vector	Contains the three applied forces in wind-fixed axes.
Second	Vector	Contains the three applied moments in body-fixed axes.
Third	Scalar or vector	Contains one or more rates of change of mass. This value is positive if the mass is added (accreted) to the body in wind axes. It is negative if the mass is ejected (ablated) from the body in wind axes.
Fourth (Optional)	Three-element vector	Contains one or more relative velocities at which the mass is accreted to or ablated from the body in wind axes.

Output	Dimension Type	Description
First	Three-element vector	Contains the velocity in the fixed Earth reference frame.
Second	Three-element vector	Contains the position in the flat Earth reference frame.
Third	Three-element vector	Contains the wind rotation angles [bank, flight path, heading], within ±pi, in radians.
Fourth	3-by-3 matrix	Applies to the coordinate transformation from flat Earth axes to wind-fixed axes.
Fifth	Three-element vector	Contains the velocity in the wind-fixed frame.
Sixth	Two-element vector	Contains the angle of attack and sideslip angle, in radians.
Seventh	Two-element vector	Contains the rate of change of angle of attack and rate of change of sideslip angle, in radians per second.
Eighth	Three-element vector	Contains the angular rates in body-fixed axes, in radians per second.
Ninth	Three-element vector	Contain the angular accelerations in body-fixed axes, in radians per second squared.
Tenth	Three-element vector	Contains the accelerations in body-fixed axes with respect to body frame.
Eleventh	Scalar element	Contains a flag for fuel tank status: 1 indicates that the tank is full. 0 indicates that the integral is neither full nor empty. -1 indicates that the tank is empty.
Twelfth (Output)	Three-element vector	Contains the accelerations in body-fixed axes with respect to inertial frame (flat Earth). You typically connect this signal to the accelerometer.

Assumptions and Limitations

The block assumes that the applied forces are acting at the center of gravity of the body.

References

Stevens, Brian, and Frank Lewis, Aircraft Control and Simulation, Second Edition, John Wiley & Sons, 2003.

Zipfel, Peter H., Modeling and Simulation of Aerospace Vehicle Dynamics. Second Edition, AIAA Education Series, 2007.

Documentation

Simple Variable Mass 6DOF Wind (Wind Angles)

Library

Description

Parameters

Main

State Attributes

Inputs and Outputs

Assumptions and Limitations

References

See Also

Extended Capabilities

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

Introduced in R2006a

Aerospace Blockset Documentation

Support

Documentation

Simple Variable Mass 6DOF Wind (Wind Angles)

Library

Description

Parameters

Main

State Attributes

Inputs and Outputs

Assumptions and Limitations

References

See Also

Extended Capabilities

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

Introduced in R2006a

Aerospace Blockset Documentation

Support

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