Simple Variable Mass 6DOF (Quaternion)

Implement quaternion representation of six-degrees-of-freedom equations of motion of simple variable mass with respect to body axes

  • Library:
  • Aerospace Blockset / Equations of Motion / 6DOF

Description

The Simple Variable Mass 6DOF (Quaternion) implements a quaternion representation of six-degrees-of-freedom equations of motion of simple variable mass with respect to body axes.

For a description of the coordinate system and the translational dynamics, see the description for the Simple Variable Mass 6DOF (Euler Angles) block. For more information on the integration of the rate of change of the quaternion vector, see Algorithms.

Limitations

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

Ports

Input

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Applied forces, specified as three-element vector.

Data Types: double

Applied moments, specified as three-element vector.

Data Types: double

One or more rates of change of mass (positive if accreted, negative if ablated), specified as a scalar.

Data Types: double

One or more relative velocities, specified as a three-element vector, at which the mass is accreted to or ablated from the body in body-fixed axes.

Data Types: double

Output

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Velocity in the flat Earth reference frame, returned as a three-element vector.

Data Types: double

Position in the flat Earth reference frame, returned as a three-element vector.

Data Types: double

Euler rotation angles [roll, pitch, yaw], returned as three-element vector, in radians.

Data Types: double

Coordinate transformation from flat Earth axes to body-fixed axes, returned as a 3-by-3 matrix.

Data Types: double

Velocity in body-fixed frame, returned as a three-element vector.

Data Types: double

Angular rates in body-fixed axes, returned as a three-element vector, in radians per second.

Data Types: double

Angular accelerations in body-fixed axes, returned as a three-element vector, in radians per second squared.

Data Types: double

Accelerations in body-fixed axes with respect to body frame, returned as a three-element vector.

Data Types: double

Fuel tank status, returned as

  • 1 — Tank is full.

  • 0 — Tank is neither full nor empty.

  • -1 — Tank is empty.

Data Types: double

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

This port appears only when the Include inertial acceleration check box is selected.

Data Types: double

Parameters

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Main

Input and output units, specified as Metric (MKS), English (Velocity in ft/s), or English (Velocity in kts).

UnitsForcesMomentAccelerationVelocityPositionMassInertia
Metric (MKS) NewtonNewton meterMeters per second squaredMeters per secondMetersKilogramKilogram meter squared
English (Velocity in ft/s) PoundFoot poundFeet per second squaredFeet per secondFeetSlugSlug foot squared
English (Velocity in kts) PoundFoot poundFeet per second squaredKnotsFeetSlugSlug 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, specified according to the following table.

Mass TypeDescriptionDefault 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 Simple 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: Simple Variable

Equations of motion representation, specified according to the following table.

RepresentationDescriptionDefault For

Euler Angles

Use Euler angles within equations of motion.

Quaternion

Use quaternions within equations of motion.

The Quaternion selection conforms to the previously described equations of motion.

Programmatic Use

Block Parameter: rep
Type: character vector
Values: Euler Angles | Quaternion
Default: Quaternion

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]

The three-element vector for the initial velocity in the body-fixed coordinate frame.

Programmatic Use

Block Parameter: Vm_0
Type: character vector
Values: [0 0 0] | three-element vector
Default: [0 0 0]

The three-element vector for the initial Euler orientation angles [roll, pitch, yaw], in radians.

Programmatic Use

Block Parameter: eul_0
Type: character vector
Values: [0 0 0] | three-element vector
Default: [0 0 0]

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

Programmatic Use

Block Parameter: pm_0
Type: character vector
Values: [0 0 0] | three-element vector
Default: [0 0 0]

The initial mass of the rigid body.

Programmatic Use

Block Parameter: mass_0
Type: character vector
Values: 1.0 | scalar
Default: 1.0

A scalar value for the inertia of the body.

Programmatic Use

Block Parameter: inertia
Type: character vector
Values: eye(3) | scalar
Default: eye(3)

A scalar value for the empty mass of the body.

Programmatic Use

Block Parameter: mass_e
Type: character vector
Values: 0.5 | scalar
Default: 0.5

A scalar value for the full mass of the body.

Programmatic Use

Block Parameter: mass_f
Type: character vector
Values: 2.0 | scalar
Default: 2.0

A 3-by-3 inertia tensor matrix for the empty inertia of the body.

Programmatic Use

Block Parameter: inertia_e
Type: character vector
Values: eye(3) | scalar
Default: eye(3)

A 3-by-3 inertia tensor matrix for the full inertia of the body.

Programmatic Use

Block Parameter: inertia_f
Type: character vector
Values: 2*eye(3) | scalar
Default: 2*eye(3)

The gain to maintain the norm of the quaternion vector equal to 1.0.

Programmatic Use

Block Parameter: k_quat
Type: character vector
Values: 1.0 | scalar
Default: 1.0

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

Select this check box to add an inertial acceleration port.

Programmatic Use

Block Parameter: abi_flag
Type: character vector
Values: off | on
Default: off

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.

Specify position state names.

Programmatic Use

Block Parameter: xme_statename
Type: character vector
Values: '' | comma-delimited list surrounded by braces
Default: ''

Specify velocity state names.

Programmatic Use

Block Parameter: Vm_statename
Type: character vector
Values: '' | comma-delimited list surrounded by braces
Default: ''

Specify quaternion vector state names. This parameter appears if the Representation parameter is set to Quaternion.

Programmatic Use

Block Parameter: quat_statename
Type: character vector
Values: '' | comma-delimited list surrounded by braces
Default: ''

Specify body rotation rate state names.

Programmatic Use

Block Parameter: pm_statename
Type: character vector
Values: '' | comma-delimited list surrounded by braces
Default: ''

Specify Euler rotation angle state names.

Programmatic Use

Block Parameter: eul_statename
Type: character vector
Values: '' | comma-delimited list surrounded by braces
Default: ''

Specify mass state name.

Programmatic Use

Block Parameter: mass_statename
Type: character vector
Values: '' | comma-delimited list surrounded by braces
Default: ''

Algorithms

The equation of the integration of the rate of change of the quaternion vector follows. The gain K drives the norm of the quaternion state vector to 1.0 should ε become nonzero. You must choose the value of this gain with care, because a large value improves the decay rate of the error in the norm, but also slows the simulation because fast dynamics are introduced. An error in the magnitude in one element of the quaternion vector is spread equally among all the elements, potentially increasing the error in the state vector.

[q˙0q˙1q˙2q˙3]=12[0pqrp0rqqr0prqp0][q0q1q2q3]+Kε[q0q1q2q3]ε=1(q02+q12+q32+q42)

References

[1] Stevens, Brian, and Frank Lewis, Aircraft Control and Simulation. Second Edition. Hoboken, NJ: John Wiley & Sons, 2003.

[2] Zipfel, Peter H., Modeling and Simulation of Aerospace Vehicle Dynamics. Second Edition. Reston, VA: AIAA Education Series, 2007.

Introduced in R2006a