Glossary

Dot over quantity: the derivative with respect to time of the contents of the parentheses .

Hat over quantity: the contents of the parentheses are approximate.

Angle-of-attack: the aerodynamic angle between the projection of the relative wind onto the airplane's plane of symmetry and a suitably defined body fixed -axis.

Sideslip angle: The aerodynamic angle between the velocity vector and the airplane's plane of symmetry.

, ,

Vector norms: is the square root of the sum of the squares of the entries in the vector. It appears everywhere. is the sum of the absolute values of the entries and is the greatest absolute value. and frequently appear in linear programming problems.

Either:

1. Every combination of control effector deflections that are admissible; in other words, that are within the limits of travel or deflection.
2. A normally diagonal matrix used to specify the dynamics in a dynamic-inversion control law.

The effects, usually body-axis moments, moment coefficients, or angular accelerations, of every combination of control effector deflections in , q.v. (sense 1). Sometimes called the AMS, for 'attainable moment set' or subset.

Bank angle: one of three angles that define a 3-2-1 (--) rotation from inertial to body-fixed reference frames.

Either:

1. (Primarily) A subset of the attainable moments () consisting of all the moments that are generated by a particular control allocation method.
2. A plane surface that arises in Banks' method of allocation for the three-moment problem.

Heading angle: one of three angles that define a 3-2-1 (--) rotation from inertial to body-fixed reference frames.

A subset of : all admissible controls that a particular control-allocation method can return as solutions to a control-allocation problem.

Pitch attitude: one of three angles that define a 3-2-1 (--) rotation from inertial to body-fixed reference frames.

One of the matrices of the linearized equations of motion: is the system matrix, is control effectiveness matrix, and is the output matrix.

The non-dimensional stability or control derivative of with respect to : it is the non-dimensional form of .

Complementary: a superscript to certain dynamic responses.

Controllable: a superscript to certain dynamic responses.

,

Desired: a subscript to a dynamic response, or any other quantity.

Body-fixed reference frames. The origin is at the airplane's center of mass. The axes and lie in the airplane's plane of symmetry. completes the right-hand system. Once defined, a body-fixed reference system's orientation with respect to the body does not change. Two frequently used body-fixed reference frames are the principal axes and the stability-axis system.

Local-horizontal reference frame. The axes , , and are oriented north, east, and down, respectively. The earth is flat.

Wind-axis system. The axis lies in the direction of flight, opposite the relative wind. is in the plane of symmetry, oriented downward.

Either:

1. Acceleration of gravity, or
2. The non-dimensional units of load factor , q.v.

With subscripts; moment of inertia.

Kinematic: a superscript to certain dynamic responses.

Lift, side force, and drag: wind-axis forces in the -, - and -directions, respectively.

Body-axis moments about the axis (rolling), axis (pitching), and axis (yawing), respectively.

Either:

1. Lift, or
2. Rolling moment, depending on context.

Lateral-directional, meaning all motions, accelerations, forces, and so on, that are not longitudinal, q.v. Sometimes lat-dir.

Longitudinal, meaning all motions, accelerations, forces, and so on, that take place in the airplane's plane of symmetry. Pitching moments, velocities, and accelerations are about the airplane's -axis but the motion is in the - plane.

The mass of the airplane.

Load factor, the ratio of lift to weight, . Measured in s.

Body-axis roll rate, pitch rate, and yaw rate, respectively.

A generalized inverse of a matrix : and , with appropriate dimensions.

Subscript, 'evaluated in reference conditions'.

Vector of control effector variables.

,

Vector of control effector limits, minimum or maximum.

,

Vector of control effector limits, lower or upper. This notation seems preferred by linear programmers over , , q.v.

Names of body-axes.

A weighting matrix, generally diagonal and positive.

Names of wind axes.

Where is a force or moment and is a state or control, a dimensional derivative, . It is the dimensional form of , q.v. The definition does not include division by mass or moment of inertia. If is a control effector the result is called a control derivative, otherwise it is called a stability derivative.

Body-axis forces in the -, - and -directions, respectively.

Names of axes. With no subscripts usually taken to be body-axes.

ACTIVE

Advanced Control Technology for Integrated Vehicles. A research F-15 with differential canards, axisymmetric thrust vectoring, and other novel features.

ADMIRE

Aero-Data Model In a Research Environment, simulation code. See Appendix B.

Admissible

Of a control effector or suite of control effectors, those deflections that are within the physical limits of employment.

AMS

Attainable moment subset or set, .

Angular accelerations

See Objectives.

ARI

Aileron-rudder interconnect. Normally used to reduce adverse yaw due to aileron deflection.

Attainable

Of moments or accelerations; that which can be generated by some admissible combination of control effectors. The term may be applied globally, meaning there is some theoretical combination, or locally, to a particular control allocation method, meaning those combinations of control effectors that the method will generate using its rules.

Basic feasible solution

Of linear programs, a basic solution to the equality constraints in a linear program that also solves the inequality constraints.

Basic solution

Of linear programs, a solution to the linear equality constraints of a linear program in 'standard form' with of the decision variables at their bound.

CAS

Control augmentation system.

Control effectiveness

A measure of the effect of utilizing a control effector, either moment, moment coefficient, or angular acceleration.

Control authority

The aggregate effect of the effectiveness of all the control effectors in whatever combination.

Control power

Angular acceleration per unit of control deflection.

CHR

Cooper-Harper rating; sometimes HQR.

Constraint

Of a control effector, a limiting position, usually imposed by the hardware. It may also refer to a limit on the rate of travel. In linear programming, a constraint may refer to the position limits, but also of an equality that must be satisfied. Thus is an inequality constraint, and is an equality constraint.

Control effector

The devices that directly effect control by changing forces or moments, such as ailerons or rudders. When we say 'the controls' with no qualification, we usually mean the control effectors. The sign convention for conventional flapping control effectors follows a right-hand rule, with the thumb along the axis about which the effector is designed to generate moments, and the curled fingers denoting the positive deflection of the trailing edge.

Control inceptor

Cockpit devices that control, through direct linkage or a flight-control system or computer, the control effectors. Positive control inceptor deflections correspond to positive deflections of the effectors they are connected to, barring such things as aileron-rudder interconnects (ARI, q.v.).

Cycling

Of a linear program, a condition in which a sequence of vertices is visited by a solver for which the objective function does not decrease, eventually returning to the starting point in the cycle. Cycling represents a failure to converge and must be addressed by choosing an exchange rule designed to prevent it.

Degenerate basic solution

Of linear programs, a basic solution to a linear program in which one of the decision variables in the basis is at its bound in addition to the non-basic variables.

Decision variables

The set of unknown parameters being optimized in a linear program.

FBW

Fly by wire. The pilot flies the computer, the computer flies the airplane.

FQ

Flying qualities.

Ganged

Said of mechanical devices that are linked so that they move in fixed relation to each other, such as ailerons.

HARV

High angle-of-attack research vehicle.

HQ

Handling qualities.

HQR

Handling qualities rating.

Interior point method...