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Stability derivatives, and also control derivatives, are measures of how particular forces and moments on an aircraft change as other parameters related to stability change (parameters such as airspeed, altitude, angle of attack, etc.). For a defined "trim" flight condition, changes and oscillations occur in these parameters.
For any given configuration and flight condition, a complete set of stability and control derivatives can be determined without resort to outside information. A spectrum of methods is presented, ranging from very simple and easily applied techniques to quite accurate and thorough procedures.
The United States Air Force Stability and Control Digital DATCOM is a computer program that implements the methods contained in the USAF Stability and Control DATCOM to calculate the static stability, control and dynamic derivative characteristics of fixed-wing aircraft. Digital DATCOM requires an input file containing a geometric description ...
With a symmetrical rocket or missile, the directional stability in yaw is the same as the pitch stability; it resembles the short period pitch oscillation, with yaw plane equivalents to the pitch plane stability derivatives. For this reason, pitch and yaw directional stability are collectively known as the "weathercock" stability of the missile.
The longitudinal stability of an aircraft, also called pitch stability, [2] refers to the aircraft's stability in its plane of symmetry [2] about the lateral axis (the axis along the wingspan). [1] It is an important aspect of the handling qualities of the aircraft, and one of the main factors determining the ease with which the pilot is able ...
Tuning a control loop is the adjustment of its control parameters (proportional band/gain, integral gain/reset, derivative gain/rate) to the optimum values for the desired control response. Stability (no unbounded oscillation) is a basic requirement, but beyond that, different systems have different behavior, different applications have ...
A Lyapunov function for an autonomous dynamical system {: ˙ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative ˙ = is non positive (these conditions are required on some region containing the origin).
This control law will guarantee global exponential stability since upon substitution into the time derivative yields, as expected V ˙ = − κ V {\displaystyle {\dot {V}}=-\kappa V} which is a linear first order differential equation which has solution