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Investigations of Describing Function Technique

Report Number: AFFDL TR 65-137
Author: Graham, Dunstan
Author: Hofmann, Lee Gregor
Corporate Author: Systems Technology, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1966-02
Pages: 110
Contract: AF 33(615)-1474
Project: 8219
Task: 821904
AD Number: AD0631314

Three problems were chosen so as to explore some of the apparent limitations of describing function technique for the analysis of nonlinear systems, and to show how the technique might be extended so as to overcome the indicated deficiencies. The problems were (a) the effects of stick and valve friction in fully powered, manual aircraft control systems, (b) limit cycles in satellite attitude control with off-on jets, and (c) the effects of aerodynamic hysteresis in the stability derivatives of tilt-wing VTOL aircraft. The results indicate that new describing functions can be developed as closed-loop functions provided that specific restrictions are met, that non-sinusoidal, Fourier series describing functions or a generalized periodic input describing function can be successful, but that they are extraordinarily difficult to apply, and that the aerodynamic nonlinearities which were considered are of small practical importance.

Lockheed Martin Missiles & Fire Control
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