Limit-cycle stability study of a feedback control system by a new describing-function technique

A NEW describing-function technique is used in this paper to show the effects of several gain-controlling nonlinearities on the limit-cycle stability of an aircraft roll-stabilization system. The new method leads to a stability diagram which is divided not into the usual two regions of “stable” and “unstable” operation but rather into numerous regions each of which is associated with a particular type of limit-cycle oscillation or singular point. Such a diagram gives considerable insight into the mechanism of oscillations often observed in physical equipment. Very satisfactory agreement with analog computer studies is demonstrated for the new technique.