Abstract
A theory of stability for nonlinear feedback systems interfered with by an external periodic signal is developed. It makes use of a conventional dual-input describing function which may be available in an analytic or graphical form. The interference may take a variety of forms: the external signal may be injected into the loop, modulate the loop gain or vary any other parameter of the system, or it may interfere in a combination of the above ways. The nonlinearity may be analytic or discontinuous but it must be independent of frequency.A simple servomechanism with backlash and an injected sinusoidal signal is studied, and oscillations at frequencies subharmonic to that of the signal are examined.The stability of a self-optimising control system with sinusoidal perturbation of one parameter is examined. Symmetrical and asymmetrical criterion curves are considered. Second- and third-subharmonic oscillations are found possible: in some circumstances they are stable and self-starting; in others they are unstable, in which case external excitation may cause their onset.The systems were simulated, and experimental results were found to agree well with the theory.
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