On the Stability of a Hysteretic System under Sinusoidal Excitation
01 Dec 1965-International Journal of Control (Taylor & Francis Group)-Vol. 2, Iss: 6, pp 551-559
TL;DR: In this article, expressions for the dual input describing functions (DIDF) of a two-state relay with hysteresis were obtained by using an equivalent function generator for the nonlinearity.
Abstract: Expressions for the Dual Input Describing Functions (DIDF's) of a two-state relay with hysteresis have been obtained by using an equivalent function generator for the non-linearity. These DIDF's were then applied to analyse the effects of sinusoidal input signals on the stability of a feedback system which includes the hysteretic relay. These results, as substantiated by simulator data, indicate that, besides the stabilizing effects, the presence of sinusoidal signals at the input of the particular system studied may produce dual mode operation over a. range of input amplitudes.
01 Jan 1963
TL;DR: In this paper, a general dual input describing function (DIF) was derived for single-valued nonlinearities subjected to two arbitrary noncommensurate sine waves and applied to the problem of the stability of nonlinear systems subjected to sinusoidal forcing.
Abstract: A new general DIDF (dual input describing function) has been analytically derived for single-valued nonlinearities subjected to two arbitrary noncommensurate sine waves. The development corroborates a previous approximate development for two sine waves widely separated in frequency. The new DIDF is applied to the problem of the stability of nonlinear systems subjected to sinusoidal forcing. It is shown that the conventional DF (describing function) cannot be used for nonautonomous systems without additional safeguards. After it has been shown by the DIDF that no auto-oscillations exist for given input conditions it is proper to employ the conventional DF in any of the methods suggested in the literature to obtain the closed-loop frequency response under those conditions.
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