Stability of a Hysteretic System with Random Signal Inputs
TL;DR: The stability of a feedback system with a hysteretie relay controller, when forced by a Gaussian signal, is analysed by applying the quasi-linearization approach.
Abstract: The stability of a feedback system with a hysteretie relay controller, when forced by a Gaussian signal, is analysed by applying the quasi-linearization approach.A method for computing the sinusoidal and random signal gains of a non-linear element, based on the evaluation of the input—output cross power of the clement, is first explained. Knowledge of these two gains for an ideal relay is then used to find the corresponding gains for a hysteretic relay. These gains are finally used for analysing the effects of both high-frequency and low-frequency random signals on the auto-oscillations of a second-order system with the hysteretic relay. Results of simulator studies are also presented.
Citations
More filters
01 Feb 1968
TL;DR: It is shown, by comparing experimentally measured equivalent gains with theoretical gain expressions, that the f(x,x?) model is a poor approximation to an actual double-valued relay.
Abstract: The paper considers some theoretical methods which have been proposed for linearising double-valued relay nonlinearities with Gaussian inputs. Most methods depend on the description of the relay as a function of the input and its derivative, which will be referred to as the f(x,x?) model. It is shown, by comparing experimentally measured equivalent gains with theoretical gain expressions, that the f(x,x?) model is a poor approximation to an actual double-valued relay. Some qualitative and approximate theoretical results are derived for double-valued relays without resorting to the f(x,x?) model. These predict the following two effects, which are clearly seen in the experimental measurements, and which are not given by existing methods: (a) the equivalent gains depend on the input signal spectrum and (b) the imaginary part of the equivalent gain is very small. It almost always makes a negligible contribution to the overall equivalent gain.
1 citations
References
More filters
TL;DR: This IEEE Classic Reissue provides at an advanced level, a uniquely fundamental exposition of the applications of Statistical Communication Theory to a vast spectrum of important physical problems.
Abstract: This IEEE Classic Reissue provides at an advanced level, a uniquely fundamental exposition of the applications of Statistical Communication Theory to a vast spectrum of important physical problems. Included are general analysis of signal detection, estimation, measurement, and related topics involving information transfer. Using the statistical Bayesian viewpoint, renowned author David Middleton employs statistical decision theory specifically tailored for the general tasks of signal processing. Dr. Middleton also provides a special focus on physical modeling of the canonical channel with real-world examples relating to radar, sonar, and general telecommunications. This book offers a detailed treatment and an array of problems and results spanning an exceptionally broad range of technical subjects in the communications field. Complete with special functions, integrals, solutions of integral equations, and an extensive, updated bibliography by chapter, An Introduction to Sta istical Communication Theory is a seminal reference, particularly for anyone working in the field of communications, as well as in other areas of statistical physics. (Originally published in 1960.)
1,257 citations
TL;DR: In this article, a class of limit cycling feedback control systems is investigated using a simple and practical analytic tool to determine input-output dynamic response characteristics, and the nature of the dynamic response adaptivity of such systems is shown.
Abstract: A class of limit cycling feedback control systems is investigated using a simple and practical analytic tool to determine input-output dynamic response characteristics. The nature of the dynamic response adaptivity of such systems is shown. A model is derived for the dynamic response characteristics of the amplitude of the limit cycle. Experimental verification is given for each of the principal theoretical results.
27 citations
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.
24 citations
01 Jan 1964
TL;DR: In this paper, the modified nonlinearity is introduced and its value calculated in some cases, under certain conditions, its use may be extended to deal with double-valued nonlinearities, and the concept may be applied to the design of a simple adaptive system.
Abstract: Methods for obtaining the response of a nonlinearity to several uncorrelated inputs are considered. The majority of these methods involve approximate solutions that can lead to rapid calculation of the various output terms, and in most cases a sufficiently high degree of accuracy can be obtained without excessive labour. The concept of the modified nonlinearity is introduced and its value calculated in some cases. It is shown how, under certain conditions, its use may be extended to deal with a double-valued nonlinearity. An example is given to illustrate how the concept may be applied to the design of a simple adaptive system.
18 citations