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Journal ArticleDOI

A Multiple-input Quasi-linearization Method with Applications†

01 Jul 1966-International Journal of Control (Taylor & Francis Group)-Vol. 4, Iss: 1, pp 73-86
TL;DR: In this paper, a general approach for computing the multiple-input equivalent gains of a non-linear element in the minimum mean square error sense is described. But the method is not applicable for elements with zero or finite memory, and results for the single input cases can be obtained from the results for larger input cases by taking the limits as all but one (or two) of the signals tend to zero.
Abstract: The paper describes a general approach for computing the multiple-input equivalent gains of a non-linear element in the minimum mean square error sense and is an extention of the method developed earlier for computing the equivalent gain for Gaussian input (Nath and Mahalanabis 1966). The method is general in the sense that it is equally well applicable for elements with zero or finite memory, and that results for the single (or dual) input cases can be obtained from the results for larger input cases by taking the limits as all but one (or two) of the signals tend to zero. The results of application of the method to representative non-linearities of each class with two or three uncorrelated inputs are given examples. Finally, the stability of a hysteretic system with random single input is briefly examined by following the quasi-linearization analysis.
Citations
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Journal ArticleDOI
TL;DR: It is shown here that this approach is equally good for the more general problem of evaluating the output power‡ series of a non-linearity of either single-valued or double-valued type.
Abstract: The paper discusses an extension of some of the earlier works of the author and his student on a procedure for evaluating the transmission properties of gaussian signals through non-linear devices. It is based on the application of the envelope-phase representation of such signals and subsequent application of the Fourier series expansion of the instantaneous output of the non-linearity. The earlier investigations were concerned mainly with the evaluation of the input-output cross-power‡ terms. It is shown here that this approach is equally good for the more general problem of evaluating the output power‡ series of a non-linearity of either single-valued or double-valued type. An application of those computations in the field of nonlinear filtering is discussed.
References
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Journal ArticleDOI
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

Journal ArticleDOI
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