A. K. Mahalanabis

Bio: A. K. Mahalanabis is an academic researcher from University of Calcutta. The author has contributed to research in topic(s): Describing function & Linearization. The author has an hindex of 1, co-authored 4 publication(s) receiving 2 citation(s).

Stability of a Hysteretic System with Random Signal Inputs

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.

A Multiple-input Quasi-linearization Method with Applications†

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.

On the Stability of a Hysteretic System under Sinusoidal Excitation

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.

A Method of Finding the Equivalent Gains of Double-valued Non-linearities†

Abstract: A method for computing the sine wave equivalent gain or describing function of a, double-valued non-linearity is presented. The method is illustrated by considering four common types of such a non-linearity and t.he gains for each of these characteristics as obtained by following the present procedure and the conventional procedure are compared. It is also pointed out that the present procedure can have advantage over the conventional procedure in that the stability analysis can be simplified raid the design of an optimum compensation schema can be facilitated.

Double-valued relays with random inputs

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.

Application of the envelope-phase representation in some non-linear noise problems†

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.