Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
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TL;DR: In this article, a novel integral-derivative observer (SIDO) using sigmoid function is developed, which can simultaneously provide continuous integral and differential estimates with almost no drift phenomena and chattering effect, as well as acceptable noise-tolerance performance from output measurement.
9 citations
TL;DR: In this paper, the stability of limit cycles in feedback systems which have hysteresis nonlinearities is investigated. But the analysis is based on the Loeb criterion, and it is well known that analyses which are based on describing functions may lead to erroneous conclusions, which may explain the presence of distortions in solutions of the class of feedback systems considered herein.
Abstract: In this paper, we concern ourselves with the stability of limit cycles in feedback systems which have hysteresis nonlinearities. Although the quasi-static analysis of limit cycles (Loeb criterion) predicts, in most cases correctly, the stability properties of limit cycles, it is well known that analyses which are based on the method of describing functions may lead to erroneous conclusions. In this paper, we show to what extent the describing function method can be given a rigorous mathematical basis. We show that for a specific example, the main result of this paper predicts correctly the stability of a limit cycle while the Loeb criterion yields an incorrect result. Also, we show that our analysis explains to a certain extent the presence of distortions in solutions of the class of feedback systems considered herein.In arriving at the main result of this paper, use is made of several known facts for functional differential equations and of a result on integral manifolds.
9 citations
01 Mar 2003
TL;DR: In this article, a method for the computation of the magnitude and phase envelopes of uncertain transfer functions is presented, which is different from those based on the interval polynomial method of Kharitonov, and has the major advantage that the representation is more applicable to practical situations where typically the coefficients of the various factored terms relate to physical parameters of a mathematical model.
Abstract: A method for the computation of the magnitude and phase envelopes of uncertain transfer functions is presented. The idea is to factor the transfer function into its real and complex pair roots and find the maximum and minimum magnitudes of the gain and phase of each factor. The Bode envelopes of the given uncertain system are then found from those of the individual factors. This approach, which is different from those based on the interval polynomial method of Kharitonov, has the major advantage that the representation is more applicable to practical situations where typically the coefficients of the various factored terms relate to physical parameters of a mathematical model. Further, the method results in the narrowest Bode envelopes and therefore can yield improved controller designs. The describing function analysis and absolute stability problem of nonlinear systems with variable plant parameters are also studied. An approach which enables one to predict the existence of limit cycles in a control system which simultaneously contains nonlinearities and parametric uncertainties is given. The proposed method makes use of the popular describing function technique and these narrowest possible Bode envelopes of linear uncertain transfer functions in factored form. The technique can be used to cover the cases of linear elements, which have a multilinear or nonlinear uncertainty structure, and a nonlinear element with or without memory. New formulations of the circle and off-axis circle criteria are given for use with Bode diagrams so that the absolute stability of nonlinear systems with variable plant parameters can be studied. Examples are given to show how the proposed method can be used to assess the effects of parametric variations in feedback loops.
9 citations
TL;DR: An optimal (suboptimal) periodic control for a single-input single-output time-invariant linear system is shown to be easily obtainable via a describing function approach.
Abstract: This paper deals with a periodic optimization problem. Specifically, an optimal (suboptimal) periodic control for a single-input single-output time-invariant linear system is shown to be easily obtainable via a describing function approach. This also allows pointing out some interesting features of the problem and the significant role played by the concept of resonance frequency.
9 citations
25 May 2018
TL;DR: To achieve precise identification of backlash in gear systems, a new identification method is proposed on the basis of hysteresis backlash model and the describing function method, which results reveal can achieve precise backlash identification.
Abstract: To achieve precise identification of backlash in gear systems, a new identification method is proposed on the basis of hysteresis backlash model and the describing function method. A Discrete Fourier Transform is used to extract the fundamental components from the system output digital. Then the relationship between the phase angle of describing function and that of the fundamental components is utilized to identify backlash. A sinusoidal excitation with small amplitude and low frequency is applied as the system input, in order to reduce the impact and collision between meshing teeth, highlight the hysteresis effect and improve identification accuracy. A gear transmission system with backlash is considered as a numerical model, simulation results reveal this method can achieve precise backlash identification. Numerical tests with multi-group excitations are conducted, the results reveal that the effects of the selection of amplitude and frequency of excitation on the accuracy of the identification method can't be ignored.
9 citations