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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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Journal ArticleDOI
TL;DR: In this article, the mass flow rate characteristic of a pneumatic valve set in the frequency domain is analyzed and the describing function of nonlinearity can be determined analytically.

4 citations

Journal ArticleDOI
TL;DR: In this article, the authors address the problem of estimating the performance of a system controlled by two-sliding mode controllers, and propose a method based on invariant ellipsoid sets to predict the maximum output bound of the system.
Abstract: Sliding mode control is a simple and powerful technique for the robust control of uncertain systems. However, despite theoretical promise, real systems using sliding mode controllers have a tendency to chatter at higher frequencies. Second order or two-sliding mode controllers, can be used to suppress chatter while retaining the desirable properties of a classical sliding mode controller. These more complex controllers increase the number of parameters in the system. The affect of these new parameters on system performance is unclear, and this can make it difficult to tune the controllers to meet a desired performance criteria. This study addresses the problem of estimating the performance of a system controlled by two-sliding mode controllers. Describing functions are proposed to estimate chattering amplitude and settling time, and a new method is presented, based on invariant ellipsoid sets, to predict the maximum output bound of the system. The aim is assist in producing a systematic approach for practitioners wishing to directly apply sliding mode controllers with chatter suppressing properties to real applications.

4 citations

Journal ArticleDOI
TL;DR: In this article, the existence of a free vibration in a given neighbourhood of the approximate vibration obtained by the describing function method is investigated and a theorem on the estimation of frequency of the free vibration is given.
Abstract: The most popular method of investigation of periodic oscillations in nonlinear systems is the describing function method. Two theorems on the existence of a free vibration in a given neighbourhood of the approximate vibration obtained by this method are presented in the paper. Moreover, for a typical transfer function K(jω) of the linear part of the system and a typical describing function of the non-linear element, the theorem on the estimation of frequency of the free vibration is given.

4 citations

Journal ArticleDOI
01 Jul 1974
TL;DR: In this article, an analysis of ferro-oscillations in capacitor voltage transformers and series-compensated e.h.v. lines is presented, where the dual-input describing function is adopted to show the regions of existence and the influence of system parameters on such oscillations.
Abstract: The paper presents an analysis of ferro-oscillations in capacitor voltage transformers and series-compensated e.h.v. lines. The dual-input describing function is adopted to show the regions of existence and the influence of system parameters on such oscillations. A complete analytical method suitable for digital computation has been developed for determining the amplitudes of these oscillations.

3 citations

Journal ArticleDOI
TL;DR: In this article, a new theory of Hopf bifurcation at infinity can be used to study the oscillations of a train wheelset using a numerical algorithm, and the results obtained by the describing function method are also made.
Abstract: SUMMARY Many models of train wheelset systems involve Coulomb friction terms and model the flange rail forces as stiff linear springs with dead bands. For such systems, the regular theory of Hopf bifurcation is not applicable, whereas a newly developed theory of Hopf bifurcation at infinity can be used. This is because such systems are basically linear as far as very large amplitude motions are concerned. In this paper, we apply this theory to study the oscillations of a wheelset using a numerical algorithm. Comparisons with the results obtained by the describing function method are also made.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847