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Zdeněk Úředníček



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Zdeněk Úředníček


WSEAS Transactions on Systems and Control


Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 13, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 13, 2018



Describing Functions and Prediction of Limit Cycles

AUTHORS: Zdeněk Úředníček

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ABSTRACT: This paper deals with the so called describing functions method description as a simplified method of describing certain types of nonlinear systems, using the complex function of frequency response. The first part showed its using as an example of some so-called hard nonlinear systems (e.g. the mechanical chain of robots). In the actual last part, the formalization of the limit cycle prediction process is performed based on the representation of the non-linear element by describing function. The basic approach for this prediction is based on the application of an extended version of the well-known Nyquist criterion from linear control theory to a description of the systems with describing function utilization

KEYWORDS: Motion control, describing function, mechatronics systems, multiport model, limit cycles, Nyquist criterion

REFERENCES:

[1] A. R. Bergen, R .L. Franks, Justification of the Describing Function Method, S.I.A.M. J. Control, 9, pp. 568-589 (1971)

[2] J. K. Hedrick, Analysis and Control of Nonlinear Systems, J. Dyn. Sys., Meas., Control 115(2B), 351-361 (Jun 01, 1993)

[3] J. C. Hsu, A. U. Meyer, Modern Control Principles and Applications, McGraw-Hill (1968)

[4] A. M. Lyapunov, The General Problem of Motion Stability, (1892), in Russian. Translated in French, Ann. Fac. Sci. Toulouse 9, pp. 203- 474 (1907). Reprinted in Ann. Math. Study No. 17, Princeton Univ. Press (1949).

[5] R. Marino, Int. J. Control, 42, pp. 1369-1385 (1985).

[6] J.-J. Slotine, S. S. Sastry, Int. J. Control, 39, 2 (1983).

[7] Z. Chen, J. Huang.: Stabilization and Regulation of Nonlinear Systems, Springer International Publishing, Switzerland, ISBN 978-3-319- 08833-4 (2015)

[8] Z. Úředníček, Robotika, T. Bata university in Zlin (in Czech language), ISBN 978–80–7454– 223- 7 (2012)

[9] Z. Úředníček, Stabilization of telescopic inverse pendulum verification by physical models, International journal of mechanics, 10, (2016)

[10] Z. Úředníček, R. Drga, Measuring robot kinematics description and its workspace, MATEC Web Conf. 76, (2016)

[11] Z. Úředníček, Nonlinear systems - describing functions analysis and using, MATEC Web of Conferences 210, 02021 (2018)

WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 13, 2018, Art. #47, pp. 432-446


Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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