Open Access Open Access  Restricted Access Subscription or Fee Access

Control System for an Object with Interval-Given Parameters: Quality Analysis Based on Leading Coefficients of Characteristic Polynomials

Yury Chursin(1*), Dmitry Sonkin(2), Mikhail Sukhodoev(3), Ruslan Nurmuhametov(4), Vsevolod Pavlichev(5)

(1) Tomsk Polytechnic University, Russian Federation
(2) Tomsk Polytechnic University, Russian Federation
(3) Tomsk Polytechnic University, Russian Federation
(4) Tomsk Polytechnic University, Russian Federation
(5) Tomsk Polytechnic University, Russian Federation
(*) Corresponding author


DOI: https://doi.org/10.15866/ireaco.v11i4.15727

Abstract


This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust control system based on leading coefficients of characteristic polynomials. The problem of determining quality indices of a system, which characteristic polynomials are with interval coefficients, is one of the relevant ones in the robust control theory. This article deals with the interval characteristic polynomial coefficients of a control system. Based on the extended root locus method, we have determined conditions, at which the vertices of a polyhedron of coefficients will be mapped onto root domain. The root analysis carried out by us showed the conditions for achieving the minimum degree of stability of the system under consideration, as well as the maximum degree of oscillation. Thus, the paper describes the design of a method intended for finding the control leading coefficients of polynomials that will allow analyzing the minimum stability degree and the maximum oscillativity degree of control systems for objects with interval-given parameters. A complete solution to a problem of the system control is given. Thus, the stability conditions of the system are described in full.
Copyright © 2018 Praise Worthy Prize - All rights reserved.

Keywords


Characteristic Polynomial; Interval Coefficients; Root Locus; Root Localization; Parameterized Polyhedron Vertices; Stability Degree; Oscillativity Degree; Phase Equation; Angle of Leaving

Full Text:

PDF


References


C.B. Soh, C.S. Berger, K.P. Dabke, On the stability properties of polynomials with perturbed coefficients, IEEE Transactions on Automatic Control., Vol. 30: 1033-1036, 1985.
http://dx.doi.org/10.1109/tac.1985.1103807

V.L. Kharitonov, Robust Stability of Multivariate Polynomials. In Advances in Mathematical Systems Theory. Birkhäuser, Boston, MA, pp. 19-29, 2001.
http://dx.doi.org/10.1007/978-1-4612-0179-3_2

B. Senol, C. Yeroglu, Robust stability analysis of fractional order uncertain polynomials. In Proceedings of the 5th IFAC Workshop on Fractional Differentiation and its Applications., 2012.

E. Rocha, S. Mondie, M. Di Loreto, Necessary Stability Conditions for Linear Difference Equations in Continuous Time. IEEE Transactions on Automatic Control, 2018.
http://dx.doi.org/10.1109/tac.2018.2822667

A. V. Egorov, C. Cuvas, S. Mondié, Necessary and sufficient stability conditions for linear systems with pointwise and distributed delays, Automatica, Vol. 80: 218-224, 2017.
http://dx.doi.org/10.1016/j.automatica.2017.02.034

Y. Wang, Y. Xia, H. Shen, P. Zhou, SMC design for robust stabilization of nonlinear Markovian jump singular systems. IEEE Transactions on Automatic Control, Vol. 63 (Issue 1): 219-224, 2018.
http://dx.doi.org/10.1109/tac.2017.2720970

J. D. Ackermann, Kaesbauer Stable polyhedral in parametric space, Automatica, Vol. 39: 937-943, 2003.
http://dx.doi.org/10.1016/s0005-1098(03)00034-7

S.A. Gayvoronskiy, T. Ezangina, I. Khozhaev, The analysis of permissible quality indices of the system with affine uncertainty of characteristic polynomial coefficients, International Automatic Control Conference, CACS 2016, article № 7973879, pp. 30-34, 2016.
http://dx.doi.org/10.1109/cacs.2016.7973879

S.M. Tripathi, A.N. Tiwari, D.Singh, Controller Design for a Variable-Speed Direct-Drive Permanent Magnet Synchronous Generator-Based Grid-Interfaced Wind Energy Conversion System Using D-Partition Technique. IEEE Access, Vol. 5, pp. 27297-27310, 2017.
http://dx.doi.org/10.1109/access.2017.2775250

M.A. Gomez, A.V. Egorov, S. Mondié, Necessary stability conditions for neutral type systems with a single delay. IEEE Transactions on Automatic Control, Vol. 62 (Issue 9): 4691-4697, 2017.
http://dx.doi.org/10.1109/tac.2016.2625738

D. Grigoriadis, A Unified Algebraic Approach To Control Design. Routledge, 2017.
http://dx.doi.org/10.1201/9781315136523

A. Rosales, Y. Shtessel, L. Fridman, C.B. Panathula, Chattering analysis of HOSM controlled systems: frequency domain approach. IEEE Transactions on Automatic Control, Vol. 62 (Issue 8): 4109-4115, 2017.
http://dx.doi.org/10.1109/tac.2016.2619559

B.R. Barmish, R. Tempo, The robust root locus. Automatica, Vol. 26 (Issue 2): 283-292, 1990.
http://dx.doi.org/10.1016/0005-1098(90)90122-x

B. Y. Juang, Robustness of pole assignment of an interval polynomial based on the Kharitonov theorem. Proc of the SICE Annual Conference 2010 SICE 2010 (Taipei; Taiwan), pp. 3475-3484, 2010.

Y. K. Foo, Y. C. Soh, Robust root clustering of interval plants with first-order compensators, IEEE Proceedings: Control Theory and Applications, Vol. 148 (Issue 4): 315-317, 2001.
http://dx.doi.org/10.1049/ip-cta:20010554

S. A. Gayvoronskiy, T. A. Ezangina, The algorithm of analysis of root quality indices of high order interval systems Proc of the 2015 27th Chinese Control and Decision Conference (CCDC 2015) (China) (New York: IEEE), pp. 3048-3052, 2015.
http://dx.doi.org/10.1109/ccdc.2015.7162444

Y.C. Soh, Y. K. Foo, Generalized edge theorem Systems and Control Letters, Vol. 12 (Issue 3): 219-224, 1989.
http://dx.doi.org/10.1016/0167-6911(89)90053-4

V. Zhmud, L. Dimitrov, O. Yadrishnikov, Calculation of regulators for the problems of mechatronics by means of the numerical optimization method, 12th International Conference on Actual Problems of Electronic Instrument Engineering, APEIE 2014, Proceedings, article № 7040784, pp. 739-744., 2015.
http://dx.doi.org/10.1109/apeie.2014.7040784

V. Zhmud, V. Semibalamut, A. Vostrikov, Feedback systems with pseudo local loops, Testing and Measurement: Techniques and Applications, Proceedings of the 2015 International Conference on Testing and Measurement: Techniques and Applications, TMTA 2015, pp. 411-41, 2015.

A.C. Bartlett, C.V. Hollot, H. Lin, Root location of an entire polytope polynomials: it suffices to check the edges, Proc. Amer. Contr. Conf. Minneapolis: MN, 1987.
http://dx.doi.org/10.1007/bf02551236

S. A. Gayvoronskiy, T Ezangina, I. Khozhaev, Analysis of Interval Control System Robust Quality Indices on the Base of Root and Coefficient Methods, IOP Conference Series: Materials Science and Engineering, Vol. 235, No. 1, p. 012016, IOP Publishing, 2017, September.
http://dx.doi.org/10.1088/1757-899x/235/1/012016

V. Korobov, A. Lutsenko, On the Robust Stabilization of One Class of Nonlinear Discrete Systems, Journal of Mathematical Sciences, Vol. 220 (Issue 4): 2017.
http://dx.doi.org/10.1007/s10958-016-3196-0


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2020 Praise Worthy Prize