A. A. Bobtsov, M. V. Faronov, I. B. Furtat, A. A. Pyrkin, J. Wang

Read the full article  ';
Article in Russian

The paper deals with the problem of adaptive control for multi-channel linear stationary plants under parametric uncertainty with arbitrary relative degree of each local subsystem. The synthesized regulator provides stabilization of control plant on condition that for each local subsystem only output variables are measured with known relative degrees, but the order of linear differential equations is unknown. We consider the synthesis of control system for two-channel system for simplification of the synthesis method. The "serial compensator" algorithm is chosen as basic approach with A.L. Fradkov's passification theorem and additional filters containing high gain constants in their structure. Durability of the closed system in the group of pointed types of regulators is analyzed and the necessary and sufficient conditions for exponential convergence properties are considered. We suggest adaptive version of the "serial compensator" method from the practical  point of view, where customization of the gain constant is based on the integral type algorithm. We show the results of computer simulation for the third and second order subsystems under parametric uncertainty to illustrate the proposed approach workability. It is shown that the proposed technique makes it possible to synthesize control algorithms for multichannel systems under parametric uncertainty with minimal dynamical order as compared to known foreign and domestic counterparts.

Keywords: adaptive control, multichannel systems, parametric uncertainty

Acknowledgements. The work is partially financially supported by the Government of the Russian Federation (grant 074-U01), Project 14.Z50.31.0031, Government order 2014/190 (project 2118)).

 1.     Polyak B.T., Shcherbakov P.S. Robastnaya Ustoichivost' i Upravlenie [Robust Stability and Control]. Moscow, Nauka Publ., 2002, 303 p.
2.     Bukov V.N. Vlozhenie Sistem. Analiticheskii Podkhod k Analizu i Sintezu Matrichnykh Sistem [Embedding Systems. An Analytical Approach to the Analysis and Synthesis of Matrix Systems]. Kaluga, Izdatel'stvo Nauchnoi Literatury N.F. Bochkarevoi, 2006, 720 p.
3.     Miroshnik I.V., Nikiforov V.O., Fradkov A.L. Nelineinoe Adaptivnoe Upravlenie Slozhnymi Dinamicheskimi Sistemami [Nonlinear Adaptive Control of Complex Dynamic Systems]. St. Petersburg, Nauka Publ., 2000, 549 p.
4.     Fradkov A.L. Upravlenie v Slozhnykh Sistemakh [Control in Complex Systems]. Moscow, Nauka Publ., 1990, 296 p.
5.     Tsykunov A.M. Robust control algorithms with compensation of bounded perturbations. Automation and Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224. doi: 10.1134/S0005117907070090
6.     Furtat I.B. Robust synchronization of dynamical networks with compensation of disturbances. Automation and Remote Control, 2011, vol. 72, no. 12, pp. 2516–2526. doi: 10.1134/S0005117911120071
7.     Furtat I.B. Konsensusnoe upravlenie lineinoi dinamicheskoi set'yu po vykhodu s kompensatsiei vozmushchenii [Consensus control of linear dynamic network on output with compensation of desturbances]. Mekhatronika, Avtomatizatsiya, Upravlenie, 2011, no. 4, pp. 12–18.
8.     Furtat I.B. Suboptimal'noe upravlenie nelineinymi mul'tiagentymi sistemami [Suboptimal control of nonlinear multi-agent systems].Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2013, no. 1 (83), pp. 19–23.
9.     Furtat I.B. Robust control for a specific class of non-minimum phase dynamical networks. Journal of Computer and Systems Sciences International, 2014, vol. 53, no. 1, pp. 33–46. doi: 10.1134/S1064230714010055
10.Tsykunov A.M. Adaptivnoe i Robastnoe Upravlenie Dinamicheskimi Ob"ektami po Vykhodu [Adaptive and Robust Control of Dynamic Objects on Output]. Moscow, Fizmatlit Publ., 2009, 268 p.
11.Parsheva E.A. Adaptive decentralized control of multivariable plants with scalar input and output and nonminimal realization of the reference model. Automation and Remote Control, 2005, vol. 66, no. 8, pp. 1296–1304. doi: 10.1007/s10513-005-0170-6
12.Mirkin B., Gutman P.-O. Lyapunov-based adaptive output-feedback control of MIMO nonlinear plants with unknown, time-varying state delays. Proc. 9th IFAC Workshop on Time Delay Systems. Prague, Czech Republic, 2010, part. 1, pp. 33–38.
13.Mirkin B., Gutman P.-O. Adaptive output-feedback tracking: the case of MIMO plants with unknown, time-varying state delay. Systems and Control Letters, 2009, vol. 58, no. 1, pp. 62–68. doi: 10.1016/j.sysconle.2008.08.001
14.Cavallo A., Natale C. A robust output feedback control law for MIMO plants. Proc. 15th IFAC World Congress. Barcelona, Spain, 2002, vol. 15, part. 1, pp. 335–345.
15.Ge S.S., Li Z. Robust adaptive control for a class of MIMO nonlinear systems by state and output feedback. IEEE Transactions on Automatic Control, 2014, vol. 59, no. 6, pp. 1624–1629. doi: 10.1109/TAC.2013.2294826
16.Qi R., Tao G., Jiang B. Adaptive control of MIMO time-varying systems with indicator function based parametrization. Automatica, 2014, vol. 50, no. 5, pp. 1369–1380. doi: 10.1016/j.automatica.2014.03.005
17.Chen M., Ge S.S., Ren B. Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica, 2011, vol. 47, no. 3, pp. 452–465. doi: 10.1016/j.automatica.2011.01.025
18.Ambrose H., Qu Z. Model reference robust control for MIMO systems. International Journal of Control, 1997, vol. 68, no. 3, pp. 599–623.
19.Fomin V.N., Fradkov A.L., Yakubovich V.A. Adaptivnoe Upravlenie Dinamicheskimi Ob"ektami [Adaptive Control of Dynamic Objects]. Moskow, Nauka Publ., 1981, 448 p.
20.Narendra K.S., Annaswamy A. Stable Adaptive Systems. New Jersey, Prentice Hall, 2005, 512 p.
21.Bobtsov A.A. Robust output-control for a linear system with uncertain coefficients. Automation and Remote Control, 2002, vol. 63, no. 11, pp. 1794–1802. doi: 10.1023/A:1020907415730

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2024 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.