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Editor-in-Chief
Nikiforov
Vladimir O.
D.Sc., Prof.
Partners
doi: 10.17586/2226-1494-2022-22-2-232-238
Control of MIMO linear plants with a guarantee for the controlled signals to stay in a given set
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Article in Russian
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Abstract
For citation:
Nguyen Ba Huy, Furtat I.B. Control of MIMO linear plants with a guarantee for the controlled signals to stay in a given set. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2022, vol. 22, no. 2, pp. 232–238 (in Russian). doi: 10.17586/2226-1494-2022-22-2-232-238
Abstract
In this paper, we propose a new method for synthesizing the control of multi-input multi output linear plants with a guarantee of finding controlled signals in given sets under conditions of unknown bounded disturbances. The problem is solved in two stages. At the first stage, the coordinate transformation method is used to reduce the original constrained problem to the problem of studying the input-to-state stability of a new extended system without constraints. At the second stage, the control law for the extended system is obtained by solving a series of linear matrix inequalities. To illustrate the effectiveness of the proposed method, simulation in the MATLAB/Simulink is given. The simulation results show the presence of controlled signals in the given sets and the boundness of all signals in the control system. The proposed method is recommended for use in control problems where it is required to maintain controlled signals in given sets, for example, control of an electric power network, control of the reservoir pressure maintenance process, etc.
Keywords: multi-input multi-output linear plants, coordinate transformation, stability, linear matrix inequalities
Acknowledgements. The proposed method and the main result were obtained under the Russian Science Foundation Grant No. 18-79-10104 at IPME RAS. Numerical simulations were performed at RFBR grant No. 20-08-00610.
References
Acknowledgements. The proposed method and the main result were obtained under the Russian Science Foundation Grant No. 18-79-10104 at IPME RAS. Numerical simulations were performed at RFBR grant No. 20-08-00610.
References
-
Furtat I., Nekhoroshikh A., Gushchin P. Synchronization of multi‐machine power systems under disturbances and measurement errors.International Journal of Adaptive Control and Signal Processing, 2022, in press. https://doi.org/10.1002/acs.3372
-
Pavlov G.M., Merkurev G.V. Energy Systems Automation. St. Petersburg, Papirus Publ., 2001, 388 p. (in Russian)
-
Verevkin A.P., Kiriushin O.V. Control of the formation pressure system using finite-state-machine models. Oil and Gas Territor, 2008, no. 10, pp. 14–19. (in Russian)
-
Bouyahiaoui C., Grigoriev L.I., Laaouad F., Khelassi A. Optimal fuzzy control to reduce energy consumption in distillation columns. Automation and Remote Control, 2005, vol. 66, no. 2, pp. 200–208. https://doi.org/10.1007/s10513-005-0044-y
-
Ruderman M., Krettek J., Hoffmann F., Bertram T. Optimal state space control of DC. IFAC Proceedings Volumes, 2008, vol. 42, no. 2, pp. 5796–5801. https://doi.org/10.3182/20080706-5-KR-1001.00977
-
Furtat I.B., Gushchin P.A. Control of dynamical plants with a guarantee for the controlled signal to stay in a given set. Automation and Remote Control, 2021, vol. 82, no. 4, pp. 654–669. https://doi.org/10.1134/S0005117921040044
-
Furtat I., Gushchin P. Nonlinear feedback control providing plant output in given set. International Journal of Control, 2021, in press. https://doi.org/10.1080/00207179.2020.1861336
-
Furtat I., Gushchin P. Control of dynamical systems with given restrictions on output signal with application to linear systems. IFAC-PapersOnLine, 2020, vol. 53, no. 2, pp. 6384–6389. https://doi.org/10.1016/j.ifacol.2020.12.1775
-
Boyd S., El Ghaoui L., Feron E., Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. SIAM, 1994, 198 p. SIAM studies in applied mathematics; vol. 15.
-
Herrmann G., Turner M.C., Postlethwaite I. Linear matrix inequalities in control. Lecture Notes in Control and Information Sciences, 2007, vol. 367, pp. 123–142. https://doi.org/10.1007/978-1-84800-025-4_4
-
Sontag E.D. Input to state stability: Basic concepts and results. Lecture Notes in Mathematics, 2008, vol. 1932, pp. 163–220. https://doi.org/10.1007/978-3-540-77653-6_3
-
Dashkovskiy S.N., Efimov D.V., Sontag E.D. Input to state stability and allied system properties. Automation and Remote Control, 2011, vol. 72, no. 8, pp. 1579–1614. https://doi.org/10.1134/S0005117911080017
-
Fridman E. A refined input delay approach to sampled-data control. Automatica, 2010, vol. 46, no. 2, pp. 421–427. https://doi.org/10.1016/j.automatica.2009.11.017
-
Löfberg J. YALMIP: a toolbox for modeling and optimization in MATLAB. Proc. of the IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), 2004, pp. 284–289. https://doi.org/10.1109/CACSD.2004.1393890
-
Sturm J.F. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 1999, vol. 11, no. 1, pp. 625–653. https://doi.org/10.1080/10556789908805766