On a stable solution of the problem of disturbance reduction

• Autorzy: Maksimov Vyacheslav I.

Identyfikatory

DOI

10.34768/amcs-2021-0013

• Języki publikacji: EN

Abstrakty

EN

We study the problem of active reduction of the influence of a disturbance on the output of a linear control system. We consider a system of linear differential equations under the action of an unknown disturbance and a control to be formed. Our goal is to design an algorithm for reducing the disturbance by means of an appropriate control on the basis of inaccurate measurements of the system phase coordinates. This algorithm should form a feedback control that would guarantee that the trajectory of a given system tracks the trajectory of the reference system, i.e., the system described by the same differential equations but with zero control and disturbance. We present an algorithm for solving this problem. The algorithm, based on the constructions of guaranteed control theory, is stable with respect to informational noises and computational errors.

Słowa kluczowe

EN

disturbance reduction; dynamical controlled system; guaranteed control theory

PL

redukcja zakłóceń; system sterowany dynamicznie; teoria sterowania

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2021
• Tom: Vol. 31, no. 2
• Strony: 187--194
• Opis fizyczny: Bibliogr. 18 poz., wykr.

Twórcy

autor

Maksimov Vyacheslav I.

• Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya St., Yekaterinburg 620990, Russia

Bibliografia

• [1] Cayero, J., Rotondo, D., Marcego, B., and Puig, V. (2019). Optimal state observation using quadratic boundedness: Application to UAV disturbance estimation, International Journal of Applied Mathematics and Computer Science 29(1): 99–109, DOI: 10.2478/amcs-2019-0008.
• [2] Falsone, A., Deori, L., Ioli, D., Garatti, S. and Prandini, M. (2019). Optimal disturbance compensation for constrained linear systems operating in stationary conditions: A scenario-based approach, Automatica 110: 108537.
• [3] Favini, A., Maksimov, V. and Pandolfi, L. (2004). A deconvolution problem related to a singular system, Journal of Mathematical Analysis and Applications 292(1): 60–72.
• [4] Gan,W.S. and Kuo, S.M. (2002). An integrated audio and active noise headsets, IEEE Transactions on Consumer Electronics 48(2): 242–247.
• [5] Keesman, K.J. and Maksimov, V.I. (2008). On feedback identification of unknown characteristics: A bioreactor case study, International Journal of Control 81(1): 134–145.
• [6] Kwakernaak, H. (2002). H2-optimization—Theory and applications to robust control design, Annual Reviews in Control 26(1): 45–56.
• [7] Maksimov, V.I. (2002). Dynamical Inverse Problems of Distributed Systems, VSP, Utrecht/Boston.
• [8] Maksimov, V. (2011). The tracking of the trajectory of a dynamical system, Journal of Applied Mathematics and Mechanics 75(6): 667–674.
• [9] Maksimov, V.I. and Mordukhovich, B.S. (2017). Feedback design of differential equations of reconstruction for second-order distributed systems, International Journal of Applied Mathematics and Computer Science 27(3): 467–475, DOI: 10.1515/amcs-2017-0032.
• [10] Maksimov, V. (2016). Game control problem for a phase field equation, Journal of Optimization Theory and Applications 170(1): 294–307.
• [11] Maksimov, V. and Tröltzsch, F. (2020). Input reconstruction by feedback control for the Schlögl and FitzHugh–Hagumo model, International Journal of Applied Mathematics and Computer Science 30(1): 5–22, DOI: 10.34768/amcs-2020-0001.
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• [14] Samarskii, A.A. (1971). Introduction to the Theory of Difference Schemes, Nauka, Moscow, (in Russian).
• [15] Yu, S.-H. and Hu, J.-S. (2001). Controller design for active noise cancellation headphones using experimental raw data, IEEE/ASME Transactions on Mechatronics 6(4): 483–490.
• [16] Wasilewski, M., Pisarski, D., Konowrocki, R., and Bajer, C.I. (2019). A new efficient adaptive control of torsional vibrations included by switched nonlinear disturbances, International Journal of Applied Mathematics and Computer Science 29(2): 285–303, DOI: 10.2478/amcs-2019-0021.
• [17] Willems, J.C. (1982). Feedforward control, PID control laws, and almost invariant subspaces, Systems and Control Letters 1(4): 277–282.
• [18] Yuan, Y., Wang, Z., Yu, Y., Guo, L., and Yang, H. (20019). Active disturbance rejection control for a pneumatic motion platform subject to actuator saturation: An extended state observer approach, Automatica 107: 353–361.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).