Abstract
For nonlinear systems operating under uncertainty, this paper involves the principle of motion separation to design a state observer with nonlinear corrections in the form of sigma functions. For the systems representable in the regular form with respect to the external perturbations, the above approach yields the current estimates of the unmeasurable state variables and external perturbations without extending the dynamic order of the observer by a model that simulates the action of the external perturbations. The developed algorithms are applied in the control system of an asynchronous drive with an incomplete set of measuring devices.
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Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control and Optimization, Heidelberg: Springer, 1992.
Krasnova, S.A. and Kuznetsov, S.I., Uncontrollable Perturbations of Nonlinear Dynamic Systems: Estimation on Moving Modes, Autom. Remote Control, 2005, vol. 66, no. 10, pp. 1580–1593.
Akhobadze, A.G. and Krasnova, S.A., Solving the Tracking Problem under Uncertainty with the Joint Block Canonical Controllability and Observability Form, Upravlen. Bol’shimi Sist., 2009, no. 24, pp. 34–80.
Krasnova, S.A. and Utkin, V.A., Kaskadnyi sintez nablyudatelei sostoyaniya dinamicheskikh sistem (Cascade Synthesis of State Observers in Dynamic Systems), Moscow: Nauka, 2006.
Emel’yanov, S.V. and Korovin, S.K., Novye tipy obratnoi svyazi (New Types of Feedback), Moscow: Nauka, 1997.
Korovin, S.K. and Fomichev, V.V., Nablyudateli sostoyaniya dlya lineinykh sistem s neopredelennost’yu (States Observers for Linear Systems with Uncertainty), Moscow: Fizmatlit, 2007.
Atassi, A.N. and Khalil, H.K., A Separation Principle for the Stabilization of a Class of Nonlinear Systems, IEEE Trans. Automat. Control, 1999, vol. 44, no. 9, pp. 1672–1687.
Krasnova, S.A. and Mysik, N.S., Cascade Synthesis of a State Observer with Nonlinear Correcting Influences, Autom. Remote Control, 2014, vol. 75, no. 2, pp. 263–280.
Babin, V.A., Dik, V.V., and Krasnova, S.A., Prelimit Realizations of Discontinuous Corrections for a Sliding Mode Observer, Tr. XII Vseross. soveshchan. po problemam upravleniya (VSPU–2014) (Proc. XII All-Russian Meeting on Control Problems (AMCP-2014), Moscow: Inst. Probl. Upravlen., 2014, pp. 374–390.
Chilikin, M.G., Klyuchev, V.I., and Sandler, A.S., Teoriya avtomatizirovannogo elektroprivoda (The Theory of Automated Electric Drives), Moscow: Energiya, 1979.
Utkin, V.A., Problems of Control of an Asynchronous Electric Motor, Autom. Remote Control, 1993, vol. 54, no. 12, pp. 1769–1779.
Utkin, V.A., Krasnova, S.A., and Utkin, A.V., State Observer in Control Systems of Induction Motor Drives, Prep. 2013 IFAC Conf. on Manufacturing Modeling, Management and Control (MIM’2013), St. Petersburg, Russia, 2013, pp. 1204–1209.
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Original Russian Text © S.A. Krasnova, A.V. Utkin, 2015, published in Problemy Upravleniya, 2015, No. 5, pp. 27–36.
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Krasnova, S.A., Utkin, A.V. Sigma function in observer design for states and perturbations. Autom Remote Control 77, 1676–1688 (2016). https://doi.org/10.1134/S0005117916090149
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DOI: https://doi.org/10.1134/S0005117916090149