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Compensating for noise and perturbances in linear object control

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Abstract

We consider the problem of constructing a robust control system for a linear stationary object under unmeasurable perturbances acting on the object. The perturbances are unbounded on the input of the system and bounded on the output. Based on the system inclusion technique, we consider necessary and sufficient conditions for the linear stationary systems’ invariance to perturbances. With the auxiliary contour method, we compensate for the undesirable effects of perturbances on controlled variables. We give an illustrative example and computer modeling results.

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References

  1. Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.

    Google Scholar 

  2. Nikiforov, V.O., A Nonlinear Control System with Compensation for External Deterministic Perturbances, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1997, no. 4, pp. 69–73.

  3. Bobtsov, A.A., A Robust Output Control Algorithm for a Linear Object with Compensation for an Unknown Deterministic Perturbance, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2003, no. 2, pp. 93–97.

  4. Nikiforov, V.O., Observers of External Deterministic Disturbances. I. Objects with Known Parameters, Autom. Remote Control, 2004, vol. 65, no. 10, pp. 1531–1541.

    Article  MathSciNet  MATH  Google Scholar 

  5. Nikiforov, V.O., Observers of External Deterministic Disturbances. II. Objects with Unknown Parameters, Autom. Remote Control, 2004, vol. 65, no. 11, pp. 1724–1732.

    Article  MathSciNet  MATH  Google Scholar 

  6. Tsykunov, A.M., Robust Control Algorithms with Compensation of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.

    Article  MathSciNet  MATH  Google Scholar 

  7. Tsykunov, A.M., A Robust Control Algorithm for a Nonstationary Object with Perturbance Compensation, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2008, no. 4, pp. 33–40.

  8. Tsykunov, A.M., A Robust Control Algorithm for a Linear Dynamic Object, Mekhatronika, Avtomatiz., Upravlen., 2008, no. 8, pp. 7–12.

  9. Tsykunov, A.M., Indirect Measurements-Based Compensation of Disturbances at Control of a Linear Plant, Autom. Remote Control, 2010, vol. 71, no. 4, pp. 654–662.

    Article  MathSciNet  MATH  Google Scholar 

  10. Bukov, V.N., Vlozhenie sistem. Analiticheskii podkhod k analizu i sintezu matrichnykh sistem (System Embedding. Analytical Approach to Analysis and Design of the Matrix Systems), Kaluga: Nauch. Lit. N.F. Bochkarevoi, 2006.

    Google Scholar 

  11. Shchipanov, G.V., Theory and Methods for Designing Automated Controllers, Avtom. Telemekh., 1939, no. 1, pp. 49–66.

  12. Borukhov, V.T., Controllable Invariant Flags in the State Space of Linear Autonomous Finite-Dimensional Dynamical Systems, Diff. Uravn., 1995, vol. 31, no. 1, pp. 8–15.

    MathSciNet  Google Scholar 

  13. Gaiduk, A.R., Analytic Design of Invariant Control Systems for One-Dimensional Plants, Autom. Remote Control, 1981, vol. 42, no. 5, part 1, pp. 557–564.

    Google Scholar 

  14. Kulebakin, V.S., High Quality Invariant Control Systems, in Proc. 1st All-Union Conf. on Invariance Theory, Kiev, October 16–20, 1958, Kiev: Akad. Nauk USSR, 1959, pp. 11–39.

    Google Scholar 

  15. Luzin, N.N., On Matrix Theory of Differential Equations, Avtom. Telemekh., 1940, no. 5, pp. 4–66.

  16. Utkin, V.A., Invariance and Independence in Systems with Separable Motion, Autom. Remote Control, 2001, vol. 62, no. 11, pp. 1825–1843.

    Article  MathSciNet  MATH  Google Scholar 

  17. Horn, R.A. and Johnson, C.R., Matrix Analysis, Cambridge: Cambridge Univ. Press, 1985. Translated under the title Matrichnyi analiz, Moscow: Mir, 1989.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Astrakhan State Technical University, Astrakhan, Russia

    M. V. Zaitseva & E. A. Parsheva

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  1. M. V. Zaitseva
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  2. E. A. Parsheva
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Original Russian Text © M.V. Zaitseva, E.A. Parsheva, 2011, published in Avtomatika i Telemekhanika, 2011, No. 10, pp. 28–38.

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Zaitseva, M.V., Parsheva, E.A. Compensating for noise and perturbances in linear object control. Autom Remote Control 72, 2031–2040 (2011). https://doi.org/10.1134/S0005117911100043

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  • DOI: https://doi.org/10.1134/S0005117911100043

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