Русская версия English version

Design of selectively invariant control systems

A.R. Gaiduk

Vestnik IGEU, 2017 issue 1, pp. 46—55

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Abstract in English: 

Background: It is known that requirements for the control systems accuracy have essentially increased, which makes methods of external disturbance effect compensation relevant. The potential of the traditional method of improving accuracy by increasing the control system gains is limited by a sharp reduction in stability degree, i.e. system robustness, and increase in the overshooting and fluctuation of its transients. Such restrictions are particularly common in deviation control systems. It is suggested that these problems can be solved by a method of absolute invariancy ensuring full compensation of the effects of any limited disturbances on the system error. However, it is extremely difficult to implement such systems. In real systems of optimal control the error is minimal but cannot be equal to zero. Therefore, the problem of significantly increasing the accuracy of control systems can be solved by a method of full compensation of the effects of external disturbances on the system error, and this method should not have such drawbacks.

Materials and methods: The study employed the property of selective invariancy and the output and impact control principle to solve the problem of full compensation of the effect of external disturbances on system error. Parametric robustness of selective invariancy is reached by using the principle of internal spectral models realized based on K(p)-images of external disturbances. Output and impact control eliminates the contradiction between stability and accuracy requirements and ensures the ability to implement the control device.

Results: The authors have developed an analytical method of designing physically realizable, selectively invariant control systems in which the effect of external disturbances with known K(p)-images on the system error is fully compensated. They also found that the system error caused by these external disturbances remains equal to zero in case of deviations of most of the system parameters (except spectrum-determining ones) from the design values as long as the system remains stable.

Conclusions: Output and impact control based on the principle of internal spectral models allows developing control systems of better quality for various branches of economy by applying the analytical and modern information technologies.

Key words: control system, system error, selective invariancy, spectral model, internal model principle, parametrical robustness.

References in English: 

1. Misrikhanov, M.Sh. Invariantnoe upravlenie mnogomernymi sistemami: algebraicheskiy podkhod [Invariant control of multivariable systems: an algebraic approach]. Moscow, Nauka, 2007.

2. Kulebakin, V.S. Ob osnovnykh zadachakh I metodakh povysheniya kachestva avtomatiki upravlyaemykh system [On the main goals and methods of quality improvement of controlled system automatics]. Trudy II Vsecoyuznogo soveshchaniya po teorii avtomaticheskogo regulirovaniya. T. II [Collected works of the II-nd All-Union Meeting on Theory of Automatic Control]. Мoscow; Leningrad, Izdatel’stvo AN SSSR, 1955, pp. 184–207.

3. Kulebakin, V.S. Operatornoe K(D)-izobrazhenie funktsiy i ego prakticheskoe primenenie [Operational K(D)-image of functions and its practical application]. Trudy VVIA im. N.E. Zhukovskogo, 1958, issue 695.

4. Nadezhdin, P.V. Poluchenie fil’trov Kolmogorova-Vinera na osnove printsipa selektivnoy invariantnosti [Obtaining Kolmogorov–Wiener filters according to the selective invariancy principle]. Tezisy dokladov VI Vsesoyuznogo soveshchaniya «Teoriya invariantnosti, teoriya chuvstvitel'nosti i ikh primeneniya» [Abstracts of the VI-th All-Union Meeting «Theory of invariancy, theory of sensitivity and their applications»]. Moscow, IPU, 1982, pp. 37–38.

5. Gaiduk, A.R. Teoriya avtomaticheskogo upravleniya [Theory of automatic control: a textbook]. Moscow, Vysshaya shkola, 2010.

6. Uonеm, M. Lineynye mnogomernye sistemy upravleniya [Linear multivariable control systems]. Moscow, Nauka, 1980.

7. Gaiduk, A.R. Teoriya i metody analiticheskogo sinteza sistem avtomaticheskogo upravleniya (polinomial'nyy podkhod) [Theory and methods of analytical design of automatic control systems (a polynomial approach)]. Moscow, Fizmatlit, 2012.

8. Bobtsov, A.A., Kremlev, A.S. Algoritm kompensatsii neizvestnogo sinusoidal’nogo vozmushcheniya dlya lineynogo ne minimal’no fazovogo ob"ekta [A compensation algorithm of unknown sine-wave disturbance for linear non-minimum phase plant]. Mekhatronika, avtomatizatsiya, upravlenie, 2008, no. 10, pp. 14–17.

9. Bobtsov, A.A. Adaptivnoe upravlenie po vykhodu s kompensatsiey garmonicheskogo smeshchennogo vozmushcheniya [Adaptive output control with compensation of harmonically displaced disturbances]. Izvestiya RAN. Teoriya i sistemy upravleniya, 2009, no. 1, pp. 45–48.

10. Pyrkin, A.A., Bobtsov, A.A., Nikiforov, V.O., Kolyubin, S.A., Vedyakov, A.A., Borisov, O.I., Gromov, V.S. Compensation of Polyharmonic Disturbance of State and Output of a Linear Plant with Delay in the Control Channel. Automation and Remote Control, 2015, vol. 76, no. 12, pp. 2124–2142.

11. Nazin, S.A., Polyak, B.Т., Toptunov, М.V. Podavlenie ogranichennykh vneshnikh vozmushcheniy s pomoshch’yu metoda invariantnykh ellipsoidov [Suppression of bounded external disturbances by the method of invariant ellipsoids]. Avtomatika i telemekhanika, 2007, no. 3, pp. 106–125.

12. Nikiforov, V.O. Nelineynaya sistema upravleniya s kompensatsiey vneshnikh determinirovannykh vozmushcheniy [A nonlinear control system with compensation of the external deterministic disturbances]. Izvestiya RAN. Theoriya i sistemy upravleniya, 1997, no. 4, pp. 69–73.

13. Gaiduk, A.R. Otsenivanie vozdeystviy i invariantnost' [Estimation of disturbances and invariancy]. Avtomatika i telemekhanika, 1984, no. 3, pp. 20–29.

14. Filimonov, A.B., Filimonov, N.B. Kontseptsiya modal'noy reduktsii modeley dinamicheskikh sistem [A concept of modal reduction of dynamic system models]. Mekhatronika, avtomatizatsiya, upravlenie, 2013, no. 12, pp. 2–8.

15. Gaiduk, A.R., Plaksienko, E.A. Robastnost' redutsirovannykh dinamicheskikh sistem avtomatizatsii [Robustness of reduced dynamic automation systems]. Mekhatronika, avtomatizatsiya, upravlenie, 2016, no. 5, pp. 308–315.

16. Kopylova, L.G., Tararykin, S.V. Kompensatsiya garmonicheskikh vozmushcheniy momenta nagruzki v sledyashchikh elektromekhanicheskikh sistemakh i elementy strukturnoy optimizatsii regulyatorov [Compensation of load torque harmonic disturbances in servo electromechanical systems and elements of regulator structural optimization]. Vestnik IGEU, 2012, issue 6, pp. 44–51.

Ключевые слова на русском языке: 
система управления, ошибка системы, селективная инвариантность, спектральная модель, принцип внутренних моделей, параметрическая грубость
Ключевые слова на английском языке: 
control system, system error, selective invariancy, spectral model, internal model principle, parametrical robustness
The DOI index: 
10.17588/2072-2672.2017.1.046-055
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