Русская версия English version
Home / 2023 issue 4 / Synthesis of robust control system for transportation of long-length material based on Gramian method

Synthesis of robust control system for transportation of long-length material based on Gramian method

A.M. Abbyasov, S.V. Tararykin

Vestnik IGEU, 2023 issue 4, pp. 54—62

Download PDF

Abstract in English: 

Background. Material transportation control systems are part of many automated technological complexes for continuous production in various industries. For the coordinated operation of the aggregated machines, it is required to ensure a given quality of control of the tension of material transportation under conditions of initial uncertainty and possible variations in the internal parameters of the ACS, primarily the inertia of rotation of the measuring roller and changes in the geometry of the deformation zone of the material, i.e., it is required to provide a significant increase in robust properties.

Materials and methods. A method for the synthesis of robust control systems with dynamic (polynomial) input-output regulators is proposed. It is based on an iterative approach, at each step of which the singular numbers of gramians of controllability and/or observability are purposefully changed, a preregulator is formed.It transforms the structure of the computational model of the object in the direction of increasing controllability and/or observability.

Results. The authors have proposed a method for the synthesis of a robust control system for the transportation of long-length material based on the Gramian method. The use of an improved model of the object makes it possible to form a basic polynomial input-output controller capable of providing and maintaining the desired quality and performance indicators within the specified limits of changing the parameters of the object and the controller, including when reducing the corrective pre-regulator.

Conclusions. The results obtained allow us to demonstrate the high efficiency of a Gramian method for the synthesis of control systems with low sensitivity to variations in both the parameters of the control object and the controller own parameters.

References in English: 

1. Ayrapet'yants, G.M., Kozhevnikov, M.M., Ul'yanov, M.I. Modelirovanie dinamiki dvizheniya plenki na agregate po proizvodstvu polimerno-plenochnykh materialov [Modeling the dynamics of film movement along a unit to produce polymer-film materials]. Nauka i tekhnika, 2018, vol. 17, no. 6, pp. 528–533.

2. Dochviri, Dzh.N. Optimizatsiya perekhodnykh protsessov mnogodvigatel'nykh tiristornykh elektroprivodov s uprugimi svyazyami dlya pressovykh mekhanizmov nepreryvnykh tekhnologicheskikh mashin [Optimization of transient processes of multi-motor thyristor electric drives with elastic links for pressing mechanisms of continuous technological machines]. Elektrichestvo, 2006, no. 2, pp. 34–42.

3. Stel'mashchuk, S.V., Kapustenko, D.V. Soglasovannoe upravlenie ustroystvom transportirovki lenty s modal'nymi regulyatorami [Coordinated control of tape conveyor with modal controllers]. Uchenye zapiski Komsomol'skogo-na-Amure gosudarstvennogo tekhnicheskogo universiteta, 2019, vol. 1, no. 2(38), pp. 28–40.

4. Sheryshev, M.A. Proizvodstvo izdeliy iz polimernykh listov i plenok [Manufacture of products from polymer sheets and films]. Saint-Petersburg: Nauchnye osnovy i tekhnologii, 2011.

5. Ivanov, G.M., Ivanov, A.G. Elektroprivod v khimicheskoy i tsellyulozno-bumazhnoy otraslyakh promyshlennosti [Electric drive in chemical and cellulose-paper industries]. Moscow: MGIU, 2008.

6. Belov, M.P., Novikov, V.A., Rassudov, L.N. Avtomatizirovannyy elektroprivod tipovykh proizvodstvennykh mekhanizmov i tekhnologicheskikh kompleksov [Automated electric drive of standard production mechanisms and technological complexes]. Moscow: Izdatel'skiy tsentr «Akademiya», 2007.

7. Tararykin, S.V., Sofronov, S.V. Avtomatizatsiya protsessov proizvodstva polimernogo opticheskogo volokna [Automation of polymer optical fiber production processes]. Ivanovo, 2002.

8. Kang, H., Lee, C., Shin, K., Kim, S. Modeling and matching design of a tension controller using pendulum dancer in roll-to-roll systems. IEEE Transactions on industry applications, 2011, vol. 47, no. 4.

9. Tyutikov, V.V., Tararykin, S.V. Robastnoe modal'noe upravlenie tekhnologicheskimi ob"ektami [Robust modal control of technological objects]. Ivanovo, 2006. 256 p.

10. Anisimov, A.A., Tararykin, S.V. Iteratsionnyy metod strukturno-parametricheskogo sinteza robastnykh sistem s regulyatorom sostoyaniya [Iterative method for structural-parametric synthesis of robust systems with state controller]. Izvestiya RAN. T i SU, 2018, no. 4, pp. 42–55.

11. Kuzovkov, N.T. Modal'noe upravlenie i nablyudayushchie ustroystva [Modal control and monitoring devices]. Moscow: Mashinostroenie, 1976. 184 p.

12. Voronov, A.A. Vvedenie v dinamiku slozhnykh upravlyaemykh system [Introduction to dynamics of complex control systems]. Moscow: Nauka, 1985. 352 p.

13. Krut'ko, P.D. Polinomial'nye uravneniya i obratnye zadachi dinamiki upravlyaemykh sistem [Polynomial equations and inverse problems in dynamics of controlled systems]. Izvestiya RAN. Tekhn. Kibernetika, 1986, no. 1, pp. 125–133.

14. Gayduk, A.R. Teoriya i metody analiticheskogo sinteza sistem avtomaticheskogo upravleniya (polinomial'nykh podkhod) [Theory and methods of analytical synthesis of automatic control systems (polynomial approach)]. Moscow: FIZMATLIT, 2012. 360 p.

15. Tararykin, S.V., Tyutikov, V.V. Robastnoe modal'noe upravlenie dinamicheskimi sistemami [Robust modal control of dynamic systems]. Izvestiya RAN. Avtomatika i telemekhanika, 2002, no. 5, pp. 41–55.

16. Mironovskiy, L.A., Solov'ev, T.N. Analiz i sintez modal'no-sbalansirovannykh sistem [Analysis and synthesis of modally balanced systems]. A i T, 2013, no. 4, pp. 59–79.

17. Biryukov, D.S., Dudarenko, N.A., Ushakov, A.V. Kontrol' vyrozhdeniya dinamicheskikh sistem: gramiannyy podkhod [Degeneracy Control of Dynamical Systems: Gramian Approach]. Izvestiya vuzov. Priborostroenie, 2013, no. 4, pp. 34–37.

18. Oder, R., McFarlen, D. Balanced Canonical Forms for Minimal System: A Normalized Coprime Factor Approach. Linear Algebra Appl, 1989, vol. 122–124, pp. 23–64.

19. Moore, B.C. Principal Component Analysis in Linear System: Controllability, Observability and Model Reduction. IEEE Trans. Automat. Control, 1981, V.AC-26, pp. 17–32.

20. Lavrent'ev, M.M. O nekotorykh nekorrektnykh zadachakh matematicheskoy fiziki [On some ill-posed problems of mathematical physics]. Novosibirsk: Izdatel'stvo Sibirskogo otdeleniya AN SSSR, 1962. 92 p.

21. Tikhonov, A.N., Arsenin, V.Ya. Metody resheniya nekorrektnykh zadach [Methods for solving ill-posed problems]. Moscow: Nauka. Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1979. 285 p.

22. Rozenvasser, E.N. Yusupov, R.M. Chuvstvitel'nost' sistemy upravleniya [Sensitivity of control system]. Moscow: Nauka. Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1981. 464 p.

Key words in Russian: 
двухканальная САУ, транспортирование материала, грамианный метод, полиномиальный регулятор, робастная система управления
Key words in English: 
two-channel ACS, material transportation, Gramian method, polynomial regulator, robust control system
The DOI index: 
10.17588/2072-2672.2023.4.054-062
Downloads count: 
29