|Article title||AUTOMATION OF NONLINEAR MULTYVARIABLE TECHNOLOGICAL PROCESSES BASED ON NONLINEAR-QUADDRATIC FUNCTIOAL|
|Authors||A.R. Gaiduk, E.A. Plaksienko|
|Section||SECTION I. AUTOMATION AND CONTROL|
|Month, Year||05, 2016 @en|
|Abstract||Many technological and industrial processes are multivariable as they are characterized several controlled variable and several control actions – controls. The problem of automation of such processes is complicated that they are nonlinear and are described by the several nonlinear equations, and requirements to the differe nce automated variables can be various. In view of the extremely big variety of the nonlinearities the problem of construction of the automation systems for the nonlinear multivariable processes is very difficult. The article is devoted to develop of the analytical design method of the optimal automation algorithms of the nonlinear multivariable technological processes. The method development is based on the idea of academician A.A. Krasovsky – to use uncertain qualities criteria, some functions and parameters of which are appointed during the decision of the optimization problem. For the decision of the problem the method of transformation of the set nonlinear equations of an automation system are involved in special, Jordan controlled form also. This form allows analytically finding, socalled, linearization control which the nonlinear equations of the process, without loss of accuracy of the description, become linear and the initial uncertain nonlinear-quadratic functional passes in usual the quadratic criterion. The final kind of optimal algorithm of automation is defined as a result of the decision with help MATLAB of known Riccati equation. The basic scientific results of this article are conditions of resolvability of the optimal automation problem of multivariable nonlinear technological process both at absence of connections between subsystems, and at presence of these connections. The received conditions consist in restrictions on derivatives of the automation process nonlinearities. The conditions of asymptotic stability of the steady-state process of the multivariable nonlinear automation systems both in domain and global are found also. The developed design method can be applied to construction of the systems of automation of chemical, power and other technological processes and also processes of the special purpose, because the nonlinear equations of many of these processes can be converted to the Journal controlled form. The method allows providing desirable properties of optimal nonlinear automation multivariable systems by a choice of the corresponding values of the parameters of uncertain nonlinear-quadratic criteria.|
|Keywords||Technological process; multivariable; nonlinearity; automation; Jordan controlled form; design; uncertain nonlinear-quadratic criteria; stability; transient.|
|References||1. Voznesenskiy I.N. O regulirovanii mashin c bol'shim chislom reguliruemykh parametrov [On regulation of machines with a large number of control parameters], Avtomatika i telemekhanika [Automation and Remote Control], 1938, No. 4, pp. 4-5.
2. Rotach V.Ya. Teoriya avtomaticheskogo upravleniya teploenergeticheskimi protsessami: Uchebnik dlya vuzov [Theory of automatic control of heat power processes: Textbook for high schools]. Moscow: Energoatomisdat, 1985, 296 p.
3. Glazunuv V. Ph., Prokushev S.V. Avtomatizatsiya oborudovaniya dlya nepreryvnoi obrabotki tekstil'nykh materialov [Automation of equipment for the continuous treatment of textile materials]. Ivanovo: IGEU Publ., 2002, 348 p.
4. Gayduk A.R. Ob upravlenii mnogomernymi ob''ektami [On the control of multivariable plants], Avtomatika i telemekhanika [Automation and Remote Control], 1998, No. 12, pp. 22-37.
5. Tyan V.K. Reduktsiya sinteza mnogomernykh lineinykh system upravleniya k sintezu odnomernykh s tipovym ob''ektom [The reduction of the synthesis of multivariable linear control systems to the synthesis of a one-dimensional typical plant]. Mekhatronica, avtomatizatsiya, upravlenie [Mechatronics, automation, control], 2008, No. 4, pp. 2-7.
6. Matveev A.S. From LQR design to nonconvex global optimization: homage to contribution and impact of V.A. Yakubovich. Proc. 1st Conference on Modeling, Identification, and Control of Nonlinear Systems, 2015, IFAC-Papers On Line, 48-11, 2015, pp. 551-556.
7. Neydorf R.A. Bivariate “Cut-Glue” approximation of strongly nonlinear mathematical models based on experimental data, SAE Int. J. Aerosp. 8(1): 2015, doi:10.4271/2015-01-2394. Available at: http://papers.sae.org/2015-01-2394.
8. Sovremennye metody upravleniya mnogosvyaznymi dinamicheskimi sistemami [Modern control techniques of multivariable dynamic systems], Ed. by A.A. Krasovskogo. Issue 2. Moscow: Energoatomisdat, 2003, 556 p.
9. Filimonov N.B. Problema kachestva processov upravleniya: smena optimizatsionnoi paradigmy [Problem of control processes quality: change of optimization paradigm] Mekhatronika, avtomatizatsiya, upravlenie [Mechatronics, automation, control], 2010, No. 12, pp. 2-10.
10. Adamiec-Wόjcik I., Brzozowska L. Homogenous transformations in dynamic of off-shore slender structures. Dynamical systems theory. Łόdź, December 2-5, Poland. 2013, pp. 307-316.
11. Kim P.D. Teoriya avtomaticheskogo upravleniya. T. 2. Mnogomernye, nelinei-nye, optimal'nye i adaptivnye sistemy [Multivariable, nonlinear, optimal and adaptive systems]. Moscow, Fizmatlit, 2004, 464 p.
12. Luk'yanov A.G., Utkin V.I. Metody svedeniya uravnenii dinamicheskikh sistem k regulyarnoi forme [Methods of transformation of dynamic systems equations to a regular form]. Avtomatika i telemekhanika [Automation and Remote Control], 1981, No. 4, pp. 5-13.
13. Gaiduk A.R. Teoriya i metody analiticheskogo sinteza sistem avtomaticheskogo upravleniya (Polinomial'nyi podkhod). [Theory and methods of analytical synthesis of automatic control systems (Polynomial approach)]. Moscow: Fizmatlit, 2012, 360 p.
14. Stojković N.M., Gaiduk A.R. Analytical design of quasilinear control systems, Facta Universitatis. Series: Automatic Control and Robotics, 2014, Vol. 13, No. 2, pp. 73-84.
15. Fradkov A.L., Andrievsky B.A., Anan'evskiy M.S. Passification based on synchronization of nonlinear systems under communication constraints and bounded disturbances, Automatica, 2015, Vol. 55, pp. 287-293.
16. Gaiduk A.R. Astatic control design for nonlinear plants on base of JCF, Transaction on Electrical and Electronic Circuits and Systems, 2013, Vol. 3, Nо 2, рр. 80-84.
17. Tsirlin A.M. Optimal'noe upravlenie tehnologicheskimi processami [Optimal control of technological processes]. Moscow: Energoatomisdat. 1986, 406 p.
18. Neydorf R.A. Syntheses of time quasi-optimal asymptotically stable control laws. SAE Technical Papers 2015-01-2481, 2015, doi:10.4271/2015-01-2481.
19. Gaiduk A.R., Plaksienko E.A., Shapovalov I.O. Optimal control based on Jordan controlled form. Proceedings of the 14th International Conference on Circuits, Systems, Electronics, Control & Signal Processing (CSECS '15). Selcuk University, Konya, Turkey. May 20-22, 2015, pp. 13-18.
20. Voevoda A.A., Shoba E.V. Stabilizatsiya trekhmassovoi sistemy: modal'nyi metod sinteza v prostranstve sostoyanii s nablyudatelem ponizhennogo poryadka [Stabilization of three-mass system: modal synthesis method in state space with a reduced order observer], Sbornik nauchnykh trudov NGTU [Collection of scientific papers of NSTU], 2010, No. 1 (59), pp. 25-34.
21. Gaiduk A.R., Plaksienko E.A., Kolokolova K.V. Sintez algoritmov upravleniya nelineinymi mnogomernymi ob''ektami na osnove UFZh [Synthesis of control algorithms for nonlinear multivariable plants based on JCF], Nauchnyi vestnik NGTU [Scientific Bulletin of NSTU], 2015, No. 2 (59), pp. 59-72. doi:10.17212/1814-1196.
22. Demidovich B.P. Lektsii po matematicheskoi teorii ustoichivosti. [Lectures on the mathematical theory of stability]. Moscow: Nauka, 1967, 472 p.
23. Gaiduk A.R., Plaksienko E.A. Optimal'noe po kvadratichnomu kriteriyu upravlenie nelineinymi sistemami [Optimal control of systems on nonlinear quadratic criterion]. Nauchnyi vestnik NGTU [Scientific Bulletin of NSTU], 2014, No. 4 (57), pp. 7-18.