Authors A. N. Popov
Month, Year 07, 2018 @en
Index UDC 681.51
DOI 10.23683/2311-3103-2018-7-143-154
Abstract Paper is devoted to the usage of synergetic control theory for synthesis of automatic tracking control systems. The tracking regulator should provide change of one of control object variables according to some temporary signal arriving on an input of a system and being a priori unknown function of time. At design of the majority of the tracking control systems the frequency methods of synthesis assuming the linear mathematical description of the control object are used. These methods allow to define structure and parameters of the linear compensating element which provides stability of a system and the set astaticism number on entrance influence. Such approach becomes ineffective if dynamics of a control object is significantly nonlinear. Research objective is development of analytical procedures of synthesis of the tracking regulators for the general class of nonlinear systems. Two approaches to holding a procedure of synergetic synthesis of the tracking regulators are presented in a paper. The first of them assumes calculation of derivatives of an entrance signal on time. The second approach is based on the idea by the current piecewise linear approximation of an entrance signal and synthesis of the asymptotic observer of coefficient of an inclination of the approximating straight line. In this case the tracking control system operates only with an entrance signal and its differentiation is not required. The offered approaches are illustrated by simple examples. For confirmation of theoretical researches computer modeling of the synthesized tracking control systems at various entrance signals is carried out. By their results it is possible to draw a conclusion that the offered approaches allow to synthesize the regulators capable to fulfill the setting influences of the general class of continuous functions of time and can form a theoretical basis for design of the tracking control systems for nonlinear dynamic objects.

Download PDF

Keywords Tracking control systems; synergetic feedback synthesis; asymptotic observer synthesis.
References 1. Akhmetzhanov A. A., Kochemasov A.V. Sledyashchie sistemy i regulyatory. ucheb. posobie [Tracking systems and regulators. textbook]. Moscow: Energoatomizdat, 1986, 286 p.
2. Barskiy A.G. Optiko-elektronnye sledyashchie sistemy: ucheb. posobie [Opto-electronic tracking systems: a tutorial]. Moscow: Universitetskaya kniga; Logos, 2009, 200 p.
3. Shubladze A.M., Popadyso V.E., Kuznetsov S.I., Krotov A.V., Gulyaev S.V., Ol'shvang V.R., Malakhov V.A. Bystrodeystvuyushchie sledyashchie PI-sistemy maksimal'noy stepeni ustoychivosti dlya upravleniya tekhnologicheskimi ob"ektami neftegazovoy otrasli [High-speed tracking PI-systems of maximum degree of stability for control of technological objects of oil and gas industry], Avtomatizatsiya, telemekhanizatsiya i svyaz' v neftyanoy promyshlennosti [Automation, telemechanization and communication in the oil industry], 2011, No. 8, pp. 3-6.
4. Nikiforov V.O., Luk'yanova G.V. Sledyashchaya sistema kombinirovannogo upravleniya [Tracking system of combined control], Nauchno-tekhnicheskiy vestnik Sankt-Peterburgskogo gosudarstvennogo universiteta informatsionnykh tekhnologiy, mekhaniki i optiki [Journal scientific and technical of St. Petersburg state University of information technologies, mechanics and optics], 2011, No. 6 (76), pp. 39-43.
5. Ivanchura V.I., Prokop'ev A.P. Optimizatsiya sledyashchey sistemy avtomaticheskogo upravleniya [Optimization of the tracking system of automatic control], Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva [Bulletin of the Siberian state aerospace University. academician M. F. Reshetnev], 2011, No. 5 (38), pp. 44-49.
6. Shapran A.A., Ustyugova A.A. Sintez sistemy upravleniya sledyashchim privodom povyshennoy tochnosti [Synthesis of control system of the tracking drive of the increased accuracy], Vestnik Ural'skogo gosudarstvennogo universiteta putey soobshcheniya [Bulletin of the Ural state University of railway engineering], 2013, No. 3 (19), pp. 45-49.
7. Lysov V.E., Sarantsev S.S. Sintez korrektiruyushchego zvena sledyashchego elektroprivoda podachi koordinatno-rastochnogo stanka dlya kompensatsii nelineynosti tipa «lyuft» v kinematicheskoy tsepi [Synthesis of the corrective link of the tracking electric drive of the coordinate boring machine for compensation of nonlinearity of the "backlash" type in the kinematic chain],Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriya: Tekhnicheskie nauki [.Bulletin of Samara state technical University. Series: Technical Sciences], 2012, No. 1 (33), pp. 148-155.
8. Bo Xiao, H.K. Lam, Ge Song, Hongyi Li Output-Feedback Tracking Control for Interval Type-2 Polynomial Fuzzy-Model-Based Control Systems, IEEE Transactions on Industrial Electronics., 2013, Vol. 60, No. 12, pp. 5830-5840.
9. Chang, Yeong-Chan. Robust tracking control for nonlinear MIMO systems via fuzzy approaches, Automatica, 2010, Vol. 36, No. 10, pp. 1535-1545.
10. Ivanchura V.I., Prokop'ev A.P., Emel'yanov R.T. Model' sledyashchey sistemy avtomaticheskogo upravleniya s nechetkim regulyatorom [Model of the tracking system of automatic control with fuzzy controller], Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva [Bulletin of the Siberian state aerospace University. academician M. F. Reshetnev], 2012, No. 3 (43), pp. 15-20.
11. Putov V.V., Zung Ch.A., Kuang F.K. Adaptivnaya elektromekhanicheskaya sledyashchaya sistema s dvukh- i trekhmassovymi nelineynymi uprugimi ob"ektami i neyronechetkim upravleniem [Adaptive Electromechanical tracking system with two- and three-mass nonlinear elastic objects and neuro-fuzzy control], Izvestiya SPbGETU «LETI» [Izvestiya Etu "LETI"], 2018, No. 5, pp. 21-24.
12. Reshetnikova G.N. Sledyashchaya sistema adaptivnogo upravleniya s prognoziruyushchey model'yu ponizhennogo poryadka [Tracking system of adaptive control with predictive mode of reduced order], Vestnik Tomskogo gosudarstvennogo universiteta [Bulletin of Tomsk state University], 2006, No. 290, pp. 237-240.
13. Mal'tsev G.N., Afonin G.I. Optimizatsiya parametrov adaptivnogo kontura sledyashchey sistemy avtomaticheskogo upravleniya na osnove analiza chastotnoy kharakteristiki [Optimization of parameters of the adaptive circuit of the automatic control tracking system based on the analysis of the frequency response], Izvestiya vysshikh uchebnykh zavedeniy. Priborostroenie [News of higher educational institutions. Instrument making], 2014, Vol. 57, No. 7, pp. 26-31.
14. Celentano L. Pseudo-PID robust tracking design method for a significant class of uncertain MIMO systems, in IFAC-PapersOnLine, 2017, Vol. 50, No. 1, pp. 1545-1552.
15. Celentano L., Basin M.V. An Approach to Design Robust Tracking Controllers for Nonlinear Uncertain Systems, in IEEE Transactions on Systems, Man, and Cybernetics: Systems (Early Access), 2018. DOI: 10.1109/TSMC.2018.2834908.
16. Kim S.H. H∞ Output-Feedback Tracking Control for Networked Control Systems, Mathematical Problems in Engineering. Vol. 2015. Article ID 724389, 10 p. Available at:
17. Kolesnikov A.A. Sinergeticheskaya teoriya upravleniya [Synergetic control theory]. Moscow: Energoatomizdat, 1994, 344 p.
18. Sovremennaya prikladnaya teoriya upravleniya: Sinergeticheskiy podkhod v teorii upravleniya [Modern applied control theory: Synergetic approach in control theory], ed. by A.A. Kolesnikova. Part 2. Taganrog: Izd-vo TRTU, 2000, 344 p.
19. Kolesnikov A.A. Sinergeticheskaya teoriya upravleniya: konceptsii, metody, tendencii razvitiya [Synergetic control theory: concepts, methods, and tendencies of development], Izvestiya TRTU [Izvestiya TSURE], 2001, No. 5 (23), pp. 7-27.
20. Kolesnikov A.A. Sinergeticheskaya konceptsiya sistemnogo sinteza: edinstvo processov samoorganizacii i upravleniya [Synergetic concept of system synthesis: unity of processes of self-organization and management] Izvestiya TRTU [Izvestiya TSURE], 2006, No. 6 (51), pp. 10-38.
21. Kolesnikov A.A., Veselov G.E., Popov A.N., Kolesnikov Al.A., Topchiev B.V., Mushenko A.S., Kobzev V.A. Sinergeticheskie metody upravleniya slozhnymi sistemami: mekhanicheskie i ehlektromekhanicheskie sistemy [Synergetic methods of control of complex systems: mechanical and Electromechanical systems]. 2nd ed. Moscow: Librokom, 2013, 304 p.
22. Kolesnikov A.A., Veselov G.E., Popov A.N., Kuz'menko A.A., Pogorelov M.E., Kondrat'ev I.V. Sinergeticheskie metody upravleniya slozhnymi sistemami: Ehnergeticheskie sistemy [Synergetic methods of management of complex systems: Energy systems]. 2nd ed. Moscow: Knizhnyy dom «LIBROKOM», 2013, 248 p.
23. Veselov G.E., Popov A.N., Radionov I.A. Ehnergosberegayushchee upravlenie asinhronnym tyagovym dvigatelem: sinergetichesky podkhod [Energy-saving control of asynchronous traction motor: synergetic approach], Mekhatronika, avtomatizaciya, upravlenie [Mechatronics, automation, control], 2013, No. 2, pp. 18-22.
24. Veselov G.E., Popov A.N., Radionov I.A. Sinergeticheskoe upravlenie asinkhronnym tyagovym elektroprivodom lokomotivov [Synergetic control of asynchronous traction electric drive of locomotives], Izvestiya RAN. Teoriya i sistemy upravleniya [Izvestiya RAS. Theory and control systems], 2014, No. 4, pp. 166-180.
25. Popov A.N., Radionov I.A., Mushenko A.S. Synergetic Design of Autopiloting Systems with Complex Optimization of Train Traction, Proceedings of 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems (MICNON 2015), June 24-26, 2015, Saint Petersburg, Russia, pp. 467-472.
26. Popov A.N. Sinergeticheskiy sintez regulyatorov dlya zadach generatsii kolebatel'nykh rezhimov v tekhnicheskikh sistemakh [Synergetic synthesis of controllers for the task of generation of oscillatory modes in engineering systems], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2012, No. 4 (129), pp. 156-162.
27. Popov A.N. Sinergeticheskiy sintez avtopilotov dlya zadach formirovaniya etalonnykh traektoriy dvizheniya v gorizontal'noy ploskosti [Sovremennaya nauka i innovatsii], 2016,
No. 4, pp. 29-36.

Comments are closed.