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Article title ON IDENTIFIABILITY OF CLOSED-LOOP LINEAR DYNAMICAL SYSTEMS UNDER NORMAL OPERATING CONDITIONS
Authors E.Yu. Zybin
Section SECTION III. AUTOMATION AND CONTROL
Month, Year 04, 2015 @en
Index UDC 681.5.015.4
DOI
Abstract The work is devoted to the study of identifiability conditions of closed-loop linear dynamic systems under normal operating conditions. It is known that many of the theoretical results in the identification of open-loop systems do not apply to closed-loop systems with linear feedback. This is due to the unidentifiability and convergence problems closed-loop systems. The convergence problem is solved by modifying the method of identification in order to take into account correlations of disturbances of input and output signals. The unidentifiability problem without a priori information about the system or disturbances is solved either by supplying additional external signals or by changes in regulator. Both methods lead to a change in system processes, so the reliable identification of closed-loop systems under normal operating conditions is possible only when the nominal input is not zero and satisfies certain requirements. This statement is based on studies control systems without precompensator. In such systems, the input can be arbitrary, which makes it possible in some cases successfully identify system without making any changes to the control system. This paper investigates the identification problem of closed-loop systems containing a regulator in the feedback loop, and a precompensator in the direct loop. The conditions of solvability of the identification problem, identifiability conditions and formulas describing the set of all unidentifiable models obtained. It is shown that in the general case, when the control system contains precompensator, reliable identification under normal operating conditions may be unsolvable in principle irrespective of the properties of the input signal.

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Keywords Identifiability; identification; closed-loop systems; normal operating conditions.
References 1. Raybman N.S., Chadeev V.M. Oblasti primeneniya razlichnykh metodov identifikatsii [The field of application of various methods for the identification], Avtomatika i telemekhanika [Automation and Remote Control], 1969, No. 6, pp. 203-204.
2. Shardt Y., Huang B. Closed-loop identification condition for ARMAX models using routine operating data, Automatica, 2011, Vol. 47, No. 7, pp. 1534-1537.
3. Gustavsson I., Ljung L., Soderstrom T. Identification of processes in closed loop – identifiability and accuracy aspects, Automatica, 1977, Vol. 13, No. 1, pp. 59-75.
4. Rotach V.Ya. Po povodu rabot, svyazannykh s identifikatsiey ob"ektov v usloviyakh ikh normal'nogo funktsionirovaniya [Regarding the work related to identification of objects in terms of their normal functioning], Avtomatika i telemekhanika [Automation and Remote Control], 1969, No 6, pp. 201-202.
5. Eykhoff P. Trends and progress in system identification: IFAC Series for Graduates, Research Workers & Practising Engineers. Burlington. Elsevier Science. 2014, 418 р.
6. Hjalmarsson H. From experiment design to closed-loop control, Automatica, 2005, Vol. 41, No. 3, pp. 393-438.
7. Van den Hof, P.M.J, and R.J.P. Schrama. Identification and control - closed-loop issues, Automatica.,1995, Vol. 31, No. 12, pp. 1751-1770.
8. Kos'yanchuk V.V. Kontrol' i diagnostirovanie podsistem v zamknutom konture upravleniya [Control and diagnostic subsystems in closed-loop control], Izvestiya Rossiyskoy akademii nauk. Teoriya i sistemy upravleniya [Journal of Computer and Systems Sciences International], 2004, No. 1, pp. 67-76.
9. Zybin E.Yu., Kos'yanchuk V.V. Analiticheskiy sintez mnogosvyaznykh otkazoustoychivykh sistem upravleniya s uproshchennoy skhemnoy realizatsiey [Analytical synthesis of multiply-connected fault-tolerant control systems with a simplified circuit implementation], Izvestiya Rossiyskoy akademii nauk. Teoriya i sistemy upravleniya [Journal of Computer and Systems Sciences International], 2010, No. 1, pp. 108-117.
10. Kos'yanchuk V.V., Konstantinov S.V., Kolodyazhnaya T.A., Red'ko P.G., Kuznetsov I.P. Perspektivnyy oblik otkazoustoychivykh tsifrovykh sistem upravleniya manevrennykh LA [Promising the appearance of fault-tolerant digital control systems maneuverable LA], Polet. Obshcherossiyskiy nauchno-tekhnicheskiy zhurnal [Polet. All-Russian scientific-technical journal], 2010, No. 2, pp. 20-27.
11. Kos'yanchuk V.V., Glasov V.V. Sintez algoritmov rekonfiguratsii sistem upravleniya invariantnykh k rezhimam poleta [Synthesis of reconfiguration algorithms of invariant control systems to flight modes], Aviakosmicheskoe priborostroenie [Aerospace Instrumentation], 2010, No. 11, pp. 18-26.
12. Zybin E.Yu. Ob identifikatsii i modelirovanii nekotorykh diskretnykh sistem [On the identification and modeling of some discrete systems], Sbornik trudov Vtoroy traditsionnoy vserossiyskoy molodezhnoy letney shkoly "Upravlenie, informatsiya i optimizatsiya" [Proceedings of the Second traditional all-Russia youth summer school "Control, information and optimization"]. Moscow: IPU RAN, 2010, pp. 64-74.
13. Zybin E.Yu., Misrikhanov M.Sh., Ryabchenko V.N. O reshenii zadachi identifikatsii lineynykh diskretnykh sistem metodom kanonizatsii [On the solution of the problem of identification of linear discrete systems by the method of canonization], Vestnik IGEU [Vestnik IGEU], 2005, No. 5, pp. 192-196.
14. Zybin E.Yu., Kos'yanchuk V.V. Ob absolyutnoy prognoziruemosti lineynykh avtonomnykh diskretnykh dinamicheskikh sistem v prostranstve sostoyaniy [About absolute predictability of the linear Autonomous discrete dynamical systems in state space], Aktual'nye voprosy issledovaniy v avionike: teoriya, obsluzhivanie, razrabotki: sb. tezisov dokl. II Vserossiyskoy nauchno-prakticheskoy konferentsii «AVIATOR», Voronezh, 11-13 fevralya 2015 g [Current issues of research in avionics: theory, maintenance, development: book of abstracts II all-Russian scientific-practical conference "the AVIATOR", Voronezh, 11-13 February 2015]. Voronezh: VUNTs VVS «VVA», 2015, pp. 127-130.
15. Ljung L. System identification: theory for the user. Upper Saddle River, N.J., Prentice Hall, 1999, 609 р.
16. Ljung L. Prediction error estimation methods, Circuits, systems, and signal processing, 2002, Vol. 21, No. 1, pp. 11-21.
17. Van der Veen G., van Wingerden J.-W., Bergamasco M., Lovera M., Verhaegen M. Closed-loop subspace identification methods: an overview, IET Control Theory & Applications, 2013, Vol. 7, No. 10, pp. 1339-1358.
18. Chiuso A.; Giorgio P. Prediction error vs. subspace methods in closed-loop identification, Proc. of the 16th IFAC World Congress, Czech Republic, Prague 2005, pp. 84.
19. Gevers M., Bombois X., Hildebrand R., Solari G. Optimal experiment design for open and closed-loop system identification, Communications in Information and Systems, 2011, Vol. 11, pp. 197-224.
20. Qian J., Dufour P., Nadri M., Morosan P.D. Closed loop optimal experiment design for on-line parameter estimation, Proc. of the 13th European Control Conference (ECC). Strasbourg, France, 2014, pp. 1813-1818.
21. Nguyen V.V., Wood E.F. Review and unification of linear identifiability concepts, SIAM Review, 1982, Vol. 24, No. 1, pp. 34-51.
22. Jorgensen S.B., Lee, J.H. Recent advances and challenges in process identification, Proc. of the Sixth International Conference on Chemical Process Control, Tucson, 2002, pp. 55-74.
23. Petrov B.H. Teryaev E.D., Shamrikov B.M. Usloviya parametricheskoy identifitsiruemosti upravlyaemykh ob"ektov v razomknutykh i zamknutykh avtomaticheskikh sistemakh [Conditions for parametric identifiability of managed objects in open-loop and closed-loop automatic systems], Tekhnicheskaya kibernetika [Engineering Cybernetics], 1977, No. 2, pp. 160-175.
24. Zybin E.Yu., Misrikhanov M.Sh., Ryabchenko V.N. O minimal'noy parametrizatsii resheniy lineynykh matrichnykh uravneniy [Minimal parametrization of solutions of linear matrix equations], Vestnik IGEU [Vestnik IGEU], 2004, No. 6, pp. 127-131.
25. Zybin E.Yu., Kos'yanchuk V.V. Sintez sistemy upravleniya mnogosvyaznogo ob"ekta na osnove tekhnologii vlozheniya [The synthesis of control systems multivariable object-based technology attachment], Avtomatika i telemekhanika [Automation and Remote Control], 2002, No. 8, pp. 22-36.
26. Bukov V.N., Ryabchenko V.N., Zybin E.Yu. Deliteli nulya proizvedeniya matrits i ikh ispol'zovanie pri issledovanii bilineynykh uravneniy [Zero divisors of a product of matrices and their use in the study of bilinear equations], Vestnik. Kievskogo un-ta. (Fiziko-matematicheskie nauki) [Bulletin of Kiev University. (Physics and mathematics)], 2004, Issue 2, pp. 24-33.

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