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The problem of control of rod heating process with nonseparated conditions at intermediate moments of time

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of control of rod heating process by changing the temperature along the rod whose ends are thermally insulated is considered. It is assumed that, along with the classical boundary conditions, nonseparated multipoint intermediate conditions are also given. Using the method of separation of variables and methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions, a constructive approach is proposed to build the sought function of temperature control action. A necessary and sufficient condition is obtained, which the function of the distribution of the rod temperature must satisfy, so that under any feasible initial, nonseparated intermediate, and final conditions, the problem is completely controllable. As an application of the proposed approach, control action with given nonseparated conditions on the values of the rod temperature distribution function at the two intermediate moments of time is constructed.
Rocznik
Strony
481--493
Opis fizyczny
Bibliogr. 21 poz., wzory
Twórcy
  • Institute of Mechanics of the National Academy of Sciences of Armenia, Yerevan State University, Armenia
Bibliografia
  • [1] A.G. Butkovskii: Control Methods for Systems with Distributed Parameters. Nauka, 1975 (in Russian).
  • [2] A.G Butkovskii, S.A Malyi, and Yu.N. Andreev: Optimal Control of Metal Heating. Moscow, Metallurgy, 1972 (in Russian).
  • [3] A.I. Egorov: Optimal Control of Thermal and Diffusion Processes. Nauka, 1978 (in Russian).
  • [4] A.I. Egorov and L.N. Znamenskaya: Introduction to the Theory of Control of Systems with Distributed Parameters. Textbook, Saint Petersburg, LAN, 2017 (in Russian).
  • [5] E.Ya. Rapoport: Structural Modeling of Objects and Control Systems with Distributed Parameters. Higher School, 2003 (in Russian).
  • [6] A.N. Tikhonov and A.A. Samarskii: Equations of Mathematical Physics. Nauka, 1977 (in Russian).
  • [7] V.I. Ukhobotov and I.V. Izmest’ev: A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source. Trudy Instituta Matematiki i Mekhaniki, UrO RAN, 25(1), (2019), 297-305 (in Russian), DOI: 10.21538/0134-4889-2019-25-1-297-305.
  • [8] V.I. Ukhobotov and I.V. Izmest’ev: The problem of controlling the proces of heating the rod in the presence of disturbance and uncertainty. IFAC Papers OnLine, 51(32), (2018), 739-742, DOI: 10.1016/j.ifacol.2018.11.458.
  • [9] V.I. Butyrin and L.A. Fylshtynskyi: Optimal control of the temperature field in the rod when changing the control zone programmatically. Applied Mechanics, 12(84), (1976), 115-118 (in Russian).
  • [10] M.M. Kopets: Optimal control over the process of heating of a thin core. Reports of the National Academy of Sciences of Ukraine, 7, (2014), 48-52 (in Ukrainian), http://dspace.nbuv.gov.ua/handle/123456789/87951.
  • [11] N.V. Gybkina, D.Yu. Podusov, and M.V. Sidorov: The optimal control of a homogeneous rod final temperature state. Radioelectronics and Informatics, 2 (2014), 9-15 (in Russian).
  • [12] E.Y. Vedernikova and A.A. Kornev: To the problem of rod heating. Moscow Univ. Math. Bull., 69, (2014), 237-241, DOI: 10.3103/S0027132214060023.
  • [13] J.F. Bonnans and P. Jaisson: Optimal control of a parabolic equation with time-dependent state constraints. SIAM Journal on Control and Optimization, 48(7), (2010), 4550-4571.
  • [14] A. Lapin and E. Laitinen: Iterative solution of mesh constrained optimal control problems with two-level mesh approximations of parabolic state equation. Journal of Applied Mathematics and Physics, 6, (2018), 58-68, DOI: 10.4236/jamp.2018.61007.
  • [15] K. Kunisch and L. Wang: Time optimal control of the heat equation with pointwise control constraints. ESAIM: Control, Optimisation and Calculus of Variations, 19(2), (2013), 460-485, http://eudml.org/doc/272753.
  • [16] J.M. Lemos, L. Marreiro, and B. Costa: Supervised multiple model adaptive control of a heating fan. Archives of Control Sciences, 18(1), (2008), 5-16.
  • [17] S.H. Jilavyan, E.R. Grigoryan, and A.Zh. Khurshudyan: Heating control of a finite rod with a mobile source. Archives of Control Sciences, 31(2), (2021), 417-430, DOI: 10.24425/acs.2021.137425.
  • [18] V.R. Barseghyan: Control problem of string vibrations with inseparable multipoint conditions at intermediate points in time. Mechanics of Solids, 54(8), (2019), 1216-1226. DOI: 10.3103/S0025654419080120.
  • [19] V.R. Barseghyan: Optimal control of string vibrations with nonseparate state function conditions at given intermediate instants. Automation and Remote Control, 81(2), (2020), 226-235, DOI: 10.1134/S0005117920020034.
  • [20] V.R. Barseghyan: Control of Compound Dynamic Systems and of Systems with Multipoint Intermediate Conditions. Nauka, 2016 (in Russian).
  • [21] V.R. Barseghyan and T.V. Barseghyan: On an approach to the problems of control of dynamic system with nonseparated multipoint intermediate conditions. Automation and Remote Control, 76(4), (2015), 549-559, DOI: 10.1134/S0005117915040013.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cca52ec0-ab45-4814-a1d0-cceebbab15ea
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