Abstract
The method of increasing the efficiency of the computational procedure for determining an optimal control of the temperature field of load-bearing structures of autonomous objects is proposed. Optimization of temperature distributions using controlled heat sources ensures the reduction of the temperature component of the measurement information error, which comes from heat-releasing information measuring systems placed on the structure. As an example, a supporting structure in the form of a rectangular isotropic prism is analyzed. The computational procedure uses a finite element mathematical model of the optimization object in the ANSYS software environment.
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References
Livshits, M., Derevyanov, M., Kopytin, S.: Distributed control of temperature regimes of structural elements of autonomous objects. Materials of the XIV Minsk International Forum on Heat and Mass Transfer, Minsk, V. 1. Part 1. pp. 719–722. [in Russian] (2012)
Rapoport, E.: Alternance Method in Applied Optimization Problems. Moscow. Nauka, 2000, 335 p. [in Russian] (2000)
Livshitc, M., Sizikov, A.: Multi-criteria optimization of refinery. In: EPJ Web of Conferences. Thermophysical Basis of Energy Technologies 2015. vol. 110. https://doi.org/10.1051/epjconf/201611001035 (2016)
Borodulin, B., Livshits, M.: Optimal control of temperature modes of the instrumental constructions of autonomous objects. In: EPJ Web of Conferences. Volume 110, Thermophysical Basis of Energy Technologies (2016)
Borodulin, B., Livshits M., Korshikov S.: Optimization of temperature distributions in critical cross-sections of load-bearing structures of measurement optical systems of autonomous objects. MATEC Web of Conferences. Volume 92, Thermophysical Basis of Energy Technologies (TBET-2016) Tomsk, Russia, October 26–28 (2016)
Butkovskii, A.: Theory of Optimal Control of Distributed-Parameter Systems. Moscow: Nauka, 1965, 474 p. [in Russian] (1965)
Lions, J.: Control of Distributed Singular Systems. Gauthier-Villars, Paris, 1985. 552 p. (1985)
Warga, J.: Optimal Control of Differential and Functional Equations. Academic Press, New York, London, 1972. xiii + 531 p. (1972)
Di Loreto, M., Damak, S., Eberard, D., Brun, X.: Approximation of linear distributed parameter systems by delay systems. Automatica, pp. 162–68. https://doi.org/10.1016/j.automatica.2016.01.065 (2016)
Felgenhauer, U., Jongen, H.Th., Twilt, F., Weber, G.: Semi-infinite optimization: structure and stability of the feasible set. J. Optim. Theory Appl., 3, 529–452. (1992)
Rapoport, E.Y.: Optimal Control of Distributed-Parameter Systems. Moscow:Â Vysshaya Shkola, 2009, 677 p. [in Russian] (2009)
Pleshivtseva, Y., Rapoport, E.: Parametric optimization of systems with distributed parameters in problems with mixed constraints on the final states of the object of control. J. Comput. Syst. Sci. Int. 57, 723 (2018). https://doi.org/10.1134/S1064230718050118
Rapoport, E., Pleshivtseva, Y.: Optimal control of nonlinear objects of engineering thermophysics. Optoelectron. Instrument. Proc. 48, 429 (2012). https://doi.org/10.3103/S8756699012050019
Chichinadze, V.: Solving non-convex nonlinear optimization problems. Nauka, Moscow 1983, 256 p. [in Russian] (1983)
Gill, F., Murray, W., Wright, M.: Practical optimization. Academic Press, New York, 1981. 509Â pp. (1981)
Li, R., Liu, W., Ma, H., Tang, T.: Adaptive finite-element approximation for distributed elliptic optimal control problems. SIAM J. Contr. Optim., 4, 1244–1265 (2003)
Murat, F., Tartar, L.: On the control of the coefficients in partial equations. SIAM J. Contr. Optim., 4, 1244–1265 (2003)
Lian, T., Fan, Z., Li, G.: Lagrange optimal controls and time optimal controls for composite fractional relaxation systems. Adv Differ Equ. 1, 233. https://doi.org/10.1186/s13662-017-1299-7. (2017)
Felgenhauer, U.: Structural properties and approximation of optimal controls. Nonlinear Anal. 3, 1869–1880 (2001)
Buttazzo, G., Kogut, P.: Weak optimal controls in coefficients for linear elliptic problems. Rev. Mat. Complut. 24, 83–94 (2018)
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The work was supported by the Russian Foundation for Basic Research projects No. 17-08-00593.
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Livshits, M.Y., Nenashev, A.V., Borodulin, B.B. (2020). Efficient Computational Procedure for the Alternance Method of Optimizing the Temperature Regimes of Structures of Autonomous Objects. In: Kravets, A., Bolshakov, A., Shcherbakov, M. (eds) Cyber-Physical Systems: Industry 4.0 Challenges. Studies in Systems, Decision and Control, vol 260. Springer, Cham. https://doi.org/10.1007/978-3-030-32648-7_7
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