Vibrational Control of Objects with Distributed Parameters Using Hydrotreating of Motor Fuels as an Example
Using an industrial reactor of hydrotreating of motor fuels as an example dynamical features of models of systems with distributed parameters are studied. The model takes into consideration non-linear effects of absorbing hydrogen by liquid phase, adsorpt
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Vibrational Control of Objects with Distributed Parameters Using Hydrotreating of Motor Fuels as an Example Ali Gasan Nagiev, Firuza Allahkuli Aliyeva and Hasan Ali Nagiyev
Abstract Using an industrial reactor of hydrotreating of motor fuels as an example dynamical features of models of systems with distributed parameters are studied. The model takes into consideration non-linear effects of absorbing hydrogen by liquid phase, adsorption, desorption and chemical reactions on the surface of a catalyst. On the basis of abundant information material of computational model experiments representing evolution of distribution functions over the longitudinal coordinate of the reactor high sensitivity of such systems to vibrational modes of control is revealed. A mode is detected which represents the formation of “a bean” of wanes, its propagation along the reactor and repetition with a frequency depending on kinetic parameters of physical laws taken into account. An efficiency function allowing to evaluate the results of industrial systems with distributed parameters with respect to impulse and vibrational control strategies is proposed. Keywords Dynamical systems with distributed parameters · Oscillating control · Hydrodesulfurization process · Optimization
19.1 Introduction Dynamical systems represented by differential equations in partial derivatives constitute a class of controlled objects which are full of specific features in dynamics. Industrial systems of continuous production are usually employed in stationary conditions with stabilization of some thermal and/or concentration fields following the spatial coordinates. By prescribed integral criteria optimal modes are sought as stationary solutions of differential equations written both in time and space. Among the A.G. Nagiev · F.A. Aliyeva Sumgayit State University, block 43, Sumqayit, Azerbaijan H.A. Nagiyev (B) The Institute of Mathematics and Mechanics of ANAS, 9 F.Agayev Str., 370141 Baku, Azerbaijan e-mail: [email protected] © Springer Science+Business Media Singapore 2017 J. Xu et al. (eds.), Proceedings of the Tenth International Conference on Management Science and Engineering Management, Advances in Intelligent Systems and Computing 502, DOI 10.1007/978-981-10-1837-4_19
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first researches in which attention was drawn to the possibility of attaining greater optimality from using artificially of attaining greater optimality from using artificially generated vibrations along both spatial coordinates can be mentioned papers [2, 8, 12]. Then this conception began to be used very widely [6, 7, 9]. Propagating as vibrations control actions which periodically change in time create a certain steady kind of distribution of state parameter along spatial coordinates of an object. In transient modes these distributions, analysis of nature of their evolution are the principal mechanisms of processes. Responses of objects with distributed parameters to external actions are rather specific. At the same time, one can single out certain
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