UDC 519.622
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2 Institute of Control Systems, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
 vugarhashimov@gmail.com
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OPTIMIZING THE ARRANGEMENT OF LUMPED SOURCES AND MEASUREMENT
POINTS OF PLATE HEATING PROCESS
Abstract. Using the example of control of the heating process of a thin plate, the authors propose an approach for the synthesis of lumped controls of objects with distributed parameters. At the same time, the locations of both lumped controls and control points are optimized. Formulas for the components of the functional gradient are obtained for the optimized parameters. They allow using first-order optimization methods for numerical solution of the problem.
Keywords: heating, thin plate, synthesis of control, point source, measurement point, non-local condition, gradient projection method.
FULL TEXT
REFERENCES
- Utkin V.I. Sliding modes in optimization and control problems [in Russian]. Moscow: Nauka, 1981. 368 p.
- Kuliev S.Z. Synthesis of zone controls for one heating problem with delay in unseparated boundary conditions. Kibernetika i sistemnyj analiz. 2018. Vol. 54, N 1. P. 124–136.
- Ray W.H. Advanced process control. McGraw-Hill Book Company, 1980. 376 p.
- Butkovsky A.G. Control methods for distributed systems [in Russian]. Moscow: Nauka, 1975. 568 p.
- Egorov A.I. Fundamentals of control theory [in Russian]. Moscow: Fizmatlit, 2004. 504 p.
- Sergienko I.V., Deineka V.S. Optimal control of distributed systems with conjugation conditions. New York: Kluwer Acad. Publ., 2005. 383 p.
- Vasiliev F.P. Optimization methods [in Russian]. Moscow: Factorial Press, 2002. 824 p.
- Aida-zade K.R., Abdullaev V.M. An approach to the synthesis of process control with distributed parameters. Avtomatika i telemekhanika. 2012. N 9. P. 3–19.
- Tikhonov A.N., Samarskiy A.A. Equations of mathematical physics [in Russian]. Moscow: Nauka, 1977. 735 p.
- Nakhushev A.M. Loaded equations and their application [in Russian]. Moscow: Nauka, 2012. 232 p.
- Abdullaev V.M., Aida-zade K.R. A numerical method for solving loaded non-local boundary value problems for ordinary differential equations. Zhurn. vychisl. matematiki i mat. fiziki. 2014. Vol. 54, N 7. P. 1096–1109.
- Aida-zade K.R. An approach for solving nonlinearly loaded problems for linear ordinary differential equations. Proceeding of the Institute Mathematics and Mechanics NAS Azerbaijan. 2018. Vol. 4, N 2. P. 338–350.
- Alikhanov A.A., Berezgov A.M., Shkhanukov-Lafishev M.Kh. Boundary-value problems for some classes of loaded differential equations and difference methods for their numerical implementation. Zhurn. vychisl. matematiki i mat. fiziki. 2008. Vol. 48, N 9. P. 1619–1628.
- Samara A.A. Theory of Difference Schemes [in Russian]. Moscow: Nauka, 1989. 616 p.
- Aida-zade K.R., Bagirov A.G. On the problem of placing oil wells and managing their flow rates. Avtomatika i Telemekhanika. 2006. N 1. P. 52–62.
