Yu.P. Korniushin – Dr.Sc. (Eng.), Professor, 

Kaluga branch of the Bauman MSTU

E-mail: theroland@yandex.ru

The problem of synthesis of controllers forming control is considered, providing tracking of the object phase coordinates for an arbitrarily changing signal for a class of nonlinear control objects. The aim of the work is to develop a new method for the synthesis of physically feasible controllers for servo systems for a class of nonlinear control objects forming feedback control. The results: a synthesis algorithm is proposed that includes: 1. Linearization of the dynamics equation of an object according to the Newton – Kantorovich scheme. 2. Parameterization of the quality functional and linearized equations describing the dynamics of the object. Parameterization is performed using the theory of matrix operators. 3. Finding the optimal program control over a certain time interval, as a function depending on the initial state of the object and the signal being monitored. The synthesis of optimal program control is based on the necessary conditions for the minimum of the Lagrange function. 4. Defrosting the initial and final state of the control object, the formation of the controller control algorithm and the organization of the iterative process using a specific Newton – Kantorovich scheme. The proposed algorithm for solving the problem allows for the class of systems with analytical nonlinearities to build a controller that works in real time. The practical significance lies in the fact that the proposed algorithm can be used in the design of systems that automatically monitor the frequency and phase of input oscillations in radio receivers, systems for automatically tracking the temporal position of radio and video pulses in radar, radio navigation, radio control, sighting systems, goniometric tracking systems, designed to track targets, track artificial Earth satellites or other near space objects, etc.

1. Krasovskii N.N. Teoriya upravleniya dvizheniem. Lineinye sistemy. M.: Nauka. 1968. 476 s. (in Russian)
2. Boltyanskii V.G. Matematicheskie metody optimalnogo upravleniya. M: Nauka. 1969. 408 s. (in Russian)
3. Braison A., Kho Yu-Shi Prikladnaya teoriya optimalnogo upravleniya. M.: Mir. 1972. 544 s. (in Russian)
4. Aleksandrov V.V., Boltyanskii V.G., Lemak S.S., Parusnikov N.A., Tikhomirov V.M. Optimalnoe upravlenie dvizheniem. M.: FIZMATLIT. 2005. 376 s. (in Russian)
5. Gaiskii V.A., Egupov N.D., Kornyushin Yu.P. Primenenie funktsii Uolsha v sistemakh avtomatizatsii nauchnykh issledovanii. Kiev: Naukova dumka. 1993. 212 s. (in Russian)
6. Kornyushin Yu.P., Egupov N.D., Kornyushin P.Yu. Identifikatsiya nelineinykh ob’ektov i sistem upravleniya s ispolzovaniem apparata matrichnykh operatorov. Inzhenernyi zhurnal: nauka i innovatsii. 2014. № 6. URL = http://engjournal.ru/catalog/appmath/hidden/1315.html (data obrashcheniya: 12.09.2019). (in Russian)
7. Pupkov K.A., Egupov N.D. Metody inzhenernogo sinteza slozhnykh sistem upravleniya: analiticheskii apparat, algoritmy prilozheniya v tekhnike. Ch. II. Vychislitelno-analiticheskii eksperiment: apparat matrichnykh operatorov i vychislitelnye tekhnologii. M.: Izd-vo MGTU im. N.E. Baumana. 2012. 416 s. (in Russian)
8. Lapin S.V., Egupov N.D. Teoriya matrichnykh operatorov i ee prilozhenie k zadacham avtomaticheskogo upravleniya. M.: Izd-vo MGTU im. N.E. Baumana. 1997. 496 s. (in Russian)
9. Kornyushin Yu.P., Melnikov D.V., Egupov N.D., Kornyushin P.Yu. Issledovanie i raschet parametrov elementov sistemy regulirovaniya chastoty vrashcheniya rotora turbiny s uchetom parametricheskoi neopredelennosti matematicheskoi modeli. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki. 2014. № 1. S. 78–93. (in Russian)
10. Kornyushin Yu.P., Melnikov D.V., Egupov N.D., Kornyushin P.Yu. Sintez dopolnitelnogo regulyatora dlya stabilizatsii uglovoi skorosti rotora parovoi turbiny. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki. 2015. № 5. S. 100–112. (in Russian)