Solving the problem of minimax closed-loop control of liquid-propellant launch vehicle fuel consumption control

Abstract

The paper provides mathematical formalization and a method of solving the problem of minimax (guaranteed) closed-loop terminal control of fuel consumption of a liquid-propellant launch vehicle power plant. The initial discrete-continuous nonlinear model of the controlled object is linearized along the given reference phase path and is approximated by a linear discrete-time multistep dynamical system. The approximated system includes the state vector, the control vector and the disturbance vector that defines the error of formation of the approximated model. Taking into account the geometrical constrains of control and disturbance vectors in the approximated system, we formulate the main problem of minimax closed-loop terminal control of propellant consumption of the launch vehicle’s propulsion system. This problem consists in solving a number of auxiliary tasks of minimax open-loop terminal control. To solve each of these tasks we use an instrument of development and analysis of generalized attainability domains of the approximated linear discrete dynamical system. These techniques are implemented by modifying the general recurrent algebraic method. To solve the problems under consideration we propose an approach and an appropriate numerical algorithm that is reduced to the implementation of a finite sequence of only one-step algebraic and optimization operations. The efficiency of the proposed approach to solving the problem under consideration is demonstrated and verified by a computer simulation example. This simulation example consists in controlling the process of propellant consumption for “Soyuz-2.1b” launch vehicle’s third stage propulsion system.

About the authors

A. F. Shorikov

Ural Federal University

Author for correspondence.
Email: a.f.shorikov@urfu.ru

Doctor of Science (Phys. & Math.), Professor

Russian Federation

V. I. Kalev

Scientific and Production Association of Automatics named after Academician N.A. Semikhatov

Email: persona@npoa.ru

Leading Engineer of the Department of Motion Control

Russian Federation

References

  1. Petrov B.N. Izbrannye trudy. T. 2. Upravlenie aviatsionnymi i kosmicheskimi apparatami [Selectas. Vol. 2. Air- and spacecraft control]. Moscow: Nauka Publ., 1983. 328 p.
  2. Chelomey V.N. Pnevmogidravlicheskie sistemy dvigatel'nykh ustanovok s zhidkostnymi raketnymi dvigatelyami [Pneumatic / hydraulic systems of liquid-propellant engine power plants]. Moscow: Mashinostroenie Publ., 1978. 289 p.
  3. Zavadskiy V.K., Ivanov V.P., Kablova E.B., Klenovaya L.G. Propellant-consumption control systems (mission, design concept, algorithms for systems). Sbornik trudov Vserossiyskoy konferentsii «Aktual'nye problemy raketno-kosmicheskoy tekhniki (V Kozlovskie chteniya)» (September, 11-15, 2017, Samara). Samara: Samarskiy Nauchnyy Tsentr RAN Publ., 2017. P. 243-254. (In Russ.)
  4. Shorikov A.F. Minimaksnoe otsenivanie i upravlenie v diskretnykh dinamicheskikh sistemakh [Minimax estimation and control in discrete dynamical systems]. Ekaterinburg: Ural University Publ., 1997. 242 p.
  5. Tyulyukin V.A., Shorikov A.F. Ob odnom algoritme postroeniya oblasti dostizhimosti lineynoy upravlyaemoy sistemy. V sb.: «Negladkie Zadachi Optimizatsii i Upravlenie». Sverdlovsk: UrO AN SSSR Publ., 1988. P. 55-61. (In Russ.)
  6. Shorikov A.F., Bulaev V.V., Goranov A.Yu., Kalev V.I. Approximation of attainability domains of nonlinear discrete-time controlled dynamical systems. BSU Bulletin. Mathematics, Informatics. 2018. No. 1. P. 52-65. doi: 10.18101/2304-5728-2018-1-52-65 (In Russ.)
  7. Shorikov A.F., Kalev V.I. Linear discrete-time dynamical model forming for solving optimal terminal fuel consumption problem of launch vehicle. Proceedings of the Fifth International Scientific Conference «Information Technologies and Systems» (February, 24-28, 2016, Bannoe). Chelyabinsk: Chelyabinsk State University Publ., 2016. P. 61-66. (In Russ.)
  8. Bobrovnikov G.N., Katkov A.G. Metody izmereniya urovnya [Methods of level measurement]. Moscow: Mashinostroenie Publ., 1977. 168 p.
  9. Bryson A.E., Ho Yu-Chi. Applied optimal control. New York: Routledge Publ., 1975. 496 p.
  10. Krasovskiy N.N. Teoriya upravleniya dvizheniem [Motion control theory]. Moscow: Nauka Publ., 1968. 476 p.
  11. Krasovskiy N.N., Subbotin A.I. Pozitsionnye differentsial'nye igry [Positional differential games]. Moscow: Nauka Publ., 1974. 456 p.
  12. Chernikov S.N. Lineynye neravenstva [Linear inequalities]. Moscow: Nauka Publ., 1968. 488 p.
  13. Zoutendijk G. Methods of feasible directions: a study in linear and non-linear programming. Amsterdam: Elsevier Publ., 1960. 126 p.

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