Email this article 
Two-channel optimal discrete law of control of spacecraft with aerodynamic and inertial asymmetry during descent in Mars atmosphere
- Authors: Lyubimov V.V.1, Bakry I.1
-
Affiliations:
- Samara National Research University
- Issue: Vol 21, No 3 (2022)
- Pages: 36-46
- Section: AIRCRAFT AND SPACE ROCKET ENGINEERING
- URL: https://journals.ssau.ru/vestnik/article/view/10846
- DOI: https://doi.org/10.18287/2541-7533-2022-21-3-36-46
- ID: 10846
Cite item
Full Text
Abstract
At present, spacecraft attitude stability is of great importance for both state and private space companies and agencies. In this paper, we consider a mathematical model describing perturbed motion of spacecraft as a rigid body with significant aerodynamic and inertial asymmetry relative to the center of mass in the rarefied atmosphere of Mars. The aim of this work is to obtain an approximate discrete optimized law of controlling the spacecraft attitude using Bellman's dynamic programming and averaging methods. Discrete systems of equations used in the work were solved using the Z-transform method. The reliability of the obtained control laws was confirmed by the results of numerical integration by the numerical Euler method.
About the authors
V. V. Lyubimov
Samara National Research University
Author for correspondence.
Email: vlubimov@mail.ru
ORCID iD: 0000-0002-2410-8492
Doctor of Science (Engineering), Associate Professor, Head of the Department of Further Mathematics
Russian FederationI. Bakry
Samara National Research University
Email: ibrahimbakry0@gmail.com
ORCID iD: 0000-0002-5170-066X
Postgraduate Student, Department of Flight Dynamics and Control Systems
Russian FederationReferences
- Yaroshevskiy V.A. Dvizhenie neupravlyaemogo tela v atmosphere [Motion of an unstabilized body in the atmosphere]. Moscow: Mashinostroenie Publ., 1978. 167 p.
- Lyubimov V.V. Numerical simulation of the resonance effect at re-entry of a rigid body with low inertial and aerodynamic asymmetries into the atmosphere. CEUR Workshop Proceedings. 2015. V. 1490. P. 198-210. doi: 10.18287/1613-0073-2015-1490-198-210
- Lyubimov V.V. Dynamics and control of angular acceleration of a re-entry spacecraft with a small asymmetry in the atmosphere in the presence of the secondary resonance effect. Proceedings of the International Siberian Conference on Control and Communications, SIBCON 2015 (May, 21-23, 2015, Omsk, Russia). doi: 10.1109/SIBCON.2015.7147134
- Every mission to Mars ever. Available at: https://www.planetary.org/space-missions/every-mars-mission
- Mars missions. Available at: https://mars.nasa.gov/internal_resources/818/
- Bellman R.E. Dynamic programming. Princeton: Princeton University, 1972. 365 p.
- Sanders D.A., Verhulst F., Murdock D. Averaging methods in nonlinear dynamical systems. New York: Springer, 2007. 434 p.
- Zabolotnov Y.M. Asymptotic analysis of quasilinear equations of motion of a spacecraft with small asymmetry in the atmosphere. III. Cosmic Research. 1994. V. 32, Iss. 4-5. P. 112-115.
- Freidlin M., Wentzell A. Some recent results on averaging principle. In book: «Stochastic Analysis and Nonparametric Estimation». New York: Springer, 2006. P. 1-19. doi: 10.1007/978-0-387-75111-5_1
- Panteleev A.V., Yakimova A.S. Teoriya funktsiy kompleksnogo peremennogo i operatsionnoe ischislenie v primerakh i zadachakh. Prikladnaya matematika dlya vuzov [The theory of functions of a complex variable and operational calculus in examples and problems. Applied mathematics for universities]. Moscow: Vysshaya Shkola, 2001. 445 p.
- Atkinson K., Han W., Stewart D.E. Numerical solution of ordinary differential equations. New Jersey: John Wiley & Sons, 2009. 261 p.
- Lopez L., Mastroserio C., Politi T. Variable step-size techniques in continuous Runge-Kutta methods for isospectral dynamical systems. Journal of Computational and Applied Mathematics. 1997. V. 82, Iss. 1-2. P. 261-278. doi: 10.1016/S0377-0427(97)00048-4
Supplementary files
