Optimal control of satellite attitude and its stability based on quaternion parameters

Niknam, Mohammad Reza; Kheiri, Hossein; Abdi Sobouhi, Nadereh

doi:10.22034/cmde.2021.43439.1854

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	Optimal control of satellite attitude and its stability based on quaternion parameters
Computational Methods for Differential Equations
مقاله 12، دوره 10، شماره 1، فروردین 2022، صفحه 168-178 اصل مقاله (784.56 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.43439.1854
نویسندگان
Mohammad Reza Niknam^* ¹؛ Hossein Kheiri²؛ Nadereh Abdi Sobouhi³
¹Department of Mathematics, Islamic Azad University, Khalkhal Branch, Khalkhal, Iran.
²Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
³Department of Mathematics, Farhangian University, Tabriz, Iran.
چکیده
This paper proposes an optimal control method for the chaotic attitude of the satellite when it is exposed to external disturbances. When there is no control over the satellite, its chaotic attitude is investigated using Lyapunov exponents (LEs), Poincare diagrams, and bifurcation diagrams. In order to overcome the problem of singularity in the great maneuvers of satellite, we consider the kinematic equations based on quaternion parameters instead of Euler angles, and obtain control functions by using the Pontryagin maximum principle (PMP). These functions are able to reach the satellite attitude to its equilibrium point. Also the asymptotic stability of these control functions is investigated by Lyapunov’s stability theorem. Some simulation results are given to visualize the effectiveness and feasibility of the proposed method.
کلیدواژه‌ها
Optimal control؛ Stability؛ Quaternion؛ Chaotic systems

مراجع
[1] C. K. Chui and G. Chen, Linear Systems and Optimal Control, Springer, (1989), 81–91. [2] J. L. Crassidis and F. L. Markley, Sliding mode control using modified Rodrigues parameters, J Guidance Control Dyn, 19(6) (1996), 1381–1383. [3] A. El-Gohary, Optimal control of a programmed motion of a rigid spacecraft using redundant kinematics parame- terizations, Chaos, Solitons and Fractals, 26(4) (2005), 1053–1063. [4] A. El-Gohary and S. Tawfik, Optimal control of a rigid body motion using Euler parameters without angular velocity measurements, Mechanics Research Communications, 37(3) (2010), 354–359. [5] K. M. Fauske, Attitude stabilization of an underactuated rigid spacecraft, Siving thesis, Department of Engineering and Cybernetics, Norwegian University of Technology and Science, (2003), 27–30. [6] D. Fragopoulos and M. Innocenti, Stability considerations in quaternion attitude control using discontinuous Lyapunov functions, IEE Proc Control Theory Appl , 151(3) (2004), 253–258. [7] C. H. G. Hassmann and A. Fenili, Attitude and vibration control of a satellite with a flexible solar panel using LQR tracking with infinite time, In Proceedings of the ASME International Congress of Mechanical Engineering, Seattle, Wash, USA, (2007). [8] Q. L. Hu and G. F. Ma, Optimal sliding mode manoeuvring control and active vibration reduction of flexible spacecraft, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 220(4) (2006), 317–335. [9] M. Inarrea, Chaos and its control in the pitch motion of an asymmetric magnetic spacecraft in polar elliptic orbit, Chaos, Solitons and Fractals, 40(4) (2009), 1637–1652. [10] K. Kemih, A. Kemiha, and M. Ghanes, Chaotic attitude control of satellite using impulsive control, Chaos, Solitons & Fractals, 42(2) (2009), 735–744. [11] K. Kemih and W. Y. Liu, Constrained generalized predictive control of chaotic Lu system, ICIC Express Lett (An Int J Res Surv), 1(1) (2007), 39–44. [12] N. Koncar and A. J. Jones, Adaptive real-time neural network attitude control of chaotic satellite motion, In: SPIE international symposium applications and science of artificial neural networks, 2492, (1995), 112–123. [13] C. Li, M. Guangfu, and S. Bin, Passivity-based nonlinear attitude regulation of rigid spacecraft subject to control saturation, The Sixth World Congress on Intelligent Control and Automation, 2 (2006), 8421–8425. [14] C. Li, K. L. Teo, B. Li, and G. Ma, A constrained optimal PID-like controller design for spacecraft attitude stabilization, Acta Astronautica, 74 (2012), 131–140. [15] W. Luo, V. C. Chu, and K. V. Ling, Inverse optimal adaptive control for attitude tracking of spa cecraft, IEEE Transactions on Automatic Control, 50(11) (2005), 1639–1654. [16] Z. Ma, O. Ma, and B. N. Shashikanth, Optimal control for spacecraft to rendezvous with a tumbling satellite in a close range, IEEE/RSJ International Conference on Intelligent Robots and Systems, (2006), 4109–4114. [17] M. R. Niknam and A. Heydari, Finite-time stabilization of satellite quaternion attitude, Computational Methods for Diﬀerential Equations, 3(4) (2015), 274–283. [18] M. R. Niknam, H. Kheiri, and A. Heydari, Three-axis optimal control of satellite attitude based on Ponteryagin maximum principle, International Journal of Industrial Mathematics, 8(1) (2016), 37–44. [19] D. K. Parrish and D. B. Ridgely, Attitude Control of a Satellite Using the SDRE Method, Proceedings of the 1997 American Control Conference, (1997). [20] Y. Park, Robust and optimal attitude stabilization of spacecraft with external disturbances, Aerospace Science and Technology, 9(3) (2005), 253–259. [21] Y. Park, Robust and optimal attitude control of spacecraft with disturbances, International Journal of Systems Science, 46(7) (2015), 1222–1233. [22] Y. Park, M. J. Tahk, and J. Park, Optimal stabilization of Takagi-Sugeno fuzzy systems with application to spacecraft control, Journal of Guidance, Control, and Dynamics, 24(4) (2001), 767–777. [23] P. Razzaghi, E. A. Khatib, and S. Bakhtiari, Sliding mode and SDRE control laws on a tethered satellite system to de-orbit space debris, Advances in Space Research, 64(1) (2019), 18–27. [24] H. Schaub, J. L. Junkins, and R. D. Robinett, New penalty functions and optimal control formulation for spacecraft attitude control problems, Journal of Guidance, Control, and Dynamics, 20(3) (1997), 428–434. [25] L. L. Show, J. C. Juang, and Y. W. Jan, An LMI-based nonlinear attitude control approach, IEEE Trans Control Syst Tech, 11(1) (2003), 73–87. [26] A. Sinha and D. W. Miller, Optimal sliding mode control of a flexible spacecraft under stochastic disturbances, Journal of Guidance, Control, and Dynamics, 18(3) (1993), 486–492. [27] A. P. M. Tsui and A. J. Jones, The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem, Physica, 135(1-2) (2000), 41–62. [28] R. Wisniewski, Satellite attitude control using only electromagnetic actuation, Ph.D. Thesis, The University of Aalborg, Denmark, (1996). [29] B. Zhang, K. Liu, and J. Xiang, A stabilized optimal nonlinear feedback control for satellite attitude tracking, Aerospace Science and Technology, 27(1) (2013), 17–24.
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Optimal control of satellite attitude and its stability based on quaternion parameters