Impulsive Control of Attitude Satellite With Quaternion Parameters
الموضوعات : مجله بین المللی ریاضیات صنعتی
M. R. Niknam
1
(Department of Mathematics, Khalkhal Branch, Islamic Azad University, Khalkhal, Iran.)
N. Abdi Sobouhi
2
(Department of Education, Farhangian University, Tabriz, Iran.)
الکلمات المفتاحية: Satellite attitude, Lyapunov exponent, Impulsive control, Quaternion, Chaotic system,
ملخص المقالة :
This article uses impulsive control along with quaternion parameters instead of Euler angles in kinematics equations of satellite. ‎The quaternion parameters are applied to overcome singularity problem in the numerical solution. ‎It is assumed that the satellite is subjected to deterministic external perturbations. ‎At first, ‎the chaotic behavior of system is investigated when there is no control on the system. ‎Then, ‎impulsive control is used to stabilize the satellite attitude around the equilibrium point of origin. ‎Finally, ‎simulation results are given to visualize the effectiveness and feasibility of the proposed ‎method.
[1] J. L. Crassidis, F. L. Markley, Sliding mode control using modified Rodrigues parameters, J Guidance Control Dyn 19 (1996) 1381-1383.
[2] K. M. Fauske, Attitude stabilization of an underactuated rigid spacecraft, Siving thesis, Department of Engineering and Cybernetics, Norwegian University of Technology and Science 13 (2003) 511-523.
[3] D. Fragopoulos, M. Innocenti, Stability considerations in quaternion attitude control using discontinuous Lyapunov functions, IEE Proc Control Theory Appl. 151 (2004) 253-258.
[4] K. Kemih, A. Kemiha, M. Ghanes, Chaotic attitude control of satellite using impulsive control, Chaos, Solitons & Fractals 42 (2009) 735-744.
[5] K. Kemih, W. Y. Liu, Constrained generalized predictive control of chaotic Lu system, ICIC Express Lett, An Int. J. Res. Surv. 1 (2007) 39-44.
[6] N. Koncar, A. J. Jones, Adaptive real-time neural network attitude control of chaotic satellite motion, Proc, SPIE 2492, Applications and Science of Artificial Neural Networks, (1995), http://dx.doi.org/10.1117/12.205121/.
[7] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of impulsive differential eqations, World Scientific, Sangapore,(1989).
[8] C. Li, M. Guangfu, 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.
[9] X. D. Li, X. Y. Yang, J. D. Cao, Eventtriggered impulsive control for nonlinear delay systems, Automatica 117 (2020) 108-129.
[10] M. R. Niknam, H. Kheiri, N. Abdi Sobouhi, Optimal control of satellite attitude and its stability based on quaternion parameters, Computational Methods for Differential Equations 10 (2022) 168-178.
[11] M. R. Niknam, A. Heydari, Finite-time stabilization of satellite quaternion attitude, Computational Methods for Differential Equations 3 (2015) 274-283.
[12] M. R. Niknam, H. Kheiri, A. Heydari, Threeaxis optimal control of satellite attitude based on Ponteryagin maximum principle, International Journal of Industrial Mathematics 8 (2016) 37-44.
[13] Y. Park, Robust and optimal attitude control of spacecraft with disturbances, International Journal of Systems Science 46 (2015) 1222-1233.
[14] R. F. Rao, S. M. Zhong, Impulsive control on delayed feedback chaotic financial system with Markovian jumping, Adv. Diff. Equ 20 (2020) 1-18. http://dx.doi.org/10.1186/s13662-019-2438-0/
[15] L. L. Show, J. C. Juang, Y. W. Jan, An LMIbased nonlinear attitude control approach, IEEE Trans Control Syst Tech 11 (2003) 73-87.
[16] L. L. Show, J. C. Juang, Y. W. Jan, C. T. Lin, Quaternion feedback attitude control design: a nonlinear H1 approach, Asian J. Control 5 (2003) 406-411.
[17] A. P. M. Tsui, A. J. Jones, The control of higher dimensional chaos: comparative results for the chaotic satellite attitude control problem, Physica 135 (2000) 41-62.
[18] R. Wisniewski, Satellite attitude control using only electromagnetic actuation, Ph.D. Thesis, The University of Aalborg, Denmark, (1996).
[19] X. Zhang, A. Khadra, D. Li, D. Yang, Impulsive stability of chaotic systems represented by T-S model, Chaos, Solitons & Fractals 41 (2009) 1863-1869.
[20] Y. Zhang, J. Sun, Robust synchronization of coupled delayed neural networks under general impulsive control, Chaos, Solitons & Fractals 41 (2009) 1476-1480.
[21] R. Zhang, Z. Xu, S. X. Yang, X. He, Generalized synchronization via impulsive control, Chaos, Solitons & Fractals 38 (2008) 97-105.
