Backstepping control of Chaotic Attitude Control of Satellite K. Kemih*, M. Halimi**, H. Fanit*, H. Salit * " *L2EI Laboratory, Jijel University, Jijel 18000, Algeria **CRAN/ENSEM, 2 Avenue de la Foret de Haye 54516 Vandœuvre Cedex " Abstract: A backstepping control system is proposed to control the attitude dynamics of a satellite subjected to deterministic external perturbations which induce chaotic motion when no control is affected in this paper. The proposed method is a systematic recursive design approach based on the choice of Lyapunov functions for constructing feedback control laws. The effectiveness of the proposed control scheme is verified by the simulated results. Keywords: backstepping control, satellite attitude control, chaotic systems, Lyapunov function. 1. INTRODUCTION Chaotic systems are described by a set of nonlinear and deterministic dynamical equations. Although its equations completely define their evolution, they are unpredictable in the long term. This non-predictability in the long term due to the fact that chaotic systems are very sensitive to initial conditions. The control of chaotic system has received increased research attention [1-7], since the classical work on chaos control was first presented by Ott and al. [8]. In the last decade, several works interested to attitude control systems of satellites using new advanced nonlinear control theory which ensured better performances. In [9] impulsive control has been used to Chaotic attitude control of satellite. More recently, Mohammad bagheri and all [10] proposed the model predictive control method to stabilize the Lorenz-type chaotic attitude of a satellite. In other development, Backstepping design has been widely used for controlling chaotic systems [11-13] since backstepping approach provides a recursive method ensure global stability, tracking and transient performance for a board class of system in strict-feedback form. Backstepping approach has been used in [10] to control intermittent chaotic transport in inertia ratchet that model the motion of a particle in an asymmetric periodic potential, and in [11] to the control and synchronization of chaos in RCL-Shunted Josephson junction. The work presented in this paper deals with the application of the backstepping control system to control the attitude dynamics of a satellite subjected to deterministic external perturbations which induce chaotic motion. This paper is organized as follows. After this introduction, Sec. 2 focuses on the description of the attitude dynamics of satellite. The matter discussed in Sec. 3 concerns the Backstepping control of Chaotic Attitude Control of Satellite. Finally, simulation results are presented in Sec. 4 in order to shown method effectiveness. 2. DESCRIPTION OF THE ATITTUDE DYNAMICS OF SATELLITE The dynamical equation of the rigid satellite attitude control system is [14]: ( ) ( ) ( ) w ww C w ww C w ww C ‚ E E W ¥ W ¥ E ‚ W W ¥ E E ¥ W ‚ ¥ ¥ E W E W ¥ Ê K ?K /K - Í Í K ?K /K - Ë Í ÍK ?K /K - Ì (1) where 荊 諜 , 荊 超 , 荊 跳 are the principal moments of inertia, x w , y w , z w are angular velocities about the principal x, y, z axes fixed in the rigid body, and Cx, Cy, Cz are torques applied about these axes at time t. If we choose 荊 諜 噺 ぬどどど"倦訣┻ 兼 態 , 荊 超 噺 にどどど"倦訣┻ 兼 態 , and 荊 跳 噺 にどどど"倦訣┻ 兼 態 with the perturbing torques defined by: 1.2 0 6/2 0 0.35 0 6 0 0.4 x x y y z z C C C y y y Ç × Ç × Ç × / È Ù È Ù È Ù ? È Ù È Ù È Ù È Ù È Ù È Ù / / É Ú É Ú É Ú (2) The dynamics of the satellite will then exhibit chaotic motion. The chaotic trajectory of the satellite is represented in Figure 1. 3. BACKSTEPPING CONTROL OF CHAOTIC ATTITUDE CONTROL OF SATELLITE WITH ONLY ONE CONTROLLER Our objective is to stabilize the system (1) to the desired values (拳 怠鳥 ┸拳 態鳥 ,"拳 戴鳥 岻┻ Proceedings of The first International Conference on Nanoelectronics, Communications and Renewable Energy 2013 444 ICNCRE ’13 ISBN : 978-81-925233-8-5 www.edlib.asdf.res.in Downloaded from www.edlib.asdf.res.in