Chaos and optimal control of steady-state rotation of a satellite-gyrostat on a circular orbit

Abstract The present paper is devoted to discuss both the chaos and optimal control of the steady rotations of a satellite-gyrostat on a circular orbit. In this the satellite is controlled with the help of three independent control moments that are developed by three rotors attached to the satellite principal axes of inertia and rotate with the help of motors rigidly mounted on the satellite body. The optimal controllers that asymptotically stabilize these chaotic rotations and minimize the required like-energy cost are derived as a function of the phase coordinates of the system. The asymptotic stability of the resulting nonlinear system is proved using the Liapunov technique. Numerical study and examples are introduced.

[1]  M. Silva.  Non-linear resonant attitude motions in gravity-stabilized gyrostat satellites , 1972 .

[2]  Andrew Y. T. Leung,et al.  Hamiltonian and chaotic attitude dynamics of an orbiting gyrostat satellite under gravity-gradient torques , 2003 .

[3]  A. V. Gorshkov.  On optimal stabilization of gyrostat rotary motion , 1979 .

[4]  Awad El-Gohary,et al.  Optimal control of the rotational motion of a rigid body using Euler parameters with the help of rotor system , 2005 .

[5]  B. Sharma,et al.  International Centre for Mechanical Science , 1973 .

[7]  Mario A. Rotea,et al.  Suboptimal Control of Rigid Body Motion with a Quadratic Cost , 1998 .

[8]  Awad El-Gohary.  Optimal control of a rotational motion of a gyrostat on circular orbit , 2000 .

[9]  T. A. Letova.  On a particular case of damping of a gyrostat rotation , 1965 .

[10]  R. Molina,et al.  Equilibria and stability for a gyrostat satellite in circular orbit , 2004 .

[11]  S. Stepanov.  On the set op steady motions of a gyrostat satellite in a central Newtonian force field and the stability of these motions: PMM vol. 33, n≗4, 1969, pp. 737–744 , 1969 .

[12]  Jerrold E. Marsden,et al.  Stabilization of rigid body dynamics by internal and external torques , 1992, Autom..

[13]  Chaotic motion in a class of asymmetrical Kelvin type gyrostat satellite , 2004 .

[14]  On the control of programmed motion of satellite-gyrostat containing fluid , 1999 .

[15]  Andrew Y. T. Leung,et al.  CHAOTIC ATTITUDE MOTION OF SATELLITES UNDER SMALL PERTURBATION TORQUES , 2000 .