Attitude Control of a Flexible Satellite by Using Robust Control Design Methods

Abstract

<p> The increase of satellite’s dimensions has caused flexibility and formation of uncertainty in their model. This is because of space missions being more complex and using light moving structures in satellites. Satellites are also encountered with various circumferential disturbance torques. This uncertainty in model and disturbance torques will cause undesirable performance of satellites’ attitude control system. So, for attitude control of these satellites, those methods should be used which are robust to uncertainty of the plant’s model and can reject the effects of disturbances and the measurement noise. One of these methods is the robust control design method. But, because of pole’s place of these satellite’s dynamics equations, the designing procedure of robust control will face difficulties. In this paper, by using an internal feedback as a novel idea, the satellite’s dynamics equations are changed in such a way that the poles will be placed in proper locations. Then, for these new equations, by regarding the effects of flexibility as uncertainty and considering the uncertainty in inertia matrix of satellite, an <em>H</em>_∞controller has been designed and for better performance, a <em>μ</em>-controller has been improved. Afterwards, these two controllers are analyzed and compared for the original dynamic equations, not for the modified ones. Also, for comparison, a classic controller has been also designed for the original plant and eventually all these three controllers are compared with each other. </p

Tuning of PID Controller using Glowworm Swarm Optimisation on a Satellite Attitude Control Reaction Wheel

“…This is then compared with the result obtained by minimising the same cost function using genetic algorithm (GA). T is the angular velocity vector of orbital reference frame which is stated in the body frame and is with respect to body frame [10]. A body axis frame is selected so as to conform its axes to main axes of inertia.…”

“…Here, ω o is used to denote the angular velocity of the orbit, C and S denote sine and cosine respectively and ω=[ω x ω y ω z ] T is the angular velocity of body frame with respect to inertial frame obtained from Euler's momentum equations as stated by reference [10]. Assume body frame axis conform to main inertial axis, then the Euler's momentum equations become [10]:…”

“…Where T d is the total disturbance momentum acting on the satellite, his angular momentum vector of rigid satellite body, h w is angular momentum vector of reaction wheel and T c is gravity gradient momentum [10].…”

“…The equation (6) and the equation (9) are the nonlinear dynamic equations of satellite's attitude [10]. This satellite has 3 reaction wheels, one on each axis.…”

“…When rotated, these reaction wheels exert a moment on the satellite in the opposite direction of their own rotation. They are rotated in the direction of the body axis [10]. The transfer function of the reaction wheel is given in equation (10), where u is the output of the controller and w is the external torque to satellite in the direction of related axis [11].…”