Sliding Mode Control and Optimization for Six DOF Satellite Formation Flying Considering Saturation
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Sliding Mode Control and Optimization for Six OOF Satellite Formation Flying Considering Saturation 1 Yunjun Xu2 Abstract This paper considers the problem of controlling both position and attitude states for a formation flying system using only thrusters. A coupled six degree of freedom position and attitude model is derived, where the coupling comes from the gravity gradient torque. Furthermore, the J2 perturbation, mass variation, thruster model, and thruster layout are considered. A globally stable chattering free sliding mode robust controller is designed with respect to functional bounded uncertainties. Based on the studies of open-loop responses, the range of control parameters is properly selected to avoid thruster saturation. A genetic algorithm is then applied to select the controller parameters. Both position and attitude states in a formation are precisely and continuously controlled for more than two years without recharging, using the selected electronic ion engine.
Introduction Dynamics and control of multiple microsatellites in a formation have been subjects of many research investigations. One of the objectives of the formation requires simultaneous positioning and pointing. Much of the literature studying formation problems is based on separated position or attitude models using various control methods. The Clohessy-Wiltshire (C-W) equation [1] has been widely used to model the leader-follower relative position dynamics of formation flying systems (FFS). Based on this linear model, Vissar and Redding [2-3] proposed Linear Quadratic Regulator (LQR) type controllers. However, the C-W equation is a linear approximation of the real system and only applicable in the near circular reference orbit case. Inalhan [4] described the relative position motion for the case of an elliptic reference orbit, where the time dependence was replaced with the true anomaly dependence. Xu and Fitz-Coy [5,6] applied a nonlinear model which can be used in 'Presented (in part) as paper AIAA-2005-6464 at the AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California, August 15-18,2005. 2Assistant Professor, School of Aerospace and Mechanical Engineering, University of Oklahoma, Email: [email protected]. 433
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any closed orbit cases including elliptic and circular reference orbits. The position and attitude models are related due to a desired pointing requirement, although the dynamics are not coupled. A sliding mode control (SMC) system is designed. The main disadvantage of the SMC used in [5, 6] is chattering. Many methods have been proposed to mitigate chattering [7]. One of them is replacing the "signum" function with a boundary layer function [7, 8]. Chattering is mitigated by the boundary layer function with the compromise in robustness reduction and steady state error increasing. Another way to solve this chattering problem is based on the higher-order sliding modes [9]. In this approach, the higher-order sliding surface is still discontinuous. But because the controller, based on the f
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