Magnetic Attitude Control with Impulsive Thrusting Using the Hybrid Passivity Theorem

Passivity-based design approaches for hybrid attitude control of spacecraft using continuous magnetic torques and impulsive thrusts are proposed. The classical passivity notions, the passivity theorem, and the Kalman-Yakubovich-Popov conditions are extended to hybrid systems and used for linear passivity-based controller design. The plant's output dynamics are manipulated such that the hybrid extended (time-varying) Kalman-Yakubovich-Popov conditions are satisfied, hence establishing the plant's passivity. Then, evoking the hybrid passivity theorem that states the negative feedback interconnection of a passive hybrid plant and an input strictly passive hybrid controller is input-output stable, two such controllers are proposed: a proportional feedback controller with constant positive gains; and a dynamic compensator, developed using the hybrid algebraic (time-invariant) Kalman-Yakubovich-Popov conditions, that actively adjusts the gains based on the system's dynamics and response. Numerical simulations validate the proposed controllers' functionality and suggest performance improvements gained via hybrid control. The effects of random sensor noise are also studied, and the results suggest enhanced immunity in terms of performance arising from the use of the dynamic compensator instead of the constant-gain controller. Presented as Paper 2017-1738 at the AIAA Guidance, Navigation, and Control Conference, Grapevine, TX, 9-13 January 2017