Minimum Error Dissipative Power Reduction Control Allocation via Lexicographic Convex Optimization for Momentum Control Systems

This brief presents a convex-optimization-based real-time control allocation algorithm to optimally utilize multiple actuators on a momentum control system while explicitly considering actuator constraints. The primary objective of the allocation is to minimize torque error and improve performance when the system saturates or becomes singular. As a secondary objective, internal bearing and gear friction are exploited to reduce power usage without the need for accurate friction models. The algorithm exploits the fact that redundant control moment gyroscopes (CMGs) and the rotors of reaction wheel assemblies (RWAs) have nonsingleton minimum torque error solutions. Thus, friction in the rotors and gimbals of the CMG and RWA can be used to find a minimum power solution among the set of minimum torque error solutions. The convex optimization framework enables real-time implementable algorithms, which fully utilize control authority without requiring tuning for changes in the number or the configuration of actuators.