Model predictive steering control law for double gimbal scissored-pair control moment gyros

Abstract

To overcome the singularity problem of control moment gyros (CMGs) and simultaneously provide a lightweight, agile, and simple dynamical system, a CMG system called a double-gimbal scissored-pair control moment gyro (DGSPCMG) was recently proposed. The DGSPCMG is a hybrid mechanism that combines scissored-pair CMGs and a double-gimbal mechanism; further, the outer singularities in this system (saturation singularities) can be escaped by steering the scissored-pair gimbals. This system generates less perturbation torque and has almost no inner singularities except at the origin and the line along the outer gimbal axis. This paper proposes model predictive control (MPC) based steering laws for the mentioned CMG system. The proposed MPC based steering laws can directly provide the optimal gimbal rate under the nonlinear constraints in real time without using the inverse of the CMG Jacobian matrix, and hence, the singularities do not have to be considered when determining the gimbal steering rate of this system. Three objective functions are considered in the steering law design: fast maneuver-weighted type, minimum control energy type, and a hybrid of these two types. The control performances of these three MPC-based steering laws are compared via numerical simulations. Results demonstrate that the hybrid type can achieve both a short rise time of the angular velocity at the initial stage of control, and smooth stabilization to the target attitude; moreover, its settling time and control effort is between those of the other two types.