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.

为了克服控制力矩陀螺（CMG）的奇异性问题，并同时提供一种轻便，灵活和简单的动力系统，最近提出了一种称为双梁剪裁对控制力矩陀螺（DGSPCMG）的CMG系统。DGSPCMG是一种混合机制，结合了剪刀对CMG和双万向节机制。此外，可以通过操纵剪刀对的万向节来逃避该系统中的外部奇点（饱和奇点）。该系统产生的摄动扭矩较小，除了原点和沿外万向轴的线外，几乎没有内部奇异点。本文针对上述CMG系统提出了基于模型预测控制（MPC）的转向规律。所提出的基于MPC的转向定律可以直接在非线性约束条件下实时提供最佳万向架速率，而无需使用CMG Jacobian矩阵的逆函数，因此，在确定该系统的万向架转向率时不必考虑奇异性。转向律设计中考虑了三个目标函数：快速机动加权类型，最小控制能量类型以及这两种类型的混合。通过数值模拟比较了这三种基于MPC的转向定律的控制性能。结果表明，混合动力型既可以在控制的初始阶段获得短的角速度上升时间，又可以平稳地稳定到目标姿态。此外，其建立时间和控制工作介于其他两种类型之间。