针对分布式部署变速双框架控制力矩陀螺阵列的板状陀螺柔性结构“姿-振”协同控制与力矩分配问题，本文基于奇异摄动法提出一种结合滑模控制器与线性二次型调节器的分层控制架构和协调振动激发与分层控制间相互干扰的力矩优化分配方法。首先，基于奇异摄动理论将陀螺柔性结构耦合动力学模型解耦为慢变姿态子系统与快变振动子系统，并分别设计滑模姿态控制器与线性二次型调节器振动抑制器，并补偿振动抑制力矩对姿态控制的干扰。在此基础上，通过分析姿态机动力矩对模态空间的激励效应及其与振动抑制力矩的关系，建立以最小化模态激励和最小化对振动抑制干扰为目标的力矩二次规划分配模型。进一步引入依赖于结构振动机械能的自适应权重系数，实现两个优化目标间的动态协调。数值仿真结果表明，相较于将力矩平均分配的方案，所构建的力矩优化分配方案在不影响姿态机动的条件下（姿态四元数最大偏差为10-4量级），使柔性结构的最大形变量降低79.13%，显著提升了大型空间柔性结构的“姿-振”协同控制性能。
This paper addresses the integrated attitude-vibration control and torque allocation problem for a plate-type flexible spacecraft equipped with a distributed array of variable-speed double-gimbal control moment gyroscopes. A hierarchical control architecture combining sliding-mode control and linear quadratic regulator (LQR), together with an optimized torque allocation strategy that coordinates modal excitation and mitigates mutual interference between vibration suppression and attitude maneuvers, is proposed based on singular perturbation theory. First, the coupled attitude-structural dynamics are decomposed via singular perturbation into a slow-varying attitude subsystem and a fast-varying vibration subsystem. A sliding-mode controller is designed for the slow subsystem to achieve robust attitude control, while an LQR-based vibration suppressor is developed for the fast subsystem. Crucially, the parasitic disturbance induced by vibration-suppression torques on the attitude dynamics is explicitly compensated in the control law. Building upon this, a torque allocation model formulated as a quadratic programming problem is established by analyzing the excitation effect of attitude maneuver torques on the modal space and their interaction with vibration-suppression torques. The objective function simultaneously minimizes modal excitation and interference with active vibration control. Furthermore, an adaptive weighting scheme, dependent on the mechanical energy of structural vibrations, is introduced to dynamically balance these two objectives. Numerical simulations demonstrate that, compared to a uniform torque distribution scheme, the proposed optimization-based allocation method reduces the peak structural deformation by 79.13%, while maintaining high-precision attitude maneuvers (with maximum quaternion error on the order of 10-4). These results confirm the significant enhancement in integrated attitude–vibration control performance for large-scale flexible space structures.
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