柔性空间机械臂的自适应H∞容错抑振混合控制

针对关节执行器存在部分失效(PLCE)故障的漂浮基柔性空间机械臂系统，提出一种自适应H∞容错抑振混合控制算法。结合拉格朗日法与弹性振动理论推导出了系统的动力学微分方程，并截取反映柔性臂杆主振型的前两阶模态作振动分析。根据奇异摄动原理对系统进行降维，并将其分解为一个刻画刚性臂杆轨迹跟踪的慢变子系统与一个刻画柔性臂杆模态振动的快变子系统；由此设计了由慢变子系统的自适应H∞容错控制器及快变子系统的线性最优减振控制器组成混合控制器。与传统容错控制器相比，所设计的自适应H∞容错控制器具有无需获取故障先验知识的优点。对比仿真结果表明：慢变子系统的容错控制器对于PLCE型关节执行器故障具备较强的鲁棒性，快变子系统的线性最优减振控制器能够将柔性臂杆的振动模态调节至较低水平，从而校验了理论分析的正确性与混合控制策略的有效性。

Adaptive H∞ Fault Tolerant and Vibration Suppressed Hybrid Control for Flexible Space Manipulator

An adaptive H∞ fault-tolerant vibration-suppressed hybrid control algorithm is proposed for a free-floating flexible space manipulator system with partial loss of control effectiveness (PLCE) fault. Based on the Lagrange method and elastic vibration theory, the dynamic differential equation of the system is deduced, and the first two modes reflecting the main vibration condition of the flexible link are intercepted for vibration analysis. According to the singular perturbation principle, the system is decomposed into a slow-varying subsystem describing the trajectory tracking motions of the rigid arms and a fast-varying subsystem describing the modal vibration of the flexible link. Thus, a hybrid controller composed of an adaptive H∞ fault-tolerant controller of the slow-varying subsystem and a linear optimal vibration-suppressed controller of the fast-varying subsystem is designed. Compared with the traditional fault-tolerant controllers, the adaptive H∞ fault-tolerant controller has the advantage of not requiring prior knowledge of actuator fault. The comparison simulation results show that the fault-tolerant controller of the slow-varying subsystem has strong robustness to the PLCE joint actuator fault, and the linear optimal vibration-suppressed controller of the fast-varying subsystem can adjust the vibration mode of the flexible link to a lower level, which verifies the correctness of the theoretical analysis and the effectiveness of the hybrid control strategy.