Fault-tolerant control allocation (FTCA) strategy is proposed for attitude stabilization of a flexible satellite with actuator redundancy. The control scheme is based on the infinite-dimensional model of a flexible satellite with no discretization, so the spillover instability is eliminated. This is one of the important benefits of the proposed control scheme over the previous FTCA schemes that have been used for the flexible satellite. The proposed scheme contains two modules. The first module provides a virtual control law to meet stabilization and vibration control objectives in the presence of uncertainties and external disturbances. There is no need to implement in-domain actuators on panels to stabilize their vibration. In this module, the virtual control is designed using adaptive integral sliding mode approach where the sliding surface includes angular velocities, internal reaction torques, and nominal control for healthy system. The second module, based on fault/failure information and using a control allocation scheme, provides redistribution of the virtual control law among the available actuators. Due to simultaneous actuator faults and control constraints, there is an error between the actual virtual control and the designed control that affects the overall system stability. To eliminate this error, gain of the virtual control signal is adjusted by an adaptive updating law. The closed-loop system stability is guaranteed for small changes in a neighborhood of the sliding surface with simultaneous vibration damping. A numerical example illustrates the effectiveness of the proposed control strategy.

提出了容错控制分配（FTCA）策略，用于具有执行器冗余的柔性卫星的姿态稳定。该控制方案基于没有离散化的柔性卫星的无穷维模型，因此消除了溢出的不稳定性。这是所提出的控制方案相对于以前用于柔性卫星的FTCA方案的重要优点之一。提议的方案包含两个模块。第一个模块提供了虚拟控制律，可以在存在不确定性和外部干扰的情况下满足稳定和振动控制的目标。无需在面板上安装域内执行器来稳定其振动。在这个模块中 虚拟控制是使用自适应积分滑模方法设计的，其中滑动表面包括角速度，内部反作用扭矩和健康系统的标称控制。第二模块基于故障/故障信息并使用控制分配方案，在可用执行器之间提供虚拟控制定律的重新分配。由于同时存在执行器故障和控制约束，因此实际虚拟控制与设计控制之间存在误差，会影响整个系统的稳定性。为了消除该误差，通过自适应更新定律来调整虚拟控制信号的增益。闭环系统的稳定性保证了滑动面附近的微小变化，同时具有减振功能。