This paper develops a new fault-tolerant control scheme for a coupled rigid-flexible system to handle control-matched uncertain faults, using backstepping based sliding mode control technique. The system dynamics is modeled by an Euler-Bernoulli beam-ODE (EBB-ODE) system. A distinct model refinement is utilized to map this EBB-ODE cascade into a Schrödinger-like PDE-ODE cascade. In order to surmount the obstacles when deriving the kernels in a one-step backstepping control design, a distinct backstepping control procedure is employed by constructing an exponentially stable target system with arbitrary decay rate. Based on the relative degrees of the selected sliding mode surfaces, a novel fault-tolerant controller is developed to drive faulty boundaries to zero in finite time and to avoid chattering effectively. A modified Lyapunov-based Riesz basis frame is adopted to prove the exponential stability and the well-posedness of closed-loop system. A numerical simulation is presented to validate the effectiveness of the developed control scheme.

本文采用基于后推的滑模控制技术，为耦合刚柔系统开发了一种新的容错控制方案，以处理与控制匹配的不确定故障。系统动力学由Euler-Bernoulli光束ODE（EBB-ODE）系统建模。利用独特的模型改进将EBB-ODE级联映射为类似Schrödinger的PDE-ODE级联。为了克服一步式反推控制设计中导出内核时的障碍，通过构建具有任意衰减率的指数稳定目标系统，采用了独特的反推控制程序。基于所选滑模表面的相对程度，开发了一种新型的容错控制器，以在有限的时间内将故障边界驱动为零，并有效避免抖动。采用改进的基于Lyapunov的Riesz基架来证明闭环系统的指数稳定性和适定性。进行了数值模拟，以验证所开发控制方案的有效性。