In this article, boundary control strategy is adopted to suppress the vibration of a flexible three‐dimensional (3D) marine riser simultaneously against both sensor and actuator faults. The flexible 3D marine riser is a distributed parameter system modeled as partial differential equations. During normal operation of the system, all the system components will behave optimally. However, if the sensor and actuator appear fault, the system will work abnormally. While the sensor is faulty, the output signal of the sensor will have errors, and this error signal will be the input signal of the actuator. In terms of actuator fault, once the actuator appears fault problem, the actuator should make up for the fault and continue working for the sake of safety. In this work, the fault degree of sensors and actuators are unknown and the boundary control schemes using Nassbaum function are developed for fault compensation. The system stability is proven by introducing an appropriate Lyapunov function. Finally, the simulation results verify the accuracy of the proposed control laws.

中文翻译：

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柔性三维船舶立管的边界振动抑制，可防止未知的传感器和执行器故障

本文采用边界控制策略来同时抑制柔性三维（3D）船用立管在传感器和执行器故障时的振动。柔性3D船用立管是一个分布式参数系统，建模为偏微分方程。在系统正常运行期间，所有系统组件均将发挥最佳性能。但是，如果传感器和执行器出现故障，则系统将无法正常工作。当传感器出现故障时，传感器的输出信号将出现错误，并且该错误信号将成为执行器的输入信号。就执行器故障而言，一旦执行器出现故障问题，为了安全起见，执行器应弥补故障并继续工作。在这项工作中 传感器和执行器的故障程度未知，并开发了使用纳斯鲍姆函数的边界控制方案以进行故障补偿。通过引入适当的Lyapunov函数证明了系统的稳定性。最后，仿真结果验证了所提出控制律的准确性。