Abstract: The problem of robust H∞ fault-tolerant control for structural nonlinear vibration systems with multi-constraints is investigated. According to structural dynamics theory, a state-space model containing multi-constraints such as input time-varying delay, actuator failure, parameter nonlinear, disturbance, etc is established. Based on state feedback and Lyapunov stability theory, a sufficient condition of the existence of robust H∞ fault-tolerant controller is derived and then transformed to the corresponding Linear Matrix Inequality（LMI）. During inferential reasoning, the matrix inequality is only amplified twice and relied on system’s delay-time, so that it is possible to sufficently reduce conservative of controller design. The resultant controller enables structural nonlinear vibration systems to retain robust stability and disturbance attenuation as well as to tolerate actuator failure. A building model with four degrees of freedom subjected to the El Centro earthquake wave is simulated and studied to examine the effectiveness of the algorithm provided above, and the results show that the proposed method is feasible.

Key words: structural vibration, robust H∞ fault-tolerant control, Linear Matrix Inequality（LMI）, input time-varying delay, nonlinear

摘要： 研究了多约束条件下非线性结构振动系统的鲁棒H∞容错控制问题。根据建筑结构力学原理，建立了包含输入时变时滞、执行器故障、非线性参数摄动以及干扰等多约束条件的结构振动系统状态模型，基于状态反馈和Lyapunov稳定性理论，提出了一个可满足多约束条件的时滞相关鲁棒H∞容错控制算法，该结果以线性矩阵不等式形式给出。在推导过程中只对矩阵不等式进行了两次放大，结果与输入时滞有关，以尽可能降低控制器设计的保守性。该方法设计的控制器能够使得时滞非线性结构振动系统具有指定H∞范数的干扰抑制能力，对执行器故障具有容错性。通过对一个四自由度建筑结构模型在 EI Centro 地震波作用下振动的控制仿真，验证了所提方法的可行性和有效性。

关键词: 结构振动, 鲁棒H∞容错控制, 线性矩阵不等式（LMI）, 输入时变时滞, 非线性