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The control system may lose the performance to suppress the structural vibration due to  the faults in sensors or actuators. This paper designs the filter to perform the fault detection and isolation (FDI) and then reforms the control strategy to achieve the fault tolerant control (FTC). The dynamic equation of the structure with active mass damper (AMD) is first formulated. Then, an estimated system is built to transform the FDI filter design problem to the static gain optimization problem. The gain is designed to minimize the gap between the estimated system and the practical system, which can be calculated by linear matrix inequality (LMI) approach. The FDI filter is finally used to isolate the sensor faults and reform the FTC strategy. The efficiency of FDI and FTC is validated by the numerical simulation of a three-story structure with AMD system with the consideration of sensor faults. The results show that the proposed FDI filter can detect the sensor faults and FTC controller can effectively tolerate the faults and suppress the structural vibration

Fault Tolerant Control for Civil Structures Based on LMI Approach