Civil Structural H∞Control Based On Linear Matrix Inequality Approach

In recent decades, the economy is developed very fast. There are a lot of infrastructures with large span or extra high, which can be damaged due to the vibration. In order to reduce the vibration of these structures, many new materials, dampers and accessory structures have been utilized to control the structural vibration. Nowadays, the hybrid control and active control were used in Guangzhou TV tower (Canton Tower) and KingKey Financial Center (KK100), respectively. Compared with increasing the structural stiffness, active control can save a lot of money. So it is necessary to do some research on active control. In this dissertation, some active control problems caused by civil structural characteristics are considered. And some research on how to make the active control robust are performed. The reaseach is all based on the Hoo theory and linear matrix inequality (LMI) approach. The primary innovative contents are as follows:(1) Considering the faults in the sensors of the control system, the filters are designed to conduct the fault detection and isolation (FDI). The control strategy is reformed to have the fault tolerant control (FTC) performance. The dynamic filter and static filter are designed. The former one is based on the dynamic H∞controller design theorem. The later one is motivated by Kalman filter theorem. These two filters are both solved by LMI approach. The static filter is then used to reform the control strategy, which can execute the fault tolerant control. Their performance are validated by numerical examples, respectively.(2) Considering the time delay for control system in the large scale civil structures, the Hoo decentralized controller is designed through double homotopy approach. The proposed method is first studied numerically with a six-story building example, and then validated experimentally through shaking table tests of a two-story frame with active mass dampers.(3) Considering the structural parametric uncertainties, the Hoo robust controller is designed based on the D-K iteration method and LMI approach, The proposed algorithm is first theoretically validated by a four-story structure numerical example, and then experimentally corroborated by a shaking table test of a two-story frame with one active mass damper.(4) Considering the time delay and the parametric uncertainties simultaneously, a innovative control strategy is proposed to design the Hoo robust decentralized controller. This new method combines D-K iteration and double homotopy approach. Finally, the proposed method is validated numerically with a four-story building example.