Integrated Design of Structural and Semi-active Control Systems: Inverse Lyapunov Approach

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An integrated design method of structural and semi-active control systems for civil structures is presented. The Vibration Control Device (VCD) that has been developed by authors is used as the semi-active control device. A new semi-active control method, which is referred to as the inverse Lyapunov approach, is proposed. In the inverse Lyapunov approach we firstly assume a bang-bang type semi-active control law based on an unknown Lyapunov function. The Lyapunov matrix that defines the Lyapunov function is optimized so that quantitative performance measures on vibration suppression of civil structures are optimized. The control design problem of the semi-active control law in the inverse Lyapunov approach results in an optimization problem of the Lyapunov matrix to construct the Lyapunov function. In the present study, in addition to the design parameters to determine the Lyapunov matrix, structural design parameters, the stiffness between neighboring two floors of the structural system itself and the parameters of the VCD, are optimized simultaneously so that the structural responses subject to recorded and/or artificial earthquake waves are optimized in the sense of the specifications on vibration suppression of civil structures. We adopt the Genetic Algorithm (GA) to get the optimal Lyapunov matrix and the structural design parameters.