Active Vibration Reduction System Optimal Control Using Linear Matrix Inequalities with No Directional Change in Controls

Significant attention has been paid recently to the reduction of building vibration in civil engineering. In this paper, the synthesis of an optimal controller utilising convex optimisation and linear matrix inequalities is presented with the incorporated concept of preserving the optimal control vector direction. The notion of avoiding directional change in controls is new to the vibration reduction systems field, although it appears attractive because of dimensionality of the problems. The controller design is analysed by means of comparing maximum node displacements in the model of the frame of the building with performance tested using the historical record of the El Centro earthquake. The simulations performed have shown that the designed controller is able to reduce maximum displacements in comparison with the cut-off saturation approach.

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