消散システム理論に基づく二値切替型セミアクティブ制御系の設計

概要

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New bang-bang type semi-active control based on the theory of dissipative systems is proposed in this paper. The bang-bang type semi-active control has been adopted mainly for the vibration control of civil structures. The switching schedule of the damping coefficient of the semi-active damper has been determined with the value of the time derivative of the Lyapunov function, generally defined as the sum of the kinetic and the potential energies of the structural systems. The objective of the conventional bang-bang type control is to maximize the rate of the energy dissipation and the control scheme cannot deal with vibration suppression performance of the specific control outputs such as the absolute displacement of each floor from a quantitative aspect. We propose a new Lyapunov function using the basic result of the dissipative systems theory in this paper. With the theory of the dissipative systems the Lyapunov matrix is obtained as the solution to LMIs (Linear Matrix Inequalities) to achieve a smaller L_2 norm of the control output of interest. A design example for a semi-active control of a 3-story civil structure is presented to show the validity of the current analysis and the effectiveness of the proposed semi-active control.
2007-11-30