Optimal control for vibration peak reduction via minimizing large responses

An optimal control method for peak response reduction and its application to a tall building structure for reducing peak earthquake responses are presented in this paper. A critical value is used for magnifying large responses and performance index. A structural control system is transformed, and the dynamical programming principle is applied to form a dynamical programming equation. For a certain higher-order power function in the index, a nonlinear optimal control law with the corresponding Riccati equation is obtained for minimizing structural large responses or peak responses. The asymptotic stability of the autonomous controlled system is proved by using the Lyapunov method. Then the proposed control method is applied to a single degree-of-freedom system and a 51-storey building structure with active mass damper on the top floor under earthquake excitation. Numerical results on peak displacements, interstorey drifts, accelerations and controls are given to illustrate the high control effectiveness of the proposed control method for peak response reduction. The proposed control method has a simple and convenient procedure for multi-degree-of-freedom structures.