Instantaneous Optimal Wilson-Θ Control Method

Abstract

A control algorithm based on the instantaneous optimal control method, is presented for on-line control of the civil engineering structures subjected to earthquake excitations. This algorithm employs the unconditionally stable Wilson-θ method to discretize the continuous second-order form of the dynamical equation of motion, and uses a new performance index having an acceleration term as well as velocity and displacement terms. This method is named the instantaneous optimal Wilson-θ method. An eight-story shear-type building frame using one active mass damper/driver mechanism installed on the roof is used to demonstrate the efficiency of the proposed control algorithm in comparison to the other optimal control methods. Behavior of different combinations of weighting matrices related to displacement, velocity, and acceleration response vectors of the entire building are examined, and compared with the complete feedback control of the response vectors.