Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.