This paper presents a theoretical study of a predictive active control system used to improve the response of multi-degree-of-freedom (MDOF) structures to earthquakes. As an example a building frame equipped with electrorheological (ER) dampers is considered. The aim of the design is to "nd a combination of forces that are produced by the ER dampers in order to obtain an optimal structural response. The mechanical response of ER #uid dampers is regulated by an electric "eld. Linear auto-regressive model with exogenous input (ARX) is used to predict the displacements and the velocities of the frame in order to overcome the time-delay problem in the control system. The control forces in the ER devices are calculated at every time step by the optimal control theory (OCT) according to the values of the displacements and of the velocities that are predicted at the next time step at each storey of the structure.
A numerical analysis of a seven-storey ER damped structure is presented as an example. It shows a signi"cant improvement of the structural response when the predictive active control system is applied compared to that of an uncontrolled structure or that of a structure with controlled damping forces with time delay. The structure's displacements and velocities that were used to obtain the optimal control forces were predicted according to an &occurring' earthquake by the ARX model (predictive control). The response was similar to that of the structure with control forces that were calculated from a &known' complete history of the earthquake's displacement and velocity values, and were applied without delay (instantaneous control).