Active structural control based on the prediction and degree of stability

Active control of buildings and structures for reducing damage due to earthquake and other environmental forces represents a relatively new research area. Most of the recent studies on this area are based on the applications of traditional linear quadratic regulator (LQR) control to the earthquake-excited structures. This paper presents the analytical solution of the modified linear quadratic regulator (MLQR) problem including a parameter α known as system stability order in the presence of unknown seismic excitation. The resulting closed-open loop active control force depends on the system state, seismic excitation and α. An approximate solution of the problem is based on the real-time prediction of near-future excitation. Since the primary focus of this study is on the relation between the system stability order α and the prediction of near-future excitation, numerical simulations of a three-storey undamped structure subjected to an El Centro earthquake are performed for different α values. It is shown that the relative displacements can be reduced significantly for each selected α value as the near-future excitation is predicted precisely and there is no significant increase in the control forces. The results also show that there is no need to predict the distant-future excitation to be able to achieve a given reduction in relative displacements as the system stability order α is increased. It is also shown that the accelerations increase in general after the fourth-step ahead prediction for a given α while they decrease as α increases.