Pole placement method to control the rocking motion of rigid blocks

In recent years only a very small number of studies analysed the use of active or semi-active control methods in order to avoid the overturning of rigid block-like structures under base excitation. In this paper, an active control algorithm, based on the pole placement method, is developed for rigid blocks starting from a description of the rocking motion through linearised equations. Such an approach is an excellent approximation for slender rigid blocks for which linearised equations can fully describe the rocking motion due to the smallness of the inclination angle. The control method has two objective: the first one is related to the possibility of vanishing the external excitation at each instant, the second one is to make the rest position of the block a stable point. The first analyses revealed the good robustness of the control algorithm to a variation of the sampling time and of the time-delay of the real control devices. Furthermore, the further parametric analyses pointed out the good effectiveness of the proposed control algorithm both in the reduction of the rocking angle and in the protection from the overturning, also in the case of blocks with low slenderness. Overturning spectra are obtained in the case of rigid block with and without active control.