Protection from overturning of rigid block-like objects with linear quadratic regulator active control

In recent years, several studies proposed new techniques aimed at improving the performances of rigid block-like objects under base excitation. The majority of these studies considered passive control methods, such as base isolation or other techniques based on the tuned mass damper principle. Only few studies considered active and semi-active control methods applied to the dynamics of rigid blocks. This paper proposes an active control method for symmetric rigid blocks that is based on the LQR approach. The optimal control law is obtained starting from the linearized equation of motion. The effectiveness of the proposed control method is investigated comparing the behaviour of rigid blocks with and without active control under harmonic and seismic excitation. The results are summarized in overturning spectra, in the case of harmonic excitation, and rocking maps, in the case of seismic excitation. Although the proposed active control method is expected to work well for slender blocks, specific analyses show that the method also improves the dynamics of no-slender blocks and is effective for blocks with different geometrical characteristics. Moreover, the results show that the control law has a good robustness with respect to the sampling time and the time delay.