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.

中文翻译：

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通过线性二次调节器主动控制来防止刚性块状物体倾覆

近年来，一些研究提出了新的技术，旨在改善基础激励下刚性块状物体的性能。这些研究中的大多数都考虑了被动控制方法，例如基础隔离或基于调谐质量阻尼器原理的其他技术。只有很少的研究考虑将主动和半主动控制方法应用于刚性块的动力学。本文提出了一种基于LQR方法的对称刚性块主动控制方法。从运动的线性化方程开始获得最佳控制律。研究了所提出的控制方法的有效性，比较了在谐波和地震激励下具有和不具有主动控制的刚性块的行为。在谐波激励的情况下，将结果汇总在倾覆光谱中，和地震地图时的摇摆图。尽管所提出的主动控制方法有望用于细长块，但具体分析表明，该方法还改善了非细长块的动力学特性，并且对于具有不同几何特征的块是有效的。此外，结果表明，控制律在采样时间和时延方面具有良好的鲁棒性。