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

Abstract

Summary 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.

Preliminary Results of Shake Table Tests of a Typical Museum Display Case Containing an Art Object

“…e seismic risk associated with these systems can be high, especially if they are housed within critical facilities (e.g., hospital or laboratory equipment [9,10] or nuclear facilities [11,12]) or have historical/cultural significance (e.g., art objects) [13][14][15]. In the light of that, several studies recently provided guidance for mitigating the seismic vulnerability of freestanding valuable and museum systems and objects [16][17][18]. However, current arrangements for those systems housed in critical facilities and museums typically do not include protection systems, except for few peculiar cases.…”

A procedure to model and design elastomeric‐based isolation systems for the seismic protection of rocking art objects

“…It has been shown by Ther and Kollár (2018) that overturning induced by seismic events can be accurately predicted under an impulsive excitation with proper duration and peak acceleration. Notably, the variation of the maximum rocking angle with respect to a geometrical property of the block under seismic excitation can be displayed by the rocking maps (Di Egidio, Contento, de Leo, & Gardoni, 2020). The seismic risk assessment of a rigid body endowed with an isolation system can be also estimated by computing the fragility functions for a given engineering demand parameter (Jaimes & Candia, 2020; Thiers‐Moggia & Málaga‐Chuquitaype, 2019).…”

“…The use of massdamper dynamic absorbers (Di Egidio et al, 2019), as well as rate-dependent or rate-independent hysteretic energy dissipation devices (Makris & Aghagholizadeh, 2019), were also studied. Other studies have been dedicated to active (Di Egidio, Contento, Olivieri, & de Leo, 2020;Simoneschi et al, 2018;Venanzi et al, 2018) and semi-active (Ceravolo et al, 2016(Ceravolo et al, , 2017 control systems to prevent the rocking of rigid bodies. Contento and Di Egidio (2014) investigated the seismic protection of freestanding rigid bodies placed on a multi-floor with the base isolation modeled as a linear viscoelastic element.…”

Base Versus Top Active Control to Improve Dynamic and Seismic Performances of Rigid Blocks

“…Some papers presented the coupling of rigid bodies with inerter devices [15,16]. Lately, some researchers studied the use of semi-active anchorages [17,18], and active control techniques [19,20,21] to increase the amplitude of base excitation required to topple a rigid block.…”