# Enhancing Friction Pendulum Isolation Systems Using Passive and Semi-Active Dampers
## 1 Introduction
Therefore, an FPS with low-friction damping (i.e., with good re-centering capacity) and with increased stiffness  
Figure 1: Variations of friction pendulum systems, R is the concave plate radius and \(\mu\) is the dynamic friction coefficient. at large displacement is desirable. To achieve this objective, the addition of a smart damper becomes a possible solution. Several studies about hybrid seismic isolation systems, which use passive isolation devices and smart devices, such as, actively controlled actuators [12; 13] or magnetorheological (MR) dampers working as a semi-active control strategy [14; 15; 16], have been developed. The main goal of using a hybrid isolation system is to limit the large base-displacement demand on the passive isolator without affecting the benefits obtained in the reduction of the acceleration or inter-story drift of the structure. To achieve this improvement, an appropriate control law that governs the response of the active or semi-active damper must be defined, otherwise, the effect on the structure may become undesirable and even unstable in the case of active isolation. [PERSON] et al. [17] studied some control laws for the design of semi-active tuned vibration absorbers (TVAs) using the groundhook concept, in which the groundhook simulates a \"hook\" between the structure to be controlled and the \"ground\", where the ground is the base support perturbated (e.g., a building foundation). [PERSON] et al. [18] have studied a control law for a single FPS with a semi-active damper, where the semi-active damper response is based on the bearings plate displacement and tries to produce zero dynamic stiffness in the system. [PERSON] et al. [19] have recently presented an optimum control algorithm that combines a linear quadratic regulator and a nonlinear robust compensator. That is, the proposed control is model-based and is a compound of a state-space feedback and a non-linear compensator to account for isolator nonlinearities. [PERSON] et al. [20] have proposed a \"Smart\" base isolation, based on using MR elastomers. This isolation system uses an optimal neuro-fuzzy logic control as a control strategy, which intends to control the structure acceleration and the base displacement, simultaneously. Other investigations are focused on full-scale experimental tests of smart-isolated structures. [PERSON] and [PERSON] [21] presented an experimental test to prove the effectiveness of an MR damper use as semi-active seismic response control. The control law used in this experiment corresponds to acceleration feedback. [PERSON] et al. [22] have carried out an experimental investigation of a hybrid isolation system which consists in a rubber bearings and an MR damper. The high-order single step control algorithm with an ON-OFF control was used. This method needs to estimate the whole system state in order to compute the optimal control force. Generally, simple control strategies based on feedbacking magnitudes that can be easily measured and/or reliably estimated are always preferred. Additionally, collocated control strategies are also preferred for stability reasons [23]. This paper presents a two-step design methodology for an FPS with a passive or semi-active damper. For the semi-active version, two ON-OFF control laws are studied in depth. The first control law is a fairly simple phase control adapted from the groundhook concept presented by [PERSON] et al. [17] for semi-active TVAs. The second control law is adapted from the energy-predictive algorithm presented by [PERSON] [24] to control the magnitude of the mechanical energy in structures with TVAs and it is applied to the problem of the semi-active isolation. The methodology proposed herein accounts for low and high-intensity earthquakes and minimizes a performance function that considers a balance between peak and root-mean-square (RMS) values (accounting for the duration of the event) of several representative performance indexes: structure acceleration, bearing plate displacement and inter-story drift.