# Enhancing Friction Pendulum Isolation Systems Using Passive and Semi-Active Dampers
## 6 Concluding Remarks  
This paper works on the design of FPS isolators with a damper that can be passive or semi-active. That is, two types of isolation systems have been considered and studied: (i) an FPS together with a passive damper (FPS+VD), and (ii) an FPS with a smart damper, (FPS+SD). For this configuration, two ON-OFF control laws have been studied. The first one is a simple collocated phase control and the second one is a model-based control law that uses an energy-predictive algorithm to decide the state of the ON-OFF control. A design methodology focused on FPSs with an additional damper has been proposed. The methodology is based on a two-step design process that accounts for low and high-intensity earthquakes. Each step is based on a performance function that weights different performance indexes in terms of their peak and RMS values. More concretely, the following remarks can be extracted:  
* The FPS with low friction exhibits large bearing displacements under the design earthquake, while the FPS with high friction is not able to cope with the bearing displacement demand under the serviceability earthquake, producing undesirable residual displacements when the earthquake ends. * The implementation of an FPS+VD allows us to use a concave plate with low friction, increasing thus the re-centering capacity and avoiding the residual displacements. Figure 19: Performance function \(\phi_{2}\) and structure energy for a range of effective FPS radii. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Serviceability Earthquake**} \\ \hline
**System** & \(R_{eff}\) & \(f_{a}\) & \(\mu\) & \(\zeta_{(e,e_{min})}\) & \(\phi_{2}\) & **Reduction (\%)** \\ \hline FPS\({}_{\mu=0.05}\) & 0.300 & 0.867 & 0.05 & - & 0.491 & 50.90 \\ FPS+VD & 0.300 & 0.867 & 0.05 & 0.500 & 0.504 & 49.60 \\ FPS+SD (Phase control) & 0.300 & 0.867 & 0.05 & 0.480 & 0.480 & 52.00 \\ FPS+SD (Energy control) & 0.300 & 0.867 & 0.05 & 0.240 & 0.470 & 53.00 \\ FPS\({}_{\mu=0.20}\) & 0.300 & 0.867 & 0.20 & - & 0.930 & 7.00 \\ \hline \hline \multicolumn{8}{c}{**Design Earthquake**} \\ \hline
**System** & \(R_{eff}\) & \(f_{a}\) & \(\mu\) & \(\zeta_{(e,e_{min})}\) & \(\phi_{2}\) & **Reduction (\%)** \\ \hline FPS\({}_{\mu=0.05}\) & 0.300 & 0.867 & 0.05 & - & 5.614 & 0.00 \\ FPS+VD & 0.300 & 0.867 & 0.05 & 0.500 & 1.476 & 0.00 \\ FPS+SD (Phase control) & 0.300 & 0.867 & 0.05 & 0.480 & 0.608 & 39.20 \\ FPS+SD (Energy control) & 0.300 & 0.867 & 0.05 & 0.240 & 0.612 & 38.80 \\ FPS\({}_{\mu=0.20}\) & 0.300 & 0.867 & 0.20 & - & 0.599 & 40.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of the results for the same effective radius size. * The FPS+SD controls the bearing plate displacement acting when needed: avoiding stroke saturation under large ground motions and showing a very low friction FPS under serviceability ground motions. Additionally, for a similar performance as compared to a single FPS or the FPS+VD, the plate size for the FPS+SD may be significantly smaller. * The single FPS performance depends importantly on the friction coefficient value; however, the FPS equipped with a damper is robust to changes of the friction coefficients, showing better performance when the damper is semi-active. * The FPS+SD has similar behavior with a phase control and an energy-predictive-based control. However, the implementation of phase control in practice could be easily implementable as compared to energy control. The phase control requires to measure the response in acceleration and this is possible using directly an accelerometer in the concave plate. The energy-predictive-based control requires measuring the velocity and displacement of the structure and, this process could take a longer time for multi-story buildings. Additionally, an accurate model is needed to get this law to be effective. * All studied configurations have been testing for the eight selected earthquakes and the FPS+SD has a robust and effective performance under earthquakes differently located.