Adaptive causal realization of rate-independent linear damping

This paper proposes an adaptive approach to achieve an accurate causal realization of rate-independent linear damping (RILD). RILD provides direct control over displacement, a benefit to low-frequency structures subjected to earthquake ground motion. The damping force generated by RILD is higher (lower) than that of linear viscous damping at lower (higher) frequencies, resulting in effective reduction of displacement and acceleration. The RILD force is proportional to displacement that is advanced in phase by π/2 radians, a noncausality that has limited its practical application. Adaptive controllers are proposed to approximate ideal (noncausal) RILD based on the dominant response frequency estimated in real-time and a filter-based causal model for RILD. By estimating the dominant response frequency, the displacement phase advance is more accurately applied. The adaptive control approach is demonstrated through the real-time hybrid simulation (RTHS) of a 5-story base-isolated building and a 14-story inter-story isolated building. A magnetorheological (MR) damper is added to the isolation layer of each structure to provide supplemental control mimicking ideal RILD. The MR damper is experimentally represented while the remainder of the structure is numerically simulated in the RTHS loop. The desired damping force is tracked by the semi-active damper, which is naturally in phase with velocity and has a controllable magnitude. The results compare well to noncausal numerical simulations in both damping forces and structural responses. Results also show clear improved seismic performance of the adaptive algorithms as compared to non-adaptive causal approximations of RILD and passive-on and off damper controllers (i.e., nonlinear hysteretic damping).