Energy state-space control of semi-active friction dampers for nonlinear structural response

The reliable performance of friction dampers in seismic retrofitting depends on precise calibration of the normal force. Yet, in practice, this parameter is often uncertain due to installation tolerances, long-term degradation, and variable site conditions. To overcome this limitation, this paper introduces a semi-active slotted-bolted connection (SASBC) that integrates liquid-crystal interfaces with an energy-based control algorithm to adapt the damper’s friction coefficient in real time. A novel energy state-space formulation is developed, providing smoother trajectories than conventional force-based models and enabling gradient-based optimization of voltage commands. Numerical simulations of a five-story reinforced-concrete residential building demonstrate the advantages of the proposed method. Passive SBC retrofits prevent collapse but increase shear demand, while the SASBC achieves comparable drift reduction with controlled shear levels, maintaining stable hysteresis even under uncertain normal force conditions. These results highlight the SASBC as a practical, robust, and adaptive retrofit solution that combines the reliability of passive devices with the responsiveness of active control to enhance seismic resilience.