Development of a Controller for Rope Vibration in a Building‐Induced Cable‐Guided Hoisting System Under Seismic Excitation

ABSTRACT This study provides a novel approach to minimizing elevator cable oscillations in a coupled model including a building and a cable‐guided hoisting mechanism under seismic excitation. A crucial component of this study is the inclusion of building vibrations that impact the cable system, which improves the model's actual usefulness. In this study, mathematical models of both the building and the elevator cable system are developed and thoroughly analyzed. An active damping device is proposed, connecting the ground and the elevator cabin, playing a crucial role in controlling oscillations. A control law is designed to regulate the oscillations of the elevator cable, with the system's stability rigorously proven using the Lyapunov Theory. The effectiveness of the proposed control law is evaluated through various earthquake scenarios. Furthermore, the system's stability is validated under four cases of operational states of the elevator, such as ascending, descending, and stopping at the lowest position, where the cable length is at its maximum.