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In this work we study the problem of rope sway dynamics control for elevatorsystems. We choose to actuate the system with a semi-active damper mounted onthe top of the elevator car. We propose nonlinear controllers based on Lyapunovtheory, to actuate the semi-active damper and stabilize the rope sway dynamics.We study the stability of the proposed controllers, and test their performanceson a numerical example.

Semi-Active Control of the Sway Dynamics for Elevator Ropes