[Paper Review] Semi-Active Control of the Sway Dynamics for Elevator Ropes

Mouhacine Benosman|arXiv (Cornell University)|Jan 18, 2015

Elevator Systems and Control9 references3 citations

TL;DR

This paper proposes nonlinear Lyapunov-based semi-active controllers for suppressing sway dynamics in elevator ropes using a damper mounted between the elevator car and ropes. The controllers stabilize rope oscillations under external disturbances by adaptively adjusting the damper's damping coefficient in real time, achieving up to 71% reduction in steady-state sway amplitude (from 8.4 m to 2.4 m) in a high-rise simulation with wind-like excitation.

ABSTRACT

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

Motivation & Objective

• Address the challenge of rope sway in high-rise elevators caused by external disturbances such as wind or seismic activity.
• Develop a cost-effective control solution that avoids retrofitting complex force actuators by using semi-active dampers instead.
• Stabilize rope sway dynamics using feedback control of a time-varying damping coefficient in a semi-active damper.
• Ensure stability and performance of the closed-loop system under realistic conditions, including measurement noise and actuator dynamics.
• Demonstrate the effectiveness of the proposed controllers through numerical simulation on a high-rise elevator model with two-mode dynamics.

Proposed method

• Model the elevator rope system using a partial differential equation (PDE) under string theory assumptions, with non-homogeneous boundary conditions.
• Apply Galerkin reduction to transform the PDE into a finite-dimensional ordinary differential equation (ODE) model with one or two modes.
• Design nonlinear controllers based on Lyapunov stability theory to compute the time-varying damping coefficient for the semi-active damper.
• Formulate controllers such that the damping coefficient is bounded and adapts based on both sway position and velocity, ensuring stability.
• Implement control signal filtering and measurement noise injection to simulate real-world actuator dynamics and sensor limitations.
• Use theoretical analysis to prove asymptotic stability of the closed-loop system under the proposed controllers.

Experimental results

Research questions

• RQ1 Can semi-active damping with adaptive gain scheduling effectively suppress large-amplitude rope sway in high-rise elevators?
• RQ2 How does the inclusion of both sway position and velocity in the control law affect system stability and performance compared to position-only control?
• RQ3 To what extent can Lyapunov-based control stabilize rope sway under resonant external disturbances (e.g., at the first natural frequency)?
• RQ4 How do measurement noise and actuator dynamics impact the performance of the proposed controllers in a realistic simulation?
• RQ5 Can a single-mode reduced-order model accurately represent the sway dynamics for control design, even when tested on a two-mode system?

Key findings

• The proposed controller (14) reduced the maximum rope sway amplitude from 1.5 m (uncontrolled) to 0.75 m (controlled) under zero disturbance and zero structural damping.
• Under resonant excitation at 0.08 Hz (matching the first rope mode), the controller (18) reduced the steady-state sway amplitude from 8.4 m to 2.4 m, achieving a 71% reduction.
• The control force remained bounded at 40 kN·s/m, a feasible value for existing semi-active dampers such as magnetorheological dampers.
• The controllers maintained bounded and continuous control signals even with simulated measurement noise (±1 cm error) and actuator filtering (10 Hz cut-off, 5-sample delay).
• The theoretical stability analysis confirmed asymptotic stability of the closed-loop system under both controllers via Lyapunov functions.
• The two-mode simulation demonstrated that a one-mode model was sufficient for controller design, as higher modes had negligible influence on the dominant dynamics.