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research-article

Axial Vibration Suppression in a PDE Model of Ascending Mining Cable Elevator

[+] Author and Article Information
Ji Wang

State Key Laboratory of Mechanical Transmission, and College of Automotive, Engineering, Chongqing University, Chongqing 400044 China
wangji@cqu.edu.cn

Shumon Koga

Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411
skoga@ucsd.edu

Yangjun Pi

State Key Laboratory of Mechanical Transmission, and College of Automotive, Engineering, Chongqing University, Chongqing 400044 China
cqpp@cqu.edu.cn

Miroslav Krstic

ASME Fellow, Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411
krstic@ucsd.edu

1Corresponding author.

ASME doi:10.1115/1.4040217 History: Received October 10, 2017; Revised May 02, 2018

Abstract

Lifting up a cage with miners via a mining cable causes axial vibrations of the cable. These vibration dynamics can be described by a coupled wave PDE-ODE system with a Neumann interconnection on a time-varying spatial domain. Such a system is actuated not at the moving cage boundary, but at a separate fixed boundary where a hydraulic actuator acts on a floating sheave. In this paper, an observer-based output-feedback control law for the suppression of the axial vibration in the varying-length mining cable is designed by the backstepping method. The control law is obtained through the estimated distributed vibration displacements constructed via available boundary measurements.The exponential stability of the closed-loop system with the output-feedback control law is shown by Lyapunov analysis. The performance of the proposed controller is investigated via numerical simulation, which illustrates the effective vibration suppression with the fast convergence of the observer error.

Copyright (c) 2018 by ASME
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