@article{6b22cda2bd5c42ada1b394e4a961cef4,
title = "Exponential regulation of the anti-collocatedly disturbed cage in a wave PDE-modeled ascending cable elevator",
abstract = "In cable elevators, large axial vibrations appear when a cage subject to disturbance is lifted up via a compliant cable. The axial vibration dynamics can be described by a wave partial differential equation (PDE) on a time-varying spatial interval with an unknown boundary disturbance. In this paper, we design an output feedback controller actuating at the boundary anti-collocated with the disturbance to regulate the state on the uncontrolled boundary of the wave PDE based on the backstepping idea and the active disturbance rejection control (ADRC) approach. The control law uses the state and disturbance information recovered from the state observer and the disturbance estimator, respectively, which are constructed via limited boundary measurements. The exponential convergence of the state on the uncontrolled boundary and uniform boundedness of all states in the closed-loop system are proved by Lyapunov analysis. Effective vibration suppression in the cable elevator with the designed controller is verified via numerical simulation.",
keywords = "ADRC, Anti-collocated disturbance, Backstepping, Exponential disturbance attenuation, Wave equation",
author = "Ji Wang and Tang, {Shu Xia} and Yangjun Pi and Miroslav Krstic",
note = "Funding Information: This work is supported by National Basic Research Program of China [ 2014CB049404 ], National Natural Science Foundation of China ( 61773112 ), 2015 Chongqing University Postgraduates Innovation Project [ CYD15023 ] and China Scholarship Council (CSC) . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Yoshihiko Miyasato under the direction of Editor Richard Middleton. Funding Information: Ji Wang received the B.Eng. degree in Mechanical Engineering and Automation from Jimei University, Xiamen, China, in 2012. From 2012 to 2014, he was a master student in Mechatronic Engineering at Chongqing University, Chongqing, China, where he has been a Ph.D. student in Mechanical Engineering from 2014. Supported by China Scholarship Council, he was a visiting graduate student in the Department of Mechanical and Aerospace Engineering at University of California, San Diego, La Jolla, CA, USA, from 2015 to 2017. His research interests include modeling and control of distributed parameter systems, active disturbance rejection control and adaptive control, with applications in mechanical systems. Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",
year = "2018",
month = sep,
doi = "10.1016/j.automatica.2018.05.022",
language = "English",
volume = "95",
pages = "122--136",
journal = "Automatica",
issn = "0005-1098",
}