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Research Papers

Second-Order Sliding Mode Control of a Perturbed-Crane

[+] Author and Article Information
Carlos Vázquez

Department of Applied Physics and Electronics,
Umeå University,
Umeå SE-901 87, Sweden
e-mail: carlos.vazquez@umu.se

Leonid Fridman

Professor
Department of Control Engineering and Robotics,
Universidad Nacional Autónoma de México,
Mexico City 04510, Mexico
e-mail: lfridman@unam.mx

Joaquin Collado

Professor
Department of Automatic Control CINVESTAV,
Av. IPN 2508,
Mexico City 07360, Mexico
e-mail: jcollado@ctrl.cinvestav.mx

Ismael Castillo

Department of Control Engineering and Robotics,
Universidad Nacional Autónoma de México,
Mexico City 04510, Mexico
e-mail: casism@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 10, 2014; final manuscript received March 24, 2015; published online April 24, 2015. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 137(8), 081010 (Aug 01, 2015) (7 pages) Paper No: DS-14-1407; doi: 10.1115/1.4030253 History: Received October 10, 2014; Revised March 24, 2015; Online April 24, 2015

A five degrees-of-freedom overhead crane system affected by external perturbations is the topic of study. Existing methods just handle the unperturbed case or, in addition, the analysis is limited to three or two degrees-of-freedom. A wide range of processes cannot be restricted to these scenarios and this paper goes a step forward proposing a control solution for a five degrees-of-freedom system under the presence of matched and unmatched disturbances. The contribution includes a model description and a second-order sliding mode (SOSM) control design ensuring the precise trajectory tracking for the actuated variables and at the same time the regulation of the unactuated variables. Furthermore, the proposed approach is supported by the design of strong Lyapunov functions providing an estimation of the convergence time. Simulations and experiments, including a comparison with a proportional-integral-derivative (PID) controller, verified the advantages of the methodology.

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Figures

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Fig. 3

Simulation: trolley position and rope length (m), payload oscillations (deg), control actions (N) versus time (s)

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Fig. 4

Velocity estimation: trolley and rope length (m/s) and payload oscillations (deg/s) versus time (s)

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Fig. 5

Experiment: trolley position and rope length (m), payload oscillations (deg), control actions (N) versus time (s)

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Fig. 6

Velocity estimation: trolley and rope length (m/s) and payload oscillations (deg/s) versus time (s)

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Fig. 7

PID: trolley position and rope length (m), payload oscillations (deg), control actions (N) versus time (s)

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