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Mathematical Problems in Engineering
Volume 2017, Article ID 4876019, 13 pages
Research Article

Integral Sliding Modes with Nonlinear -Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances

1CONACYT-Instituto Politécnico Nacional-CITEDI, Av. Instituto Politécnico Nacional 1310, Nueva Tijuana, 22435 Tijuana, BC, Mexico
2Instituto Politécnico Nacional, Av. Instituto Politécnico Nacional 1310, Nueva Tijuana, 22435 Tijuana, BC, Mexico

Correspondence should be addressed to Luis T. Aguilar; xm.npi@braliugal

Received 11 July 2016; Revised 19 October 2016; Accepted 21 November 2016; Published 17 January 2017

Academic Editor: Kalyana C. Veluvolu

Copyright © 2017 Roger Miranda-Colorado et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a methodology for controlling nonlinear time-varying minimum-phase underactuated systems affected by matched and unmatched perturbations. The proposed control structure consists of an integral sliding mode control coupled together with a global nonlinear -control for rejecting vanishing and nonvanishing matched perturbations and for attenuating the unmatched ones, respectively. It is theoretically proven that, using the proposed controller, the origin of the free-disturbance nonlinear system is asymptotically stabilized, while the matched disturbances are rejected whereas the -gain of the corresponding nonlinear system with unmatched perturbation is less than a given disturbance attenuation level with respect to a given performance output. The capability of the designed controller is verified through a flexible joint robot manipulator typically affected by both classes of external perturbations. In order to assess the performance of the proposed controller, an existing sliding modes controller based on a nonlinear integral-type sliding surface is also implemented. Both controllers are then compared for trajectory tracking tasks. Numerical simulations show that the proposed approach exhibits better performance.