ABSTRACT
A new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.
Acknowledgment
Authors acknowledge editor and reviewers effort for their precise comments to improve the quality of this paper.
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No potential conflict of interest was reported by the authors.
Notes
1. A Hölder continuous function is not necessarily differentiable in the common integer-order sense, such as Lipschitz disturbances.
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Notes on contributors
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A.J. Muñoz-Vázquez
Aldo-Jonathan Muñoz-Vázquez received the M.Sc. and Ph.D. degrees in Robotics and Advanced Manufacturing from the Research Center for Advanced Studies (CINVESTAV), Saltillo Campus, Mexico, in 2012 and 2016, respectivelly. His research interests include sliding mode control, control of robotics systems and fractional-order control.
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V. Parra-Vega
Vicente Parra-Vega received the Ph.D. degree in Mathematical Engineering and Information from the University of Tokyo, Tokyo, Japan, in 1995. His research interests include robot control, non-inertial robots, man-machine interfaces, and mechatronics. He spent a posdoctoral leave in the German Aerospace Agency in 2000, and a sabbatic leave in the University of Texas in 2010. Actually, He is full professor in the Robotics and Advanced Manufacturing Department of CINVESTAV.
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A. Sánchez-Orta
Anand Sánchez-Orta received the M.Sc. from the University of Nuevo León, Monterrey, Mexico, in 2001, and the Ph.D. degree from the University of Technology of Compiegne, Compiegne, France, in 2007. Actually, He is full professor in the Robotics and Advanced Manufacturing Department of CINVESTAV. His research interest include control theory, estimation and visual servoing with applications to robotics.