A novel continuous fractional sliding mode control

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.

KEYWORDS:

• Fractional calculus
• disturbance rejection
• sliding mode control
• robust nonlinear control
• anomalous disturbances

Acknowledgment

Authors acknowledge editor and reviewers effort for their precise comments to improve the quality of this paper.

Disclosure statement

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.

Additional information

Funding

The authors acknowledge support from Conacyt under Basic Research Grants [grant number 133346], [grant number 133544]; as well as Scholarship for PhD Studies [grant number 243206].

Notes on contributors

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.

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.

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.