An exact robust differentiator based on continuous fractional sliding modes

[+] Author and Article Information
Aldo Jonathan Muñoz-Vázquez

Mechatronic Engineering, Polytechnic University of Victoria, Mexico

Carlos Vázquez-Aguilera

Applied Physics and Electronics, Umeå University, Sweden

Vicente Parra Vega

Robotics and Advanced Manufacturing, Center for Research and Advanced Studies, Saltillo Campus, Mexico

Anand Sanchez-Orta

Industria Metalurgica 1062 Parque Industrial Saltillo Ramos Arizpe Ramos Arizpe, Coahuila 25900 Mexico

1Corresponding author.

ASME doi:10.1115/1.4039487 History: Received December 04, 2017; Revised February 21, 2018


The problem addressed in this paper is the on-line differentiation of a signal/function that possesses a continuous but not necessarily differentiable derivative. In the realm of (integer) high-order sliding modes, a continuous differentiator provides the exact estimation of the derivative f'(t), of f (t), by assuming the boundedness of its second-order derivative, f"(t), but it has been pointed out that if f'(t) is casted as a Hölder function, then f'(t) is continuous but not necessarily differentiable, and as a consequence, the existence of f"(t) is not guaranteed, but even in such a case, the derivative of f(t) can be exactly estimated by means of a continuous fractional sliding mode based differentiator. Then, the properties of fractional sliding modes, as exact differentiators, are studied. The novelty of the proposed differentiator is twofold: i) it is continuous, and ii) it provides the finite-time exact estimation of f'(t), even if f"(t) does not exist. A numerical study is discussed to show the reliability of the proposed scheme.

Copyright (c) 2018 by ASME
Topics: Reliability , Signals
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