An Exact Robust Differentiator Based on Continuous Fractional Sliding Modes

作者：Jonathan Munoz Vazquez Aldo; Vazquez Aguilera Carlos; Parra Vega Vicente; Sanchez Orta Anand

来源：Journal of Dynamic Systems Measurement and Control-Transactions of the ASME, 2018, 140(9): 091018.

DOI：10.1115/1.4039487

• robust exact differentiator
• fractional sliding modes
• Holder functions
• nonlinear systems

The problem addressed in this paper is the online 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(over dot)(t), of f(t), by assuming the boundedness of its second-order derivative, f(over double dot)(t), but it has been pointed out that if f(over dot)(t) is casted as a Holder function, then fotthorn is continuous but not necessarily differentiable, and as a consequence, the existence of f(over dot)(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(over dot)(t), even if fotthorn does not exist. A numerical study is discussed to show the reliability of the proposed scheme.

• 出版日期2018-9