Studies on fractional order differentiators and integrators: A survey

Photonic signal processing has been considered a solution to overcome the inherent electronic speed limitations. Over the past few years, an impressive range of photonic integrated signal processors have been proposed, but they usually offer limited reconfigurability, a feature highly needed for the implementation of large-scale general-purpose photonic signal processors. Here, we report and experimentally demonstrate a fully reconfigurable photonic integrated signal processor based on an InP–InGaAsP material system. The proposed photonic signal processor is capable of performing reconfigurable signal processing functions including temporal integration, temporal differentiation and Hilbert transformation. The reconfigurability is achieved by controlling the injection currents to the active components of the signal processor. Our demonstration suggests great potential for chip-scale fully programmable all-optical signal processing. Scientists experimentally demonstrate a fully configurable photonic integrated signal processor based on an InP–InGaAs material system by controlling the injection currents to the active components.

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A fully reconfigurable photonic integrated signal processor

A simple method for fabricating a constant phase element (CPE) has been discussed. Dependence of the phase angle on several physical parameters have also been elaborated. Finally, a fractional-order differentiator circuit has been constructed using the CPE, and its performance has been compared with the simulated results

Realization of a Constant Phase Element and Its Performance Study in a Differentiator Circuit

Introducing fractional operators in the adaptive control loop, and especially in Model Reference Adaptive Control (MRAC), has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. The idea of introducing fractional operators in adaptation algorithms is very recent and needs to be more established, that is why many research teams are working on the subject. Previously, some authors have introduced a fractional model reference in the adaptation scheme, and then fractional integration has been used to deal directly with the control rule. Our original contribution in this paper is the use of a fractional derivative feedback of the plant output, showing that this scheme is equivalent to the fractional integration, one with a certain benefit action on the system dynamical behaviour and a good robustness effect. Numerical simulations are presented to show the effectiveness of the proposed fractional adaptive schemes.

Ch. Ceyral

Papers

Fractional differentiation for edge detection