A Review of Recent Advances in Fractional-Order Sensing and Filtering Techniques

Abstract

The present manuscript aims at raising awareness of the endless possibilities of fractional calculus applied not only to system identification and control engineering, but also into sensing and filtering domains. The creation of the fractance device has enabled the physical realization of a new array of sensors capable of gathering more information. The same fractional-order electronic component has led to the possibility of exploring analog filtering techniques from a practical perspective, enlarging the horizon to a wider frequency range, with increased robustness to component variation, stability and noise reduction. Furthermore, fractional-order digital filters have developed to provide an alternative solution to higher-order integer-order filters, with increased design flexibility and better performance. The present study is a comprehensive review of the latest advances in fractional-order sensors and filters, with a focus on design methodologies and their real-life applicability reported in the last decade. The potential enhancements brought by the use of fractional calculus have been exploited as well in sensing and filtering techniques. Several extensions of the classical sensing and filtering methods have been proposed to date. The basics of fractional-order filters are reviewed, with a focus on the popular fractional-order Kalman filter, as well as those related to sensing. A detailed presentation of fractional-order filters is included in applications such as data transmission and networking, electrical and chemical engineering, biomedicine and various industrial fields.

Versatile Field-Programmable Analog Array Realizations of Power-Law Filters

“…Non-integer order signal processing has received significant research interest in the following fields [1][2][3][4][5][6]. The first field is electrical engineering, for implementing filters and oscillators [5,[7][8][9][10][11][12][13][14][15], chaotic systems [16], sensor systems [17], and control systems [2,[18][19][20][21].…”

“…Non-integer order signal processing has received significant research interest in the following fields [1][2][3][4][5][6]. The first field is electrical engineering, for implementing filters and oscillators [5,[7][8][9][10][11][12][13][14][15], chaotic systems [16], sensor systems [17], and control systems [2,[18][19][20][21]. This originates from the fact that both filters and oscillators offer additional degrees of freedom due to the non-integer order, which opens the door for scaling the characteristic frequencies of the filters/oscillators, as well as for precisely controlling the gradient of the transition from the pass-band to the stop-band.…”

A Review of Recent Developments in Autotuning Methods for Fractional-Order Controllers

“…for frequencies ω ≥ ω T , with A a scalar. Further information regarding the tuning, implementation and related topics to fractional order PIDs can be found in some excellent review papers [15,16,[18][19][20][21][22][23][24]. The phase shaper [25] is among the first automatic controller designs that uses fractional calculus tools.…”

On the Design of Power Law Filters and Their Inverse Counterparts

“…The theoretical concepts of fractional calculus [1][2][3], which generalized differ-integral operators, have led to significant developments in circuit theory, signal processing, control theory, bio-impedance modeling, etc. [4][5][6][7][8]. Fractional-order (FO) filters are considered as the generalization of the traditional filters [9].…”