Conceptual design of a selectable fractional-order differentiator for industrial applications

Abstract

In the past decade, researchers working on fractional-order systems modeling and control have been considering working on the design and development of analog and digital fractional-order differentiators, i.e. circuits that can perform non-integer-order differentiation. It has been one of the major research areas under such field due to proven advantages over its integer-order counterparts. In particular, traditional integer-order proportional-integral-derivative (PID) controllers seem to be outperformed by fractional-order PID (FOPID or PI λ D μ ) controllers. Many researches have emerged presenting the possibility of designing analog and digital fractional-order differentiators, but only restricted to a fixed order. In this paper, we present the conceptual design of a variable fractional-order differentiator in which the order can be selected from 0 to 1 with an increment of 0.05. The analog conceptual design utilizes operational amplifiers and resistor-capacitor ladders as main components, while a generic microcontroller is introduced for switching purposes. Simulation results through Matlab and LTSpiceIV show that the designed resistor-capacitor ladders can perform as analog fractional-order differentiation.

Realization of a carbon nanotube based electrochemical fractor

“…However, market unavailability of single component packaged fractor limited these successes much to theoretical domain. Fractors are commonly realized by different types of RC ladder circuits, mainly by domino or cross RC ladder circuits [18] or their modified versions [19], [20]. Main advantage of such realization is to have defined guidelines to achieve a particular α value.…”

Fractional Order AGC for Distributed Energy Resources Using Robust Optimization

“…There have been several recent breakthrough in the hardware realization of FO controller e.g. digital realization using fixed and floating point representation [34], analog realization for fixed order [35] and finally variable selectable order [36]. This paper shows a proof-of-concept design methodology which facilitates the hardware implementation by making the system performance almost invariant to the type of realization used for the FO differintegral operators in the FOPID controller.…”

“…The set of points S can be used for robust fitness evaluation without calling the computationally expensive objective function, while those in X need to be resampled and added to the archive. The effective fitness function is calculated by using the points from both S and X using (36).…”

Reduced Active Components Count Electronically Adjustable Fractional-Order Controllers: Two Design Examples

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