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

publication date

  • September 2014

start page

  • 697

end page

  • 716


  • 3


  • 17

International Standard Serial Number (ISSN)

  • 1311-0454

Electronic International Standard Serial Number (EISSN)

  • 1314-2224


  • 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 (lambda) D (mu) ) 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.


  • fractional calculus; fractional-order differentiator; fractional-order controller; matlab; warburg impedance; implementation; networks