Current–Mode Fractional–Order Electronically Controllable Integrator Design

This contribution presents a design of a current–mode fractional–order electronically controllable integrator which can be used as a building block for a design of fractional–order (FO) circuits. The design is based on a 2nd–order Follow–the–Leader–Feedback topology which is suitably approximated to operate as an integrator of a fractional order. The topology is based on Operational Transconductance Amplifiers (OTAs), Adjustable Current Amplifiers (ACAs) and Current Follower (CF). The proposed structure offers the ability of the electronic control of its fractional order and also the electronic control of the frequency band. Simulations in Cadence IC6 (spectre) and more importantly experimental measurements were carried out to support the proposal. If wider bandwidth where the approximation is valid is required, a higher order structure must be used as also shown in this paper by utilization of a 4th–order FLF topology

Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems