Analogue Realization of Fractional-Order Dynamical Systems

Abstract

Abstract:As it results from many research works, the majority of real dynamical objects are fractional-order systems, although in some types of systems the order is very close to integer order. Application of fractional-order models is more adequate for the description and analysis of real dynamical systems than integer-order models, because their total entropy is greater than in integer-order models with the same number of parameters. A great deal of modern methods for investigation, monitoring and control of the dynamical processes in different areas utilize approaches based upon modeling of these processes using not only mathematical models, but also physical models. This paper is devoted to the design and analogue electronic realization of the fractional-order model of a fractional-order system, e.g., of the controlled object and/or controller, whose mathematical model is a fractional-order differential equation. The electronic realization is based on fractional-order differentiator and integrator where operational amplifiers are connected with appropriate impedance, with so called Fractional Order Element or Constant Phase Element. Presented network model approximates quite well the properties of the ideal fractional-order system compared with e.g., domino ladder networks. Along with the mathematical description, OPEN ACCESSEntropy 2013, 15 4200 circuit diagrams and design procedure, simulation and measured results are also presented.

Ultra‐low voltage fractional‐order circuits using current mirrors

“…Thus, a possible solution is the substitution of CFEs by appropriate RC networks, which approximate their behavior [16,17]. A number of voltage-mode filter topologies with approximated CFEs have been already published in [18][19][20][21][22][23][24][25][26][27]. Another solution is the concept introduced in [28][29][30], where the approximation of fractional-order filter functions has been performed by appropriate integer-order functions.…”

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.…”

On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem

“…Furthermore, it appeared in the theory of the control of dynamical systems, when the controlled system and/or the controller is described by an FDE [8][9][10]. Some relevant monographs are Podlubny [10], Kilbas et al [11] and Baleanu et al [12].…”