IEEE Journal on Emerging and Selected Topics in Circuits and Systems

In this paper a generalized class of fractional-order systems is realized in digital hardware using a low-cost field programmable gate array (FPGA) device. First, fractional-order derivatives and integrals are realized in fixed-point hardware, wherein each coefficient and signal is represented with a custom number of bits. Both shift-form and delta-form structures are used for discretization, and ... View full abstract»

It has been known that finding a minimal pseudo state space realization for a fractional order transfer function is helpful in circuitry implementation of such a transfer function with the minimum number of fractional capacitors. Considering this importance, the present paper deals with finding minimal realizations for some classes of fractional order transfer functions. To this end, at first some... View full abstract»

This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating sν, with , and (2/T)ν((z-1)/(z+1))ν. The expressions of the coefficients are given in terms of ν and of the degree n of the polynomials defining the convergents. The formulas greatly reduce the effor... View full abstract»

This paper proposes a novel closed-form analytical expression of the fractional derivative of a signal in the Fourier transform (FT) and the fractional Fourier transform (FrFT) domain by utilizing the fundamental principles of the fractional order calculus. The generalization of the differentiation property in the FT and the FrFT domain to the fractional orders has been presented based on the Capu... View full abstract»

Starting with the established concepts of multi-dimensional network resonance, practical-bounded-input-bounded-output (BIBO) stability of multi-dimensional discrete systems, and the integer order approximation of fractional order filters, a new method for the realization of integer-order approximations of 2-D fractional-order systems having frequency-planar beam shaped passbands is proposed. The m... View full abstract»

This paper presents a general procedure to obtain Butterworth filter specifications in the fractional-order domain where an infinite number of relationships could be obtained due to the extra independent fractional-order parameters which increase the filter degrees-of-freedom. The necessary and sufficient condition for achieving fractional-order Butterworth filter with a specific cutoff frequency ... View full abstract»

A causal and compact fractional-order model is developed for complementary metal-oxide-semiconductor (CMOS) on-chip transmission line (T-line) at Terahertz (THz) frequencies. With consideration of the loss from frequency-dependent dispersion and nonquasi-static effects at THz, good agreement of characteristic impedance is observed between the proposed fractional-order model and the measurement up ... View full abstract»

In this paper, we propose using a numerically solved least squares fitting process to estimate the impedance parameters of a fractional order model of supercapacitors from their voltage excited step response, without requiring direct measurement of the impedance or frequency response. Experimentally estimated parameters from low capacity supercapacitors of 0.33, 1, and 1.5 F in the time range 0.2-... View full abstract»

This paper introduces the general fundamentals of the fractional order RLαCα circuit, where α is the order of the elements. The generalized complex impedance of the RLαCα circuit can be purely real, imaginary, or short circuit. The stability analyses where two regions have been classified are introduced with many numeri... View full abstract»

This paper introduces for the first time analog circuit implementations of two fundamental linear fractional order systems whose impulse responses called fractional order damped sine and cosine functions are the inverse Laplace transform of their irrational transfer functions. These analog circuit implementations are derived through rational function approximations of their irrational transfer fun... View full abstract»

The paper presents comparison of two different switching schemes of variable order derivatives. The first one is additive-switching scheme, when change of order is caused by adding a derivative at the beginning of the system. The second one, introduced in this paper, is reductive-switching scheme, when change of order is caused by removing a derivative at the beginning of the system. For both meth... View full abstract»

This paper considers finite-length impulse response (FIR) filter approximation of differentiators and integrators, collectively called differintegrators. The paper introduces and compares three different FIR filter structures for this purpose, all of which are optimized in the minimax sense using iterative reweighted l1-norm minimization. One of the structures is the direct-form structu... View full abstract»

In this survey, we present many of the fractional- order circuit models used in biomedicine and biology to fit experimentally collected impedance data. An overview of the different methods used to extract the impedance parameters from collected datasets are also presented. Applications of fractional order circuit models for modelling human tissue, plant physiology, respiratory systems, and tissue-... View full abstract»

This paper introduces the emerging tool from mathematics in engineering: fractional calculus. Consequently, it enables a novel concept of modelling biological systems by means of preserving the natural rules governing the system's dynamics, i.e., their intrinsic fractal (recurrent) structure. A generally valid ladder network model allows to preserve the anatomy of the system, thereby merging betwe... View full abstract»

In this paper, a new fractional order generalization of the diffusion equation is developed to describe the anisotropy of anomalous diffusion that is often observed in brain tissues using magnetic resonance imaging (MRI). The new model embeds three different fractional order exponents-corresponding to the principal directions of water diffusion-into the governing Bloch-Torrey equation. The model w... View full abstract»

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer-based controller are obtained in terms of linear matrix inequalities (LMIs) formulation. The proposed approach is then applied to secure communicat... View full abstract»

A new two-stage method for reduced integer order approximation of fractional multiple-input, multiple-output (MIMO) systems is proposed. In the first stage, the transfer function matrix (TFM) Gf(s) of the given fractional order MIMO system is obtained and an integer order approximate TFM R(s) is formed by applying an existing approximation method to each fractional order transfer functi... View full abstract»

This paper proposes a self-synchronization error dynamics formulation based controller for maximum photovoltaic power tracking (MPPT) of a photovoltaic (PV) array. The output power conversion of a PV array depends on atmospheric conditions, such as the solar radiation and ambient temperature, and its conversion efficiency is low. Therefore, a MPPT controller is necessary for a PV conversion system... View full abstract»

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This pape... View full abstract»

Control input energy efficiency is an important issue which should be considered in designing any control system. Due to the importance of this subject, in the present paper fractional order control systems are studied in the viewpoint of control input energy efficiency. In this study, the divergent terms of the control input energy function of fractional order control systems are obtained. It is ... View full abstract»