Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Intrinsic fractal dynamics in the respiratory system by means of pressure-volume loops

This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.

Supercondensadores

Uma nova tecnologia, os EDLC, também denominados por supercondensadores, tem-se tornado numa importante e aliciante área de interesse. Estes regem-se pelos mesmos princípios fundamentais dos condensadores clássicos, no entanto possibilitam receber capacidades superiores, devido a uma maior área de superfície e a um dielétrico menos espesso. Esta particularidade permite obter uma maior densidade energética, comparativamente com os condensadores clássicos e uma maior densidade de potência, comparativamente com as baterias. Consequentemente a utilização de supercondensadores tem aumentado, representando já uma alternativa fiável, segura e amiga do ambiente, em detrimento das baterias comuns. Assim, este projeto tem como principais objetivos, identificar os diferentes tipos de supercondensadores, apresentar as vantagens de cada tipo e explorar a sua resposta, quer no domínio das frequências quer no domínio dos tempos, e por fim modelá-los recorrendo a componentes elétricos clássicos, nomeadamente resistências e condensadores. A modelação foi realizada recorrendo ao MALTAB, através da função de minimização fminunc e foram construídos quatro modelos equivalentes, com o objetivo de modelar a resposta dos vários EDLC analisados. Por escassez de tempo o principal foco de análise recaiu sobre o EDLC de 0,022 F.

Generalized convolution

The paper revisits the convolution operator and addresses its generalization in the perspective of fractional calculus. Two examples demonstrate the feasibility of the concept using analytical expressions and the inverse Fourier transform, for real and complex orders. Two approximate calculation schemes in the time domain are also tested.

The influence of inter-domain mobility on message stream response time in wired/wireless PROFIBUS-based networks

In previous works we have proposed a hybrid wired/wireless PROFIBUS solution where the interconnection between the heterogeneous media was accomplished through bridge-like devices with wireless stations being able to move between different wireless cells. Additionally, we had also proposed a worst-case timing analysis assuming that stations were stationary. In this paper we advance these previous works by proposing a worst-case timing analysis for the system’s message streams considering the effect of inter-cell mobility.