Application of Fractional Calculus in Mechatronics

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of mechanical systems.

System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

Fractional Dynamics in Forest Fires

Every year forest fires consume large areas, being a major concern in many countries like Australia, United States and Mediterranean Basin European Countries (e.g., Portugal, Spain, Italy and Greece). Understanding patterns of such events, in terms of size and spatiotemporal distributions, may help to take measures beforehand in view of possible hazards and decide strategies of fire prevention, detection and suppression. Traditional statistical tools have been used to study forest fires. Nevertheless, those tools might not be able to capture the main features of fires complex dynamics and to model fire behaviour [1]. Forest fires size-frequency distributions unveil long range correlations and long memory characteristics, which are typical of fractional order systems [2]. Those complex correlations are characterized by self-similarity and absence of characteristic length-scale, meaning that forest fires exhibit power-law (PL) behaviour. Forest fires have also been proved to exhibit time-clustering phenomena, with timescales of the order of few days [3]. In this paper, we study forest fires in the perspective of dynamical systems and fractional calculus (FC). Public domain forest fires catalogues, containing data of events occurred in Portugal, in the period 1980 up to 2011, are considered. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses. The frequency spectra of such signals are determined using Fourier transforms, and approximated through PL trendlines. The PL parameters are then used to unveil the fractional-order dynamics characteristics of the data. To complement the analysis, correlation indices are used to compare and find possible relationships among the data. It is shown that the used approach can be useful to expose hidden patterns not captured by traditional tools.

Febrifugine derivative antimalarial activity: quantum mechanical predictors

Plasmodium falciparum resistant strain development has encouraged the search for new antimalarial drugs. Febrifugine is a natural substance with high activity against P. falciparum presenting strong emetic property and liver toxicity, which prevent it from being used as a clinical drug. The search for analogues that could have a better clinical performance is a current topic. We aim to investigate the theoretical electronic structure by means of febrifugine derivative family semi-empirical molecular orbital calculations, seeking the electronic indexes that could help the design of new efficient derivatives. The theoretical results show there is a clustering in well-defined ranges of several electronic indexes of the most selective molecules. The model proposed for achieving high selectivity was tested with success.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

Matrix fractional systems

This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole–Cole, Davidson–Cole, and Havriliak–Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

Estudio de la gestión de la variable ambiental en la generación termoeléctrica

En la actualidad, el cambio climático es uno de los temas de mayor preocupación para la población mundial y los científicos de todo el mundo. Debido al crecimiento de la población de forma exponencial, la demanda de energía aumenta acorde con ello, por lo que las actividades de producción energética aumentan consecuentemente, siendo éstas las principales causantes de la aceleración del cambio climático. Pese a que muchos países previamente habían apostado por la producción energética mediante tecnologías limpias a partir de energías renovables, hoy en día es imposible prescindir de los combustibles fósiles pues, junto a la energía nuclear, suponen el mayor porcentaje dentro del mix energético de los países más grandes del mundo, por lo que el cambio debe ser global y con todos los países implicados al unísono. Por ello, los países desarrollados decidieron acordar una serie de leyes y normas para la regulación y el control de la expansión energética en el mundo, mediante programas de incentivo a las empresas para la producción de energía limpia, libre de emisiones, sustituyendo y mejorando los procesos tecnológicos para que garanticen un desarrollo sostenible. De esta forma, se conseguiría también reducir la dependencia energética de los países productores de los recursos fósiles más importantes y a su vez, ayudar a otros sectores a diversificar su negocio y mejorar así la economía de las áreas colindantes a las centrales de producción térmica. Gracias a estos programas de incentivo o, también llamados mecanismos de flexibilidad, las empresas productoras de energía, al acometer inversiones en tecnologia limpia, dejan de emitir gases de efecto invernadero a la atmósfera. Por tanto, gracias al comercio de emisiones y al mercado voluntario, las empresas pueden vender dichas emisiones aumentando la rentabilidad de sus proyectos, haciendo más atractivo de por sí el hecho de invertir en tecnología limpia. En el proyecto desarrollado, se podrá comprobar de una forma más extensa todo lo anteriormente citado. Para ello, se desarrollará una herramienta de cálculo que nos permitirá analizar los beneficios obtenidos por la sustitución de un combustible fósil, no renovable, por otro renovable y sostenible, como es la biomasa. En esta herramienta se calcularán, de forma estimada, las reducciones de las emisiones de CO2 que supone dicha sustitución y se hallará, en función del valor de las cotizaciones de los bonos de carbono en los diferentes mercados, cuál será el beneficio económico obtenido por la venta de las emisiones no emitidas que supone esta sustitución. Por último, dicho beneficio será insertado en un balance económico de la central donde se tendrán en cuenta otras variables como el precio del combustible o las fluctuaciones del precio de la electricidad, para hallar finalmente la rentabilidad que supondría la inversión de esta adaptación en la central. Con el fin de complementar y aplicar la herramienta de cálculo, se analizarán dos casos prácticos de una central de carbón, en los cuales se decide su suscripción dentro del contexto de los mecanismos de flexibilidad creados en los acuerdos internacionales.

Common variable immunodeficiency and isosporiasis: first report case

We report a severe case of diarrhea in a 62-year-old female HIV-negative patient from whom Giardia lamblia and Isospora belli were isolated. Because unusual and opportunistic infections should be considered as criteria for further analysis of immunological status, laboratory investigations led to a diagnosis of common variable immunodeficiency (CVID). This is the first reported case of isosporiasis in a patient with CVID and illustrates the importance of being aware of a possible link, particularly in relation to primary immunodeficiency.

Fractional state space analysis of economic systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Thermal–mechanical behaviour of chitosan–cellulose derivative thermoreversible hydrogel films

CH, Chitosan; HPMC, (Hydroxypropyl)methyl cellulose; FT, Freeze-thaw; SC, Solvent casting; CH:HPMC (X:Y), pH Z, FT/SC, Chitosan and (hydroxypropyl)methyl cellulose hydrogel, at X and Y proportion (0-100), at Z pH (3.0-4.0) and prepared by freeze-thaw or solvent casting techniques; DSC, Differential scanning calorimetry; MDSC, Temperature modulated Differential scanning calorimetry; Tg, glass transition temperature; ΔH, enthalpy change; TGA, Thermogravimetric Analysis; TG, Thermogravimetry; DTG, Derivative or Differential thermogravimetry; σ, Tensile strength; ε, elongation at break; DMA, Dynamic mechanical analysis; X-Ray, X-radiation, FTIR-ATR, Attenuated total reflectance Fourier transform infrared spectroscopy; SEM, Scanning electron microscopy.

Erratum to: Thermal–mechanical behaviour of chitosan–cellulose derivative thermoreversible hydrogel films

CH, Chitosan; HPMC, (Hydroxypropyl)methyl cellulose; FT, Freeze-thaw; SC, Solvent casting; CH:HPMC (X:Y), pH Z, FT/SC, Chitosan and (hydroxypropyl)methyl cellulose hydrogel, at X and Y proportion (0-100), at Z pH (3.0-4.0) and prepared by freeze-thaw or solvent casting techniques; DSC, Differential scanning calorimetry; MDSC, Temperature modulated Differential scanning calorimetry; Tg, glass transition temperature; ΔH, enthalpy change; TGA, Thermogravimetric Analysis; TG, Thermogravimetry; DTG, Derivative or Differential thermogravimetry; σ, Tensile strength; ε, elongation at break; DMA, Dynamic mechanical analysis; X-Ray, X-radiation, FTIR-ATR, Attenuated total reflectance Fourier transform infrared spectroscopy; SEM, Scanning electron microscopy.

Predicting SO2 pollution incidents by means of additive models with optimum variable selection

The aim of this paper is to predict time series of SO2 concentrations emitted by coal-fired power stations in order to estimate in advance emission episodes and analyze the influence of some meteorological variables in the prediction. An emission episode is said to occur when the series of bi-hourly means of SO2 is greater than a specific level. For coal-fired power stations it is essential to predict emission epi- sodes sufficiently in advance so appropriate preventive measures can be taken. We proposed a meth- odology to predict SO2 emission episodes based on using an additive model and an algorithm for variable selection. The methodology was applied to the estimation of SO2 emissions registered in sampling lo- cations near a coal-fired power station located in Northern Spain. The results obtained indicate a good performance of the model considering only two terms of the time series and that the inclusion of the meteorological variables in the model is not significant.

Influence of the elevation of the left ventricular diastolic pressure on the values of the first temporal derivative of the ventricular pressure (dP/dt)

PURPOSE: To assess the effects of the elevation of the left ventricular end-diastolic pressure (LVEDP) on the value of the 1st temporal derivative of the ventricular pressure (dP/dt). METHODS: Nineteen anesthetized dogs were studied. The dogs were mechanically ventilated and underwent thoracotomy with parasympathetic nervous system block. The LVEDP was controlled with the use of a perfusion circuit connected to the left atrium and adjusted to the height of a reservoir. The elevation of the LVEDP was achieved by a sudden increase in the height of a reservoir filled with blood. Continuous recordings of the electrocardiogram, the aortic and ventricular pressures and the dP/dt were performed. RESULTS: Elevation of the LVEDP did not result in any variation of the heart rate (167±16.0bpm, before the procedure; 167±15.5bpm, after the procedure). All the other variables assessed, including systolic blood pressure (128±18.3mmHg and 150±21.5mmHg), diastolic blood pressure (98±16.9mmHg and 115±19.8mmHg), LVEDP (5.5±2.49 and 9.3±3.60mmHg), and dP/dt (4,855 ± 1,082 mmHg/s and 5,149±1,242mmHg/s) showed significant increases following the expansion of the ventricular cavity. Although the elevation of the dP/dt was statistically significant, 6 dogs curiously showed a decrease in the values of dP/dt. CONCLUSION: Sudden elevation of the LVEDP resulted in increased values of dP/dt; however, in some dogs, this response was not uniform.

Variable Ventilsteuerung für Pkw-Dieselmotoren mit Direkteinspritzung

Dieselmotor, Brennverfahren, Ventilsteuerung, Ladungswechsel