Application of fractional calculus in engineering

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. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems. Having these ideas in mind, this paper discusses a FC perspective in the study of the dynamics and control of several systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.

Some applications of fractional calculus in engineering

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, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. 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 FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

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.

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

A fractional approach to the Fermi-Pasta-Ulam problem

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

Control and dynamics of fractional order systems

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 due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fractional order electromagnetics

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.

Control and Dynamics of Fractional Order Systems

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 due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fractional Dynamics and Control of Distributed Parameter Systems

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, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. 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 some distributed parameter 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.

Porto: cidade amiga das pessoas idosas: um estudo centrado na visão de prestadores de serviços a pessoas idosas das freguesias de Cedofeita, Paranhos, St. Ildefonso, Bonfim e Campanhã

O envelhecimento da população é um fenómeno das sociedades contemporâneas simultâneo à crescente modificação do meio urbano. De modo a responder a estas alterações a Organização Mundial de Saúde (OMS) lançou o projeto Cidade Amiga das Pessoas Idosas que preconiza a adaptação das estruturas e serviços para que estes sejam acessíveis e promovam a inclusão dos cidadãos idosos. A presente investigação, de natureza qualitativa e exploratória, tem como objetivo verificar se a cidade do Porto possui características de uma cidade amiga das pessoas idosas através da visão de prestadores de serviços a pessoas idosas das freguesias de Paranhos, Cedofeita, St. Ildefonso, Bonfim e Campanhã. Pretende, assim, ser um contributo para o desenvolvimento do projeto Cidade Amiga das Pessoas Idosas na cidade portuense. Para tal, realizam-se 3 focus groups com prestadores de serviços selecionados a partir de uma amostragem por conveniência, onde se utiliza um guião de entrevista semi-estruturado com as seguintes categorias: espaços exteriores e edifícios, transportes, habitação, participação social, respeito e inclusão social, participação cívica e emprego, comunicação e informação e apoio comunitário e serviços de saúde. É possível verificar que os participantes partilham, de forma geral, uma imagem positiva da cidade do Porto, contudo, têm tendência a iniciar o discurso pelas características negativas da cidade. Colaboram também com sugestões de melhoria para a cidade. Pela perspetiva dos participantes é possível verificar que aspetos relacionados com espaços exteriores e edifícios, respeito e inclusão social e apoio comunitário e serviços de saúde se destacam pela negativa, enquanto aspetos intimos à participação social das pessoas idosas bem como, à comunicação e informação na cidade do Porto são na generalidade elogiados. Desta forma, indicam como positivo o aparecimento de novas iniciativas como as Universidades Seniores ou o projeto “Afetos” desenvolvido pela Misericórdia; as ofertas dirigidas à população sénior desenvolvidas pelas Juntas de Freguesia e a presença de jornais de distribuição gratuita, em espaços públicos. Por oposição, identificam como pouco amigo das pessoas idosas os passeios pouco largos, com obstáculos e pouco cuidados; a falta de casas de banho públicas; o desinvestimento em atividades intergeracionais e a carência de lares públicos na cidade.

O feminino na obra de Uanhenga Xitu

Interessa-nos para este artigo perscrutar as representações da vida social em narrativas do escritor angolano Uanhenga Xitu, mormente no que diz respeito à personagem feminina e ao papel da mulher nas sociedades tradicionais angolanas. Nas narrativas cujas ações se passam no interior de Angola, as representações sociais da mulher revelam um modus vivendi diferenciado daquele experimentado por mulheres que migram para a capital, Luanda, espaço em que a noção de vida comunitária, tão significativa nas sociedades tradicionais, perde seu significado. Os trabalhos lá executados, por exemplo, serão em favor do colono, como os dos empregados domésticos, e não para a coletividade. Já nos espaços interiores, mais distantes da mão pesada do colonizador, as representações da vida social dos angolanos são mais expressivas e essa diferenciação revela que a migração do campo para a cidade, no caso de um país dominado pela colonização, metaforiza o abandono de um tipo de (con)vivência social em favor de outro. Como a política colonial portuguesa foi assimilacionista, essa migração será sinônimo de busca de adesão ao modus vivendi do outro, muitas vezes para sofrer menos os efeitos da dominação. Para essa discussão, não é por livre escolha que se tratará das personagens femininas na obra de Xitu, posto que as mulheres em seus textos ganham vez e voz para a expressão do proprium angolano, como se o autor as quisesse homenagear em sinal do reconhecimento de sua importância na construção e preservação da memória, que é capaz de criar laços identitários entre as milenares gerações passadas e as futuras, como esboçaremos (Esta reflexão teve origem no estudo desenvolvido no doutoramento, intitulado Entre dois contares: o espaço da tradição na escrita de Uanhenga Xitu, defendida em 1996 na FFLCH-USP, e orientada pela Dra. Maria Aparecida Santilli, falecida em março de 2008).