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.

Chaos Dynamics in the Trajectory Conjtrol of Redundant Manipulators

Nonlinear Dynamics, chaos, Control, and Their Applications to Engineering Sciences: Vol. 6 - Applications of nonlinear phenomena

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.

Multi-agent simulation of competitive electricity markets: Autonomous systems cooperation for European market modeling

The electricity market restructuring, and its worldwide evolution into regional and even continental scales, along with the increasing necessity for an adequate integration of renewable energy sources, is resulting in a rising complexity in power systems operation. Several power system simulators have been developed in recent years with the purpose of helping operators, regulators, and involved players to understand and deal with this complex and constantly changing environment. The main contribution of this paper is given by the integration of several electricity market and power system models, respecting to the reality of different countries. This integration is done through the development of an upper ontology which integrates the essential concepts necessary to interpret all the available information. The continuous development of Multi-Agent System for Competitive Electricity Markets platform provides the means for the exemplification of the usefulness of this ontology. A case study using the proposed multi-agent platform is presented, considering a scenario based on real data that simulates the European Electricity Market environment, and comparing its performance using different market mechanisms. The main goal is to demonstrate the advantages that the integration of various market models and simulation platforms have for the study of the electricity markets’ evolution.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Competitive paths for methanol decomposition on ruthenium: a DFT study

Methanol decomposition is one of the key reactions in direct methanol fuel cell (DMFC) state-of-the-art technology, research, and development. However, its mechanism still presents many uncertainties, which, if answered, would permit us to refine the manufacture of DMFCs. The mechanism of methanol decomposition on ruthenium surfaces was investigated using density functional theory and a periodic supercell approach. The possible pathways, involving either initial C−H, C−O or O−H scission, were defined from experimental evidence regarding the methanol decomposition on ruthenium and other metallic surfaces. The study yielded the O−H scission pathway as having both the most favorable energetics and kinetics. The computational data, which present a remarkable closeness with the experimental results, also indicate methanol adsorption, the starting point in all possible pathways, to be of weak nature, implying a considerable rate of methanol desorption from the ruthenium, compromising the reaction.

Gestão de Componentes em Dinâmico

A crescente evolução das tecnologias de informação e comunicação, aliadas ao desenvolvimento industrial, proporcionou um aumento de competitividade entre as indústrias, originando uma subida do nível da relação qualidade preço. Esta premissa causou uma maior preocupação com a procura contínua pela melhoria dos processos, de forma a aumentar as actividades de valor acrescentado, eliminando todo o tipo de desperdícios. Nesta conjuntura, a Grohe Portugal Componentes Sanitários, Lda propôs uma melhoria no âmbito da gestão de stocks de componentes existentes em dinâmico. Esta acção de melhoria passa pela definição e implementação de um método de gestão destes componentes, acompanhado por um conjunto de regras de identificação de actividades e respectivos intervenientes, por forma a optimizar os meios existentes e evitar a ocorrência de falhas de componentes nas linhas. Trata-se de um método baseado no cálculo das necessidades das linhas, que através da procura média semanal e constituição dos produtos finais define um nível de prioridade entre os componentes, identificando quais os mais requisitados pelas linhas e possibilitando a gestão do dinâmico. Na contínua tentativa de combater possíveis falhas, desenvolveu-se um sistema de gestão do tipo Kanban com a capacidade de gerir o produto semi-acabado para consumo interno. Foram, ainda, criadas melhorias que permitem um acréscimo de eficiência na gestão dos componentes em estante dinâmica, diminuindo o capital imobilizado investido em stocks, levando a um rearranjo de layouts, proporcionando melhores condições de trabalho e optimizando percursos e recursos. Descreve-se detalhadamente o processo de (i) actualização, definição e implementação do método de gestão de componentes em dinâmico, acompanhado pelo respectivo conjunto de regras, (ii) a implementação de um sistema do tipo Kanban orientado às reais preocupações da empresa, (iii) a redefinição de layouts em conformidade com a actualização dos dinâmicos e (iv) a identificação e execução de um conjunto de melhorias. Todas estas actividades acompanhadas pelo impacto financeiro na organização. Por fim, efectua-se o balanço deste projecto e sugerem-se oportunidades de melhoria.

Simulation of masonry out-of-plane failure modes by multi-body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so-called local mechanisms, often associated with the out-of-plane wall behavior, whose stability is evaluated by static force-based approaches and, more recently, by some displacement-based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no-tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi-body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full-scale shaking-table tests on stone masonry buildings: a sacco-stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two-storey double-leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE).