Fractional control of legged robots

Fractional calculus (FC) is being used in several distinct areas of science and engineering, being recognized its ability to yield a superior modelling and control in many dynamical systems. This article illustrates the application of FC in the area of robot control. A Fractional Order PDμ controller is proposed for the control of an hexapod robot with 3 dof legs. It is demonstrated the superior performance of the system by using the FC concepts.

Application of fractional order concepts in the study of electrical potential

The Maxwell equations, expressing the fundamental laws of electricity and magnetism, only involve the integer-order calculus. However, several effects present in electromagnetism, motivated recently an analysis under the fractional calculus (FC) perspective. In fact, this mathematical concept allows a deeper insight into many phenomena that classical models overlook. On the other hand, genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. In this work we use FC and GA to implement the electrical potential of fractional order. The performance of the GA scheme and the convergence of the resulting approximations are analyzed.

Fractional control of dynamic systems

The concepts involved with fractional calculus (FC) theory are applied in almost all areas of science and engineering. Its ability to yield superior modeling and control in many dynamical systems is well recognized. In this article, we will introduce the fundamental aspects associated with the application of FC to the control of dynamic systems.

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.

Application of genetic algorithms in the design of an electrical potential of fractional order

Fractional calculus (FC) is currently being applied in many areas of science and technology. In fact, this mathematical concept helps the researches to have a deeper insight about several phenomena that integer order models overlook. Genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. This methodology applies the concepts that describe biological evolution to obtain optimal solution in many different applications. In this line of thought, in this work we use the FC and the GA concepts to implement the electrical fractional order potential. The performance of the GA scheme, and the convergence of the resulting approximation, are analyzed. The results are analyzed for different number of charges and several fractional orders.

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.

Three-dimensial patchy lattice model: Ring formation and phase separation

We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self- assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension ofWertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r epsilon(AB)/epsilon(AA) of the interaction between patches A and B, epsilon(AB), and between A patches, epsilon(AA) (epsilon(BB) is set to theta) as well as the relative position of the A patches, i.e., the angle. between the (lattice) directions of the A patches. We found that both r and theta (60 degrees, 90 degrees, or 120 degrees) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for theta = 120 degrees but deteriorates as. decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings. (C) 2014 AIP Publishing LLC.

Particle swarm optimization with fractional-order velocity

This paper proposes a novel method for controlling the convergence rate of a particle swarm optimization algorithm using fractional calculus (FC) concepts. The optimization is tested for several well-known functions and the relationship between the fractional order velocity and the convergence of the algorithm is observed. The FC demonstrates a potential for interpreting evolution of the algorithm and to control its convergence.

Permeabilidade e microestrutura de BAC com incorporação de fíler calcário

A durabilidade do betão está diretamente relacionada com o transporte de fluídos no seu interior que, por sua vez, está condicionado pela microestrutura do mesmo. Dadas as diferenças da estrutura porosa do betão auto-compactável (BAC) quando comparada com a de um betão convencional (BC), serão expectáveis algumas diferenças na durabilidade do primeiro. Um dos principais elementos diferenciadores entre ambos é a necessidade de quantidades significativas de material ultra fino (cimento e adições) por parte do BAC, essencialmente de modo a garantir os seus requisitos de comportamento no estado fresco. A utilização de adições, como o fíler calcário (FC), pode melhorar não só o comportamento do BAC no estado fresco como também influenciar a resistência mecânica e a durabilidade, através de uma microestrutura mais densa. Nesse sentido, o objetivo do presente trabalho é avaliar o efeito da utilização de FC na permeabilidade e na microestrutura do BAC. De modo a comprovar as referidas relações, foram efetuados estudos sobre a correlação entre as propriedades da microestrutura e os mecanismos de transporte, através da produção de misturas de BAC com 0%, 30%, 45% e 60% de substituição de cimento por FC. A caracterização físico-química das amostras de BAC foi realizada por difracção de raios-x e por microscopia eletrónica de varrimento (MEV), sendo esta última técnica também um método de caracterização morfológica. Para analisar as propriedades de transporte do BAC foram executados ensaios de absorção por imersão e absorção capilar. A análise dos resultados obtidos permitiu concluir que os betões em estudo apresentam características satisfatórias ao nível da microestrutura e propriedades de transporte. Salienta-se que em todas as amostras foi encontrada uma microestrutura densa, não tendo sido encontrada uma zona de transição entre o agregado e a pasta com características que a diferenciem da restante da pasta. Estas observações complementam os valores encontrados no estudo das propriedades de transporte, fazendo prever que as amostras apresentam uma baixa porosidade.

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.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Implementation of fractional-order electromagnetic potential through a genetic algorithm

Several phenomena present in electrical systems motivated the development of comprehensive models based on the theory of fractional calculus (FC). Bearing these ideas in mind, in this work are applied the FC concepts to define, and to evaluate, the electrical potential of fractional order, based in a genetic algorithm optimization scheme. The feasibility and the convergence of the proposed method are evaluated.

Resistividade elétrica e permeabilidade de BAC com incorporação de cinzas volantes e fíler calcário

A resistividade elétrica é uma propriedade associada tanto a características físicas como químicas do betão, permitindo avaliar a maior ou menor dificuldade de penetração dos agentes agressivos no seu interior antes de iniciado o processo de despassivação e consequente corrosão das armaduras. Este trabalho aborda as propriedades de permeabilidade, correlacionando-as com a resistividade elétrica, de betão auto-compactável (BAC) com diferentes tipos e quantidades de adições. Para esse efeito, foram produzidas misturas binárias e ternárias de BAC com recurso a cinzas volantes (CV) e fíler calcário (FC). Produziu-se um total de 11 misturas auto-compactáveis: uma só com cimento (C); três com C+CV em 30, 60 e 70% de substituição; três com C+FC em 30, 60 e 70% de substituição; quatro com C+CV+FC em combinações de 10-20, 20-10, 20-40 e 40-20% de substituição respetivamente; e, por fim, quatro misturas de acordo com as especificações LNEC E 464 em referência à norma NP EN 206-1. A avaliação da permeabilidade dos betões produzidos foi feita através do ensaio de determinação da absorção de água por capilaridade de acordo com a especificação LNEC E 393. A resistividade elétrica foi avaliada recorrendo à proposta de norma europeia apresentada pelo EU-Project CHLORTEST (EU funded research Project under 5FP GROWTH programme) e com base na recomendação técnica RILEM TC-154 EMC. Os resultados obtidos indicam que as propriedades de permeabilidade do BAC são fortemente condicionadas pelo tipo e pela quantidade de adições utilizadas, constatando-se que a adição de CV melhora significativamente algumas das propriedades estudadas principalmente em idades mais avançadas.

Tuning and application of integer and fractional order PID controllers

Fractional calculus (FC) is widely used in most areas of science and engineering, being recognized its ability to yield a superior modeling and control in many dynamical systems. In this perspective, this article illustrates two applications of FC in the area of control systems. Firstly, is presented a methodology of tuning PID controllers that gives closed-loop systems robust to gain variations. After, a fractional-order PID controller is proposed for the control of an hexapod robot with three dof legs. In both cases, it is demonstrated the system's superior performance by using the FC concepts.

In vitro susceptibility of Paracoccidioides brasiliensis yeast form to antifungal agents

A study was conducted to determine the susceptibility of P. brasiliensis yeast form to amphotericin B (A), ketoconazole (K), 5-fluorocytosine (5-FC) and rifampin (R). The three isolates tested produced minimal inhibitory concentrations (MICs) (mcg/ml) in the following range: A: 0.09-0.18; K: 0.001-0.007; 5-FC: 62.5-250 and R: 40-80. The minimal fungicidal concentrations (MFC) were several times higher than the corresponding MICs. Precise MFC for 5-FC were not obtained (> 500 mcg/ml). Combination of K plus A proved synergic, with the fractional inhibitory concentration (FIC) indices revealing synergy when the drugs were combined at the 1 to 1 and 1 to 5 MIC ratios. R (40 mcg/ml) appeared to antagonize K. These results indicate promise for the combined use of K plus A as a therapeutical regimen.