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.

Fractional analysis of traffic dynamics

This article presents a dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform. The new dynamic description integrates the concepts of fractional calculus leading to a more natural treatment of the continuum of the Transfer Function parameters intrinsic in this system. The results using system theory tools point out that it is possible to study traffic systems, taking advantage of the knowledge gathered with automatic control algorithms. Dynamics, Games and Science I Dynamics, Games and Science I Look Inside Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn

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.

Fixed point transformations in the adaptive control of fractional-order MIMO systems

Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, in connection with visco-elastic phenomena [5, 6]. The topic later obtained quite general attention [7, 8, 9], and also found new applications in material science [10], analysis of earth-quake signals [11], control of robots [12], and in the description of diffusion [13], etc.

Optimal tuning of fractional controllers using genetic algorithms

This study addresses the optimization of fractional algorithms for the discrete-time control of linear and non-linear systems. The paper starts by analyzing the fundamentals of fractional control systems and genetic algorithms. In a second phase the paper evaluates the problem in an optimization perspective. The results demonstrate the feasibility of the evolutionary strategy and the adaptability to distinct types of systems.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

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.

A flexibility reference model to achieve leagility in virtual organizations

The paper proposes a Flexibility Requirements Model and a Factory Templates Framework to support the dynamic Virtual Organization decision-makers in order to reach effective response to the emergent business opportunities ensuring profitability. Through the construction and analysis of the flexibility requirements model, the network managers can achieve and conceive better strategies to model and breed new dynamic VOs. This paper also presents the leagility concept as a new paradigm fit to equip the network management with a hybrid approach that better tackle the performance challenges imposed by the new and competitive business environments.

Application of fractional algorithms in the control of a robotic bird

In this paper, it is studied the dynamics of the robotic bird in terms of time response and robustness. It is analyzed the wing angle of attack and the velocity of the bird, the tail influence, the gliding flight and the flapping flight. The results are positive for the construction of flying robots. The development of computational simulation based on the dynamic of the robotic bird should allow testing strategies and different algorithms of control such as integer and fractional controllers.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.