Realization of fractional-order controllers: analysis, synthesis and application to the velocity control of a servo system

The synthesis and application of fractional-order controllers is now an active research field. This article investigates the use of fractional-order PID controllers in the velocity control of an experimental modular servo system. The systern consists of a digital servomechanism and open-architecture software environment for real-time control experiments using MATLAB/Simulink. Different tuning methods will be employed, such as heuristics based on the well-known Ziegler Nichols rules, techniques based on Bode’s ideal transfer function and optimization tuning methods. Experimental responses obtained from the application of the several fractional-order controllers are presented and analyzed. The effectiveness and superior performance of the proposed algorithms are also compared with classical integer-order PID controllers.

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.

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.

Abelian realization of phenomenological two-zero neutrino textures

In an attempt at explaining the observed neutrino mass-squared differences and leptonic mixing, lepton mass matrices with zero textures have been widely studied. In the weak basis where the charged lepton mass matrix is diagonal, various neutrino mass matrices with two zeros have been shown to be consistent with the current experimental data. Using the canonical and Smith normal form methods, we construct the minimal Abelian symmetry realizations of these phenomenological two-zero neutrino textures. The implementation of these symmetries in the context of the seesaw mechanism for Majorana neutrino masses is also discussed. (C) 2014 The Authors. Published by Elsevier B.V.

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.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

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.

On the fractional order control of heat systems

The differentiation of non-integer order has its origin in the seventeenth century, but only in the last two decades appeared the first applications in the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated namely the fractional PID and the Smith predictor. Extensive simulations are presented assessing the performance of the proposed fractional-order algorithms.

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.

Anticorpos neutralizantes contra poliovírus em soros de recém-nascidos antes e após imunização em massa da população brasileira de zero a cinco anos de idade. São Paulo, Brasil (1980)

Foram colhidas amostras de sangue de 178 recém-nascidos (RN) em berçários de hospital localizado no Município de São Paulo. Noventa crianças foram puncionadas antes do primeiro "Dia Nacional de Vacinação Contra a Poliomielite" e as outras 88, após o segundo "Dia Nacional de Vacinação Contra a Poliomielite", realizados em 1980. Nessas campanhas foram imunizadas as crianças com idade de zero a cinco anos, em todo o Brasil. No presente trabalho pesquisou-se os títulos de anticorpos neutralizantes contra poliovírus nos dois grupos de recém-nascidos. Após a imunização em massa verificou-se que a taxa de recém-nascidos triplo suscetíveis decresceu de 8,9% para 4,5%, enquanto que o aumento observado do triplo imunes foi de 38,9% para 52,3%; essas diferenças mostraram-se estatisticamente significantes ao nível de 5,0%. A proporção de recém-nascidos, com títulos de anticorpos neutralizantes contra poliovírus iguais ou maiores do que 8, aumentou após as campanhas de imunização, quando passaram de 68,9% para 81,8%, de 73,3% para 83,0% e de 57,8% para 70,5%, respectivamente, para os sorotipos 1, 2 e 3. Essas diferenças mostraram se estatisticamente significantes, ao nível de 5,0%, em relação aos poliovírus 1 e 3.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

Influence of the Sodium/Proton replacement on the structural, morphological and photocatalytic properties of titanate nanotubes

Titanate nanotubes (TNT) with different sodium contents have been synthesised using a hydrothermal approach and a swift and highly controllable post-washing processes. The influence of the sodium/proton replacement on the structural and morphological characteristics of the prepared materials was analysed. Different optical behaviour was observed depending on the Na+/H+ samples’ content. A band gap energy of 3.27±0.03 eV was estimated for the material with higher sodium content while a value of 2.81±0.02 eV was inferred for the most protonated material, which therefore exhibits an absorption edge in the near visible region. The point of zero charge of the materials was determined and the influence of the sodium content on the adsorption of both cationic and anionic organic dyes was studied. The photocatalytic performance of the TNT samples was evaluated in the rhodamine 6G degradation process. Best photodegradation results were obtained when using the most protonated material as catalyst, although this material has shown the lowest R6G adsorption capability.