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Application of integer and fractional models in electrochemical systems
Jesus, Isabel S.; Machado, J. A. TenreiroThis paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these system...
Fractional control with a smith predictor
Jesus, Isabel S.; Machado, J. A. TenreiroThe advantageous use of fractional calculus (FC) in the modeling and control of many dynamical systems has been recognized. In this paper, we study the control of a heat diffusion system based on the application of the FC concepts. Several algorithms are investigated and compared, when integrated within a Smith predictor control structure. Simulations are presented assessing the performance of the proposed frac...
Realization of fractional-order controllers: analysis, synthesis and applicatio...
Barbosa, Ramiro S.; Jesus, Isabel S.; Silva, Manuel F.; Machado, J. A. TenreiroThe 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 em...
Application of fractional order concepts in the study of electrical potential
Jesus, Isabel S.; Machado, J. A. TenreiroThe 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) a...
Application of fractional calculus in engineering
Machado, J. A. Tenreiro; Jesus, Isabel S.; Barbosa, Ramiro S.; Silva, Manuel F.; Reis, CecíliaFractional 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 syst...
Application of genetic algorithms in the design of an electrical potential of f...
Jesus, Isabel S.; Machado, J. A. Tenreiro; Barbosa, Ramiro S.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 ...
Effect of fractional orders in the velocity control of a servo system
Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Jesus, Isabel S.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. Experiment...
Some applications of fractional calculus in engineering
Machado, J. A. Tenreiro; Silva, Manuel F.; Barbosa, Ramiro S.; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria da Graça; Galhano, AlexandraFractional 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 est...
Control and dynamics of fractional order systems
Machado, J. A. Tenreiro; Jesus, Isabel S.; Barbosa, Ramiro S.; Silva, Manuel F.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 con...
Implementation of fractional-order electromagnetic potential through a genetic ...
Jesus, Isabel S.; Machado, J. A. TenreiroSeveral 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.
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