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.

Hand gesture recognition system based in computer vision and machine learning : applications on human-machine interaction

Sendo uma forma natural de interação homem-máquina, o reconhecimento de gestos implica uma forte componente de investigação em áreas como a visão por computador e a aprendizagem computacional. O reconhecimento gestual é uma área com aplicações muito diversas, fornecendo aos utilizadores uma forma mais natural e mais simples de comunicar com sistemas baseados em computador, sem a necessidade de utilização de dispositivos extras. Assim, o objectivo principal da investigação na área de reconhecimento de gestos aplicada à interacção homemmáquina é o da criação de sistemas, que possam identificar gestos específicos e usálos para transmitir informações ou para controlar dispositivos. Para isso as interfaces baseados em visão para o reconhecimento de gestos, necessitam de detectar a mão de forma rápida e robusta e de serem capazes de efetuar o reconhecimento de gestos em tempo real. Hoje em dia, os sistemas de reconhecimento de gestos baseados em visão são capazes de trabalhar com soluções específicas, construídos para resolver um determinado problema e configurados para trabalhar de uma forma particular. Este projeto de investigação estudou e implementou soluções, suficientemente genéricas, com o recurso a algoritmos de aprendizagem computacional, permitindo a sua aplicação num conjunto alargado de sistemas de interface homem-máquina, para reconhecimento de gestos em tempo real. A solução proposta, Gesture Learning Module Architecture (GeLMA), permite de forma simples definir um conjunto de comandos que pode ser baseado em gestos estáticos e dinâmicos e que pode ser facilmente integrado e configurado para ser utilizado numa série de aplicações. É um sistema de baixo custo e fácil de treinar e usar, e uma vez que é construído unicamente com bibliotecas de código. As experiências realizadas permitiram mostrar que o sistema atingiu uma precisão de 99,2% em termos de reconhecimento de gestos estáticos e uma precisão média de 93,7% em termos de reconhecimento de gestos dinâmicos. Para validar a solução proposta, foram implementados dois sistemas completos. O primeiro é um sistema em tempo real capaz de ajudar um árbitro a arbitrar um jogo de futebol robótico. A solução proposta combina um sistema de reconhecimento de gestos baseada em visão com a definição de uma linguagem formal, o CommLang Referee, à qual demos a designação de Referee Command Language Interface System (ReCLIS). O sistema identifica os comandos baseados num conjunto de gestos estáticos e dinâmicos executados pelo árbitro, sendo este posteriormente enviado para um interface de computador que transmite a respectiva informação para os robôs. O segundo é um sistema em tempo real capaz de interpretar um subconjunto da Linguagem Gestual Portuguesa. As experiências demonstraram que o sistema foi capaz de reconhecer as vogais em tempo real de forma fiável. Embora a solução implementada apenas tenha sido treinada para reconhecer as cinco vogais, o sistema é facilmente extensível para reconhecer o resto do alfabeto. As experiências também permitiram mostrar que a base dos sistemas de interação baseados em visão pode ser a mesma para todas as aplicações e, deste modo facilitar a sua implementação. A solução proposta tem ainda a vantagem de ser suficientemente genérica e uma base sólida para o desenvolvimento de sistemas baseados em reconhecimento gestual que podem ser facilmente integrados com qualquer aplicação de interface homem-máquina. A linguagem formal de definição da interface pode ser redefinida e o sistema pode ser facilmente configurado e treinado com um conjunto de gestos diferentes de forma a serem integrados na solução final.

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.

Fractional describing function of systems with nonlinear friction

This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.

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.

Robotic manipulators with vibrations: short time fourier transform of fractional spectra

This paper analyzes the signals captured during impacts and vibrations of a mechanical manipulator. In order to acquire and study the signals an experimental setup is implemented. The signals are treated through signal processing tools such as the fast Fourier transform and the short time Fourier transform. The results show that the Fourier spectrum of several signals presents a non integer behavior. The experimental study provides valuable results that can assist in the design of a control system to deal with the unwanted effects of vibrations.

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Fractional discrete-time signal processing: scale conversion and linear prediction

Nonlinear Dynamics, Vol. 29

Fractional signal processing: scale conversion

In Proceedings of the “ECCTD '01 - European Conference on Circuit Theory and Design, Espoo, Finland, August 2001

Real time mobile system for support in firefighting environments

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

Fractional describing function of systems with Coulomb friction

This paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed into two components, namely, the viscous and the Coulomb friction. The system dynamics is analyzed in the DF perspective revealing a fractional-order behavior. The reliability of the DF method is evaluated through the signal harmonic contents.

Fractional control of heat diffusion systems

The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to 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 and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.

Consumer energy management system with integration of smart meters

This paper develops an energy management system with integration of smart meters for electricity consumers in a smart grid context. The integration of two types of smart meters (SM) are developed: (i) consumer owned SM and (ii) distributor owned SM. The consumer owned SM runs over a wireless platform - ZigBee protocol and the distributor owned SM uses the wired environment - ModBus protocol. The SM are connected to a SCADA system (Supervisory Control And Data Acquisition) that supervises a network of Programmable Logic Controllers (PLC). The SCADA system/PLC network integrates different types of information coming from several technologies present in modern buildings. The developed control strategy implements a hierarchical cascade controller where inner loops are performed by local PLCs, and the outer loop is managed by a centralized SCADA system, which interacts with the entire local PLC network. In order to implement advanced controllers, a communication channel was developed to allow the communication between the SCADA system and the MATLAB software. (C) 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Performance assessment of a wind energy conversion system using a hierarchical controller structure

This paper deals with a hierarchical structure composed by an event-based supervisor in a higher level and two distinct proportional integral (PI) controllers in a lower level. The controllers are applied to a variable speed wind energy conversion system with doubly-fed induction generator, namely, the fuzzy PI control and the fractional-order PI control. The event-based supervisor analyses the operation state of the wind energy conversion system among four possible operational states: park, start-up, generating or brake and sends the operation state to the controllers in the lower level. In start-up state, the controllers only act on electric torque while pitch angle is equal to zero. In generating state, the controllers must act on the pitch angle of the blades in order to maintain the electric power around the nominal value, thus ensuring that the safety conditions required for integration in the electric grid are met. Comparisons between fuzzy PI and fractional-order PI pitch controllers applied to a wind turbine benchmark model are given and simulation results by Matlab/Simulink are shown. From the results regarding the closed loop point of view, fuzzy PI controller allows a smoother response at the expense of larger number of variations of the pitch angle, implying frequent switches between operational states. On the other hand fractional-order PI controller allows an oscillatory response with less control effort, reducing switches between operational states. (C) 2015 Elsevier Ltd. All rights reserved.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.