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.

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.

Climbing robots: a survey of technologies and applications

The interest in the development of climbing robots is growing rapidly. Motivations are typically to increase the operation efficiency by obviating the costly assembly of scaffolding or to protect human health and safety in hazardous tasks. Climbing robots are starting to be developed for applications ranging from cleaning to inspection of difficult to reach constructions. These robots should be capable of travelling on different types of surfaces, with varying inclinations, such as floors, walls, ceilings, and to walk between such surfaces. Furthermore, these machines should be capable of adapting and reconfiguring for various environment conditions and to be self-contained. Regarding the adhesion to the surface, they should be able to produce a secure gripping force using a light-weight mechanism. This paper presents a survey of different applications and technologies proposed for the implementation of climbing robots.

Complex dynamics in the trajectory control of redundant manipulators

Redundant manipulators allow the trajectory optimization, the obstacle avoidance, and the resolution of singularities. For this type of manipulators, the kinematic control algorithms adopt generalized inverse matrices that may lead to unpredictable responses. Motivated by these problems this paper studies the complexity revealed by the trajectory planning scheme when controlling redundant manipulators. The results reveal fundamental properties of the chaotic phenomena and give a deeper insight towards the development of superior trajectory control algorithms.

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

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.

Discretization of complex-order algorithms for control applications

In this article we describe several methods for the discretization of the differintegral operator sa, where α = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.

Control of a 6-DOF parallel manipulator through a mechatronic approach

This paper shows that a hierarchical architecture, distributing several control actions in growing levels of complexity and using resources of reconfigurable computing, enables one to take into account the ease of future modifications, updates and improvements in robotic applications. An experimental example of a Stewart—Gough platform control (a platform applied as the solution to countless practical problems) is presented using reconfigurable computing. The software and hardware developed are structured in independent blocks. This open architecture implementation allows easy expansion of the system and better adaptation of the platform to its related tasks.

Optimal fuzzy PID control tuned with genetic algorithms

Fuzzy logic controllers (FLC) are intelligent systems, based on heuristic knowledge, that have been largely applied in numerous areas of everyday life. They can be used to describe a linear or nonlinear system and are suitable when a real system is not known or too difficult to find their model. FLC provide a formal methodology for representing, manipulating and implementing a human heuristic knowledge on how to control a system. These controllers can be seen as artificial decision makers that operate in a closed-loop system, in real time. The main aim of this work was to develop a single optimal fuzzy controller, easily adaptable to a wide range of systems – simple to complex, linear to nonlinear – and able to control all these systems. Due to their efficiency in searching and finding optimal solution for high complexity problems, GAs were used to perform the FLC tuning by finding the best parameters to obtain the best responses. The work was performed using the MATLAB/SIMULINK software. This is a very useful tool that provides an easy way to test and analyse the FLC, the PID and the GAs in the same environment. Therefore, it was proposed a Fuzzy PID controller (FL-PID) type namely, the Fuzzy PD+I. For that, the controller was compared with the classical PID controller tuned with, the heuristic Ziegler-Nichols tuning method, the optimal Zhuang-Atherton tuning method and the GA method itself. The IAE, ISE, ITAE and ITSE criteria, used as the GA fitness functions, were applied to compare the controllers performance used in this work. Overall, and for most systems, the FL-PID results tuned with GAs were very satisfactory. Moreover, in some cases the results were substantially better than for the other PID controllers. The best system responses were obtained with the IAE and ITAE criteria used to tune the FL-PID and PID controllers.

Sistema de auto calibração visual para robots do ISePorto, baseado em EKF

Os sistemas de perceção existentes nos robôs autónomos, hoje em dia, são bastante complexos. A informação dos vários sensores, existentes em diferentes partes do robôs, necessitam de estar relacionados entre si face ao referencial do robô ou do mundo. Para isso, o conhecimento da atitude (posição e rotação) entre os referenciais dos sensores e o referencial do robô é um fator critico para o desempenho do mesmo. O processo de calibração dessas posições e translações é chamado calibração dos parâmetros extrínsecos. Esta dissertação propõe o desenvolvimento de um método de calibração autónomo para robôs como câmaras direcionais, como é o caso dos robôs da equipa ISePorto. A solução proposta consiste na aquisição de dados da visão, giroscópio e odometria durante uma manobra efetuada pelo robô em torno de um alvo com um padrão conhecido. Esta informação é então processada em conjunto através de um Extended Kalman Filter (EKF) onde são estimados necessários para relacionar os sensores existentes no robô em relação ao referencial do mesmo. Esta solução foi avaliada com recurso a vários testes e os resultados obtidos foram bastante similares aos obtidos pelo método manual, anteriormente utilizado, com um aumento significativo em rapidez e consistência.

Projeto, desenvolvimento e implementação de um robô nadador de inspiração biológica

A elaboração deste trabalho surge no âmbito da unidade curricular de Tese/Dissertação, pertencente ao Mestrado em Engenharia Eletrotécnica e Computadores, ramo de Automação e Sistemas, do Instituto Superior de Engenharia do Porto (ISEP). Este trabalho enquadra-se no âmbito da robótica de inspiração biológica no meio aquático. Pretendeu-se com este trabalho desenvolver e implementar um robô nadador de inspiração biológica. Inicialmente foi realizado um estudo acerca da locomoção dos peixes, para perceber a sua forma de se movimentar. Foi ainda efetuado um estudo acerca dos robôs nadadores existentes, de forma a verificar a sua constituição e formas de locomoção. Numa fase inicial foi desenvolvido um protótipo e, de seguida, procedeu-se à implementação do robô de uma forma sequencial. Implementou-se a estrutura do robô, com o objetivo de se assemelhar o mais possível com um peixe biológico. Foram utilizados servomotores para a locomoção do robô. Para que o robô possua a capacidade de se movimentar numa determinada direção recorreu-se à utilização de uma bússola digital. Posteriormente introduziu-se um emissor/recetor de radiofrequência (RF) para ligar/desligar o robô. Numa fase final procederam-se aos testes da locomoção do robô. Nos ensaios realizados verificou-se que o robô conseguiu nadar com estabilidade e com sentido de direção.

Adapted Control Methods for Cerebral Palsy Users of an Intelligent Wheelchair

The development of an intelligent wheelchair (IW) platform that may be easily adapted to any commercial electric powered wheelchair and aid any person with special mobility needs is the main objective of this project. To be able to achieve this main objective, three distinct control methods were implemented in the IW: manual, shared and automatic. Several algorithms were developed for each of these control methods. This paper presents three of the most significant of those algorithms with emphasis on the shared control method. Experiments were performed by users suffering from cerebral palsy, using a realistic simulator, in order to validate the approach. The experiments revealed the importance of using shared (aided) controls for users with severe disabilities. The patients still felt having complete control over the wheelchair movement when using a shared control at a 50% level and thus this control type was very well accepted. Thus it may be used in intelligent wheelchairs since it is able to correct the direction in case of involuntary movements of the user but still gives him a sense of complete control over the IW movement.

Desenvolvimento de um robô com pernas inspirado no Alfaiate

A elaboração deste trabalho surge no âmbito da unidade curricular de Tese/Dissertação, integrada no Mestrado em Engenharia Eletrotécnica e de Computadores do Instituto Superior de Engenharia do Porto. O trabalho enquadra-se no âmbito da robótica de inspiração biológica, mais concretamente no desenvolvimento de um robô que apresente caraterísticas de locomoção similares ao inseto Alfaiate, modificando para este efeito um robô hexápode já existente. Inicialmente efetuou-se um estudo sobre a biologia do Alfaiate e dos vários tipos de padrões de locomoção adotados pelos animais. De seguida foi realizado um estudo sobre alguns robôs já existentes inspirados neste inseto. Após a realização desta fase de estudo, foram implementadas modificações ao robô hexápode, de forma a este conseguir apoiar-se e movimentar-se sobre a superfície da água. Para tal foram utilizados apoios em esferovite para as pernas, servomotores para a atuação e um sensor de IRPD para orientar o robô na sua trajetória. Em termos de controlo da estabilidade do corpo utilizou-se um giroscópio para permitir ao robô manter o seu corpo horizontal durante a locomoção em águas agitadas. Este trabalho termina com a realização de testes a diferentes padrões de locomoção, de forma a validar o que apresenta a melhor resposta em termos de velocidade.

Load Control Timescales Simulation in a Multi-Agent Smart Grid Platform

Environmental concerns and the shortage in the fossil fuel reserves have been potentiating the growth and globalization of distributed generation. Another resource that has been increasing its importance is the demand response, which is used to change consumers’ consumption profile, helping to reduce peak demand. Aiming to support small players’ participation in demand response events, the Curtailment Service Provider emerged. This player works as an aggregator for demand response events. The control of small and medium players which act in smart grid and micro grid environments is enhanced with a multi-agent system with artificial intelligence techniques – the MASGriP (Multi-Agent Smart Grid Platform). Using strategic behaviours in each player, this system simulates the profile of real players by using software agents. This paper shows the importance of modeling these behaviours for studying this type of scenarios. A case study with three examples shows the differences between each player and the best behaviour in order to achieve the higher profit in each situation.

Development of Biomimetic Robots in the EPS Engineering Programme Capstone Project

This paper proposes the development of biologically inspired robots as the capstone project of the European Project Semester (EPS) framework. EPS is a one semester student centred international programme offered by a group of European engineering schools (EPS Providers) as part of their student exchange programme portfolio. EPS is organized around a central module (the EPS project) and a set of complementary supportive modules. Project proposals refer to open multidisciplinary real world problems. Its purpose is to expose students to problems of a greater dimension and complexity than those faced throughout the degree programme as well as to put them in contact with the socalled real world, in opposition to the academic world. Students are organized in teams, grouping individuals from diverse academic backgrounds and nationalities, and each team is fully responsible for conducting its project. EPS provides an integrated framework for undertaking capstone projects, which is focused on multicultural and multidisciplinary teamwork, communication, problem-solving, creativity, leadership, entrepreneurship, ethical reasoning and global contextual analysis. The design and development of biologically inspired robots allows the students to fulfil the previously described requirements and objectives and, as a result, we recommend the adoption of these projects within the EPS project capstone module for the benefit of engineering students.