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.

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.

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.

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.

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena

The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Complex-order dynamics in hexapod locomotion

This paper studies the dynamics of foot–ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear spring-dashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with foot-force feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot–ground transfer function, which presents complex-order dynamics.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Controlo de um robô autónomo através de redes neuronais

Neste trabalho pretende-se introduzir os conceitos associados às redes neuronais e a sua aplicação no controlo de sistemas, neste caso na área da robótica autónoma. Foi utilizado um AGV de modo a testar experimentalmente um controlo através de uma rede neuronal artificial. A grande vantagem das redes neuronais artificiais é estas poderem ser ensinadas a funcionarem como se pretende. A partir desta caraterística foram efetuadas duas abordagens na implementação do AGV disponibilizado. A primeira abordagem ensinava a rede neuronal a funcionar como o controlo por lógica difusa que foi implementado no AGV aquando do seu desenvolvimento. A segunda abordagem foi ensinar a rede neuronal artificial a funcionar a partir de dados retirados de um controlo remoto simples implementado no AGV. Ambas as abordagens foram inicialmente implementadas e simuladas no MATLAB, antes de se efetuar a sua implementação no AGV. O MATLAB é utilizado para efetuar o treino das redes neuronais multicamada proactivas através do algoritmo de treino por retropropagação de Levenberg-Marquardt. A implementação de uma rede neuronal artificial na primeira abordagem foi implementada em três fases, MATLAB, posteriormente linguagem de programação C no computador e por fim, microcontrolador PIC no AGV, permitindo assim diferenciar o desenvolvimento destas técnicas em várias plataformas. Durante o desenvolvimento da segunda abordagem foi desenvolvido uma aplicação Android que permite monitorizar e controlar o AGV remotamente. Os resultados obtidos pela implementação da rede neuronal a partir do controlo difuso e do controlo remoto foram satisfatórios, pois o AGV percorria os percursos testados corretamente, em ambos os casos. Por fim concluiu-se que é viável a aplicação das redes neuronais no controlo de um AGV. Mais ainda, é possível utilizar o sistema desenvolvido para implementar e testar novas RNA.

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.

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.

Step count algorithm adapted to indoor localization

This paper presents a step count algorithm designed to work in real-time using low computational power. This proposal is our first step for the development of an indoor navigation system, based on Pedestrian Dead Reckoning (PDR). We present two approaches to solve this problem and compare them based in their error on step counting, as well as, the capability of their use in a real time system.

Traveled Distance Estimation Algorithm for Indoor Localization

This paper presents an ankle mounted Inertial Navigation System (INS) used to estimate the distance traveled by a pedestrian. This distance is estimated by the number of steps given by the user. The proposed method is based on force sensors to enhance the results obtained from an INS. Experimental results have shown that, depending on the step frequency, the traveled distance error varies between 2.7% and 5.6%.