An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Introducing numerical analysis tools in engineering: a Scilab user case in electronics course

Software tools in education became popular since the widespread of personal computers. Engineering courses lead the way in this development and these tools became almost a standard. Engineering graduates are familiar with numerical analysis tools but also with simulators (e.g. electronic circuits), computer assisted design tools and others, depending on the degree. One of the main problems with these tools is when and how to start use them so that they can be beneficial to students and not mere substitutes for potentially difficult calculations or design. In this paper a software tool to be used by first year students in electronics/electricity courses is presented. The growing acknowledgement and acceptance of open source software lead to the choice of an open source software tool – Scilab, which is a numerical analysis tool – to develop a toolbox. The toolbox was developed to be used as standalone or integrated in an e-learning platform. The e-learning platform used was Moodle. The first approach was to assess the mathematical skills necessary to solve all the problems related to electronics and electricity courses. Analysing the existing circuit simulators software tools, it is clear that even though they are very helpful by showing the end result they are not so effective in the process of the students studying and self learning since they show results but not intermediate steps which are crucial in problems that involve derivatives or integrals. Also, they are not very effective in obtaining graphical results that could be used to elaborate reports and for an overall better comprehension of the results. The developed tool was based on the numerical analysis software Scilab and is a toolbox that gives their users the opportunity to obtain the end results of a circuit analysis but also the expressions obtained when derivative and integrals calculations, plot signals, obtain vector diagrams, etc. The toolbox runs entirely in the Moodle web platform and provides the same results as the standalone application. The students can use the toolbox through the web platform (in computers where they don't have installation privileges) or in their personal computers by installing both the Scilab software and the toolbox. This approach was designed for first year students from all engineering degrees that have electronics/electricity courses in their curricula.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.

Kinematic Manipulability of Robotic Systems

Many tasks involving manipulation require cooperation between robots. Meanwhile, it is necessary to determine the adequate values for the robot parameters to obtain a good performence. This paper discusses several aspects related with the manipulability of two co-operative robots when handling objects with different lengths and orientations. In this line of thought, a numerical tool is developed for the calculation and the graphical visualization of the manipulability measure.

Viva@Matemática project: a different way to see math

Viva@Mat is a project developed by four Math teachers from the School of Industrial Studies and Management (ESEIG) that was born with the fundamental objective of engaging ESEIG students with different math backgrounds in Math challenging activities. Some of these activities were transformed into real palpable materials and others into small interactive ones, being the great majority of them proposed by ESEIG’ students themselves. This small project rapidly grew into something we didn’t expect – it did flow over the walls of our institution to the general involving community – specifically to pre-university schools through the Viva@Math Exhibits – Orange, Blue and Green (the fourth, the Purple one is still in development). Nowadays, Viva@Math Exhibits – the public face of the Project – are itinerant and have been travelling between several, and different institutions (pre-university schools, preparatory schools, libraries, among others), around ESEIG and IPP area of influence and having registered visitors/participants of all ages. In this article we will describe the Viva@Math Project, its different activities that are categorized in some “great groups” like Numerical Trivia, Logic Activities and Mental Calculation, Puzzles, Geometric Curiosities, Magic Tricks, among others, designed to challenge students to use the underlying logical-mathematical reasoning to any ordinary and everyday activity. We will give specific and concrete examples of some of the activities developed and, also, reproduce of the general stimulating feedback the Project receives from the enrolled “actors” (teachers, students and their relatives, institutions, among others). We feel that this Project has become a small “bridge” between the pre-university schools and Higher Education Institutions (HEI), in trying to shorten the “gap” between the institutions of different levels of education and bring them to work together.

Modelação e dimensionamento de estruturas

O presente relatório refere-se ao trabalho desenvolvido durante o período de estágio curricular enquadrado no ciclo de estudos do Mestrado em Engenharia Civil do ISEP, Instituto Superior de Engenharia do Porto. O estágio desenvolveu-se ao longo de seis meses, desde Fevereiro até Julho de 2015, na empresa FASE S.A., em ambiente de gabinete, para a obtenção do grau de mestre em Engenharia Civil. Durante o período de estágio foram desenvolvidos projetos de estabilidade de estruturas metálicas e de betão armado, desde a fase de conceção, pré-dimensionamento, modelação numérica e análise de resultados, dimensionamento final, até à produção das peças desenhas e escritas constituintes de um projeto de estruturas. Foi possível analisar e dimensionar estruturas através de programas de cálculo automático e ferramentas de cálculo que serão referidas no presente relatório. Neste relatório será descrita pormenorizadamente a elaboração de um projeto em betão armado em todas as suas vertentes. Apresentam-se também as metodologias de cálculo empregues. No culminar, enunciam-se algumas conclusões de carácter geral decorrentes do trabalho desenvolvido.