Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Application 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. 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 systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.

Lanczos algorithm on the grassmann manifold

5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 8th. World Congress on Computational Mechanics (WCCM8)

Teaching and learning mathematics using moodle

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

Developing multiple - choice questions in mathematics

In this paper we wish to illustrate different perspectives used to create Multiple-Choice questions and we will show how we can improve these in the construction of math tests. As it is known, web technologies have a great influence on student’s behaviour. Based on an on-line project beginning at 2007 which has been contributing to help students on their individual work, we would like to share our experience and thoughts with colleagues who have a common concern when they have the task of constructing Multiple-Choice tests. We feel that Multiple-Choice tests play an important and a very useful supporting role in selfevaluation or self-examination of our students. Nonetheless, good Multiple–Choice Test Items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill maybe increases through study, practice and experience. This paper discusses a number of issues related to the use of Multiple-Choice questions, lists the advantages and disadvantages of this question format contrasting it with open questions. Some examples are given in this context.

How to teach mathematics with MOODLE

The aim of this article is to present a Project in the Oporto’s Institute of Accounting and Administration, which pretends to contribute for a change in the way of teaching and learning Mathematics. One of the main objectives of this project is to innovate the teaching and learning processes, exploring technologies as a pedagogical resource and to induce higher motivation to students, improve the rate of success and make available to students a set of materials adapted to their needs. This concern is justified due to the fact that students have a weak preparation, without consolidated basis. Since the year 2007/2008 the courses were adjusted to the Bologna process, which requires several changes in teacher’s and student’s roles, methodologies and assessment. The number of weekly classes has been reduced, so it was necessary to develop new strategies and methodologies to support the student. With the implementation of the Bologna Process in the Accounting degree, we felt a great need to provide other types of activities to students. To complement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio On-Line (Online Support Project). Moodle allows us to use the language TEX to create materials that use mathematical symbols. Using this functionality, we created a set of easy to use interactive resources. In MatActiva project, the students have access to a variety of different materials. We have followed a strategy that makes the project compatible with the theoretical and practical subjects/classes, complementing them. To do so, we created some resources, for instance multiple-choice tests, which are the most accessed by the students. These tests can be realized and corrected on-line and for each wrong answer there is a feedback with the resolution. We can find other types of resources: diagnostic tests, theoretical notes. There are not only the pre-requirements for subjects mathematics, but also materials to help students follow up the programs. We also developed several lessons. This activity consists of a number of pages, where each page has contents and leads to other pages, based on the student's progress. The teacher creates the choices and determines the next page that the student will see, based upon their knowledge. There is also an area of doubts, where the students can place all the mathematical doubts they have, and a teacher gives the answers or clues to help them in their work. MatActiva also offers an area where we can find some humour, curiosities, contests and games including mathematical contents to test the math skills, as well as links to pages about mathematical contents that could be useful for the study. Since ISCAP receives ERASMUS students and some of them attend mathematics, we developed some materials in English, so they can also use MatActiva. The main objectives of our project are not only to bring success in the subjects of mathematics, but also to motivate the students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence and improve their relationship with the mathematics as well as the communication between students and teachers and among students.

The active mathematics project at ISCAP

This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the students understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. To supplement our theoretical and practical classes we have developed an active mathematics project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). In the last versions of Moodle, it is possible use the TeX language to create math questions. Using this tool we created a set of interactive materials. With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students, encourage them to overcome theirs difficulties through an auto-study, giving them more confidence and the opportunity to seeing others perspectives of the mathematics subjects. In the MatActiva project the students have a big collection of information about the way of the subject works, which includes the objectives, the program, recommended bibliography, evaluation method and summaries. It works as material support for the practical and theoretical classes, the slides of the theoretical classes are available, the sheets with exercises for the students to do in the classroom and complementary exercises, as well as the exams of previous years. Students can also do diagnostic tests and evaluation tests online. Our approach is a reflexive one, based on the professional experience of the teachers that explore and incorporate new tools of Moodle with their students and coordinate the project MatActiva.

New challenges in mathematics for the european higher education

In this paper we will talk about a math project submitted to the Lifelong Learning Programme. European higher education needs a reform in order to play its full role in the Europe of Knowledge. Modernisation of higher education is necessary in the areas of curricula (Bologna process), funding and governance so that higher education institutions can face the challenges posed by globalisation and contribute more effectively to the training and retraining of the European workforce. On the other hand Mathematics is an essential component of all educational systems. Mathematical literacy is being scrutinized in assessment efforts such as the OCDE Programme for International Student Assessment (PISA). This showed a low level in Europe. Due to the Bologna Process, which brought several didactical implications for Higher Education (HE) institutions, there is the need of lifelong learning. This evolution is in conflict with the earlier mentioned lack of competencies on basic sciences, such as Mathematics. Forced by this duality, efforts are combined to share expertise in the Math field and the integration of pedagogical methodologies becomes a necessity. Thus, several European countries have proposed an International Project to the Lifelong Learning Programme, Action ERASMUS Modernisation of Higher Education, to make institutions more attractive and more responsive to the needs of the labour market, citizens and society at large. One of the main goals of the project is to attract students to math through high-quality instructional units in an understandable, exciting and attractive way.

Adaptation model for PCMAT – Mathematics collaborative learning platform

The aim of this paper is to present an adaptation model for an Adaptive Educational Hypermedia System, PCMAT. The adaptation of the application is based on progressive self-assessment (exercises, tasks, and so on) and applies the constructivist learning theory and the learning styles theory. Our objective is the creation of a better, more adequate adaptation model that takes into account the complexities of different users.

Solving a signalized traffic intersection problem with an hyperbolic penalty function

Mathematical Program with Complementarity Constraints (MPCC) finds many applications in fields such as engineering design, economic equilibrium and mathematical programming theory itself. A queueing system model resulting from a single signalized intersection regulated by pre-timed control in traffic network is considered. The model is formulated as an MPCC problem. A MATLAB implementation based on an hyperbolic penalty function is used to solve this practical problem, computing the total average waiting time of the vehicles in all queues and the green split allocation. The problem was codified in AMPL.

Engineering hybrid wired/wireless fieldbus networks - a case study

Advances in networking and information technologies are transforming factory-floor communication systems into a mainstream activity within industrial automation. It is now recognized that future industrial computer systems will be intimately tied to real-time computing and to communication technologies. For this vision to succeed, complex heterogeneous factory-floor communication networks (including mobile/wireless components) need to function in a predictable, flawless, efficient and interoperable way. In this paper we re-visit the issue of supporting real-time communications in hybrid wired/wireless fieldbus-based networks, bringing into it some experimental results obtained in the framework of the RFieldbus ISEP pilot.

Engineering real-time applications with WorldFIP: tools and analysis

WorldFIP is standardised as European Norm EN 50170 - General Purpose Field Communication System. Field communication systems (fieldbuses) started to be widely used as the communication support for distributed computer-controlled systems (DCCS), and are being used in all sorts of process control and manufacturing applications within different types of industries. There are several advantages in using fieldbuses as a replacement of for the traditional point-to-point links between sensors/actuators and computer-based control systems. Indeed they concern economical ones (cable savings) but, importantly, fieldbuses allow an increased decentralisation and distribution of the processing power over the field. Typically DCCS have real-time requirements that must be fulfilled. By this, we mean that process data must be transferred between network computing nodes within a maximum admissible time span. WorldFIP has very interesting mechanisms to schedule data transfers. It explicit distinguishes to types of traffic: periodic and aperiodic. In this paper we describe how WorldFIP handles these two types of traffic, and more importantly, we provide a comprehensive analysis for guaranteeing the real-time requirements of both types of traffic. A major contribution is made in the analysis of worst-case response time of aperiodic transfer requests.

The dark side of DEMMON: what is behind the scene in engineering large-scale wireless sensor networks

Most research work on WSNs has focused on protocols or on specific applications. There is a clear lack of easy/ready-to-use WSN technologies and tools for planning, implementing, testing and commissioning WSN systems in an integrated fashion. While there exists a plethora of papers about network planning and deployment methodologies, to the best of our knowledge none of them helps the designer to match coverage requirements with network performance evaluation. In this paper we aim at filling this gap by presenting an unified toolset, i.e., a framework able to provide a global picture of the system, from the network deployment planning to system test and validation. This toolset has been designed to back up the EMMON WSN system architecture for large-scale, dense, real-time embedded monitoring. It includes network deployment planning, worst-case analysis and dimensioning, protocol simulation and automatic remote programming and hardware testing tools. This toolset has been paramount to validate the system architecture through DEMMON1, the first EMMON demonstrator, i.e., a 300+ node test-bed, which is, to the best of our knowledge, the largest single-site WSN test-bed in Europe to date.

Engineering a search and rescue application with a wireless sensor network - based localization mechanism

The advent of Wireless Sensor Network (WSN) technologies is paving the way for a panoply of new ubiquitous computing applications, some of them with critical requirements. In the ART-WiSe framework, we are designing a two-tiered communication architecture for supporting real-time and reliable communications in WSNs. Within this context, we have been developing a test-bed application, for testing, validating and demonstrating our theoretical findings - a search&rescue/pursuit-evasion application. Basically, a WSN deployment is used to detect, localize and track a target robot and a station controls a rescuer/pursuer robot until it gets close enough to the target robot. This paper describes how this application was engineered, particularly focusing on the implementation of the localization mechanism.

Engineering PROFIBUS networks with heterogeneous transmission media

A significant number of process control and factory automation systems use PROFIBUS as the underlying fieldbus communication network. The process of properly setting up a PROFIBUS network is not a straightforward task. In fact, a number of network parameters must be set for guaranteeing the required levels of timeliness and dependability. Engineering PROFIBUS networks is even more subtle when the network includes various physical segments exhibiting heterogeneous specifications, such as bus speed or frame formats, just to mention a few. In this paper we provide underlying theory and a methodology to guarantee the proper operation of such type of heterogeneous PROFIBUS networks. We additionally show how the methodology can be applied to the practical case of PROFIBUS networks containing simultaneously DP (Decentralised Periphery) and PA (Process Automation) segments, two of the most used commercial-off-the-shelf (COTS) PROFIBUS solutions. The importance of the findings is however not limited to this case. The proposed methodology can be generalised to cover other heterogeneous infrastructures. Hybrid wired/wireless solutions are just an example for which an enormous eagerness exists.