Control Theory - an interactive online course

Katarína Žáková Faculty of Electrical Engineering and Information Technology

Slovak University of Technology Ilkovičova 3, 812 19 Bratislava, Slovakia

katarina.zakova@stuba.sk

Abstract

The aim of the article is to present an interactive online course that was developed at the Faculty of Electrical Engineering and Information Technology STU in Bratislava. It was prepared to attract students’ interest. Besides teaching materials in the traditional workbook form, new electronic media (CDs, Internet) are used to enable interactive and computer supported way of learning.

1. Introduction

Mathematical control theory is the area of application-oriented mathematics that deals with the basic principles underlying the analysis and design of control systems. To control an object means to influence its behavior so as to achieve a desired goal. In order to implement this influence, engineers build devices that incorporate various mathematical techniques [5]. At the beginning there were amplifiers for radios, radar detection equipment, aircraft, and aerospace vehicles. Recently control has been applied to cars, motorway networks, air traffic control, communication networks, manufacturing, macroeconomic control, mathematical finance, public health, the life sciences, environmental protection, weather prediction, and climate modelling [4].

The Control Theory is one of the fundamental subjects that are taught at universities of technical orientation. At the Faculty of Electrical Engineering and Information Technology (Slovak University of Technology) in Bratislava it is placed into the second year of the study.

The course is an introduction to analysis and design of feedback control systems. It presents an integrated approach to control theory from both the frequency domain and time domain. The big emphasis is devoted to modeling of various systems. Depending on the particular system and the particular circumstances, one mathematical model can be better than another one. For example, in optimal control problems, it is advantageous to use state-space representations. On the other hand, for the transient response or frequency response analysis of single input single output, linear, time-invariant systems, the transfer function representation may be more

convenient than any other [2]. Another possibility is to use the differential equation description. Once a mathematical model of a system is obtained, various analytical and computer tools can be used for analysis and synthesis purposes. For example there belongs stability of systems; root locus, Bode plots and Nyquist criterion; controllability and observability; pole placement.

2. Web based study material

Asynchronous learning resources developed as interactive courseware for the World Wide Web are receiving increasing attention because of the ease with which they can be accessed by students at the time, place and pace of their choosing [6].

Many study materials available on the World Wide Web are actually electronic texts. A web server is used to publish material that might otherwise be available in hard-copy form. As it was mentioned in [6], an interactive courseware differs from electronic texts in several important ways. First, the interactive courseware relies heavily on the use of graphics. While traditional texts attempt to use words to "paint a picture" of a concept, the interactive courseware attempts to convey concepts primarily through the use of graphics, including illustrations, photographs and video segments. Relatively few words are needed to reinforce what each graphic clearly illustrates. Secondly, interactive courseware concentrates primarily on concepts, as most of the detailed information may be contained in other instructional resources and references, including textbooks. Like the traditional classroom lecture, interactive courseware is intended to complement, not replace, textbooks. And thirdly, interactive courseware is more flexible than the strictly linear format of a textbook. Incorporated hyperlinks enables to access from one point all appropriate explanations of the topic that are published in various parts of study materials.

3. Study material structure

In order to increase the effectiveness of the learning process, all used course materials are integrated by one

unified environment. It includes tutorials in hypertext form, navigation menu, lecturer's invitation, illustrative animation examples, self-assessment tests, etc. The aim is to provide students with a compact package that incorporates qualities of standard teaching materials with possibilities of Internet.

After the opening the web page (Fig.1) an user (student) is invited by the lecturer's welcome note. Then, the created web page is divided in several sections. The student can move among these sections using a navigation menu. He or she can choose among the topic tutorials, problems for self-solution, test, communication section or announcements.

Fig. 1. The web page environment of the developed interactive online lesson

3. Tutorials

The aim of the tutorials is to illustrate a selected topic as much as possible. After its selection a new adjusted window is shown.

Fig. 2. The tutorial page for system stability The menu changes according to the topic. In spite of this it always has the same structure. It consists from

introduction where students can find learning outcomes, then there is theoretical concept, illustrative examples and examples for self-solution, Matlab illustrations and self-assessment test based mostly on multiple-choice questions. The communication section and announcements can also be reached from all tutorials.

The corresponding theory tries to explain all main aspects of the given topic. The theoretical part is supplemented by illustrative examples. In most of cases we tried to prepare Java applets to make the problem clear as much as possible.

In Fig.3 one can see a typical example of the mechanical system that represents the damping dynamics of a car wheel. The process dynamics was described by means of differential equations those numerical realizations are included in the applet. Such virtual system can be accessible through Internet and students are not restricted to install simulation software at home.

Fig. 3. Java client with the animated virtual model The main motivation for using of mechanical plants in the educational process is clear physical “visibility” of their dynamics. It leads to better understanding of a demonstrated problem.

In Fig.4. it is possible to see another example. The applet computes stability of the given system. Students can specify own characteristic polynomial and to verify their results.

Study materials are enriched by many various examples. Student can usually find solved examples that are typical for the topic. The analytical solution of the problem is mostly complemented by the solution in the software package Matlab that is widely used in the control area educational process. Finally, there is a series of examples that is determined for individual solution by student.

Fig. 4. Java applet for stability calculation

4. Problems for self-solution

The web page tries to support individual work of students. In this part student can find problems that are to be solved. Since they are not placed exactly after the topic that they belong to, student has to think about their context and connection to the subject.

5. Test

The test is an inseparable part of the developed web page. In difference of self-assessment tests that are available in frame of most of tutorials and that serve students to test their knowledge for their own purposes; this test is determined for real assessment of student. Results are counted as a part of exam. The created test is prepared as the test with simple questions, short answer questions and multiple-choice questions. To increase the difficulty of test, multiple-choice questions can have not only one but several correct answers. In addition, bad answers are penalized by negative points.

6. Communication

At online courses or distance courses in general, the communication between teacher and student plays very important role. Asynchronous communication is currently perhaps the most popular technology being used in online education. Nowadays it is mainly represented by e-mails, mailing lists, newsgroups, discussion forums, and other messaging programs [1]. For the purpose of this

interactive online course we decided to use discussion forums, frequently asked questions and mailing list.

6.1. Discussion forum

Web-based discussion forums provide a tool for sharing information outside the classroom. Due to discussion forums students and tutors can share their ideas, questions, and individual discoveries whenever they wish and wherever they have Internet access [1].

Opposite to passive reading of Web pages, Web-based discussion forum is built by active participation of its users as they submit questions, provide answers, present opinions, share pointers to other resources.

The advantages of communication through discussion forums from the pedagogical point of view are obvious. Discussion forums enable students to become active participants and to provide the group of learners with additional information. Asynchronous participation gives learners time to compose answers more carefully but also let them ask questions right at the time of study.

6.2. Frequently asked questions

The part of 'Frequently asked questions' is closely connected with the previous paragraph. Its advantage consists in the fact that questions that are frequently asked by students are grouped and answered on one place and it is not necessary to look for them in the whole discussion forum. The questions are picked up only by a simple form. Answers are promptly prepared by teachers and are transparently divided into sections.

6.3. Mailing list

Mailing list serves for distribution of information among users that subscribed in the list. It can be used not only for distribution of informative messages from teacher to students but also for sharing information among students. The support of this Internet service on the university server can facilitate communication between participants of the course because instead of remembering numbers of email addresses (schoolmates, teacher) it is sufficient to know only one email address, namely email address of mailing list.

7. Announcements

The last section of the web page is dedicated to the announcements. It can be said that this part of web page is not so important because it could be substituted by sending the message to the mailing list. In this case all participating students should be informed about the actual activities in the course. However, it is always useful to have all actual information collected on one place where

also users not subscribed in mailing list could have a look. The announcements are introduced by teacher who can also specify the time period during which the message is visualized on the web page.

In this section student can also find list of recommended literature, contact addresses, course deadlines and intermediate results.

8. Conclusions

The presented online teaching material was prepared as complementary study materials for the subject "Control Theory". All web pages are prepared in Slovak language because the course is determined for regular students at our university.

It is to note that the web page is partly prepared by students in frame of their individual projects. They participated mainly in the preparation of interactive examples in Java language. In this way the project follows several aspects: firstly its main task is to provide a compact study materials for students of the Control Theory subject. However, the plumbless role consists also in the fact that students alone have the possibility to participate in this project. They learn various techniques of web presentation, methods of input data processing and displaying. Since they are working in the same laboratory, they can share their knowledge and to grow faster.

This article shows possibilities of using Web site for presentation of teaching materials. Their interactivity is the biggest advantage in comparison to the classic textbooks. This fact was appreciated mostly by students in distance form of bachelor study.

9. References

[1] Bisták P., Kohút M. and Žáková K., "Web-Based Communication Tools in Distance Education", Proc. of Int. Conference - ICETA, Kosice/Slovakia, 2003. [2] Ogata,K., "Modern Control Engineering", 3rd Edition, Prentice Hall London, 1997. [3] Šereš P., Žáková K., "Stability of Linear Systems and its Presentation on the World Wide Web", Preprints of the Intensive Course on Multimedia and Telematics, Publishing House of STU, 1998. [4] Schuppen J. H., "Control and System Theory: Introduction", ERCIM News, No.40 - January 2000. [5] Sontag E. D., "Mathematical Control Theory: Deterministic Finite Dimensional Systems", 2nd Edition, Springer, New York, 1998. [6] Turgeon A. J., "Implications of Web-Based Technology for Engaging Students in a Learning Society", Journal of Public Service and Outreach 2(2): 32-37. [7] Žáková K., Janotík M., "Mathematical Modeling of Dynamic Systems: an interactive online lesson", 5th international conference “Virtual University”, Bratislava, December, 2004. [8] Žáková K., Šereš P. and Patay T., "Web Support for the System Theory Teaching", 19th World Conference on Open Learning and Distance Education (ICDE99), Vienna/Austria, June 20-24, 1999.