Using Multimedia and the World Wide Web to Enhance an Undergraduate Course on Digital Control Systems Helen S. Ashton*, Matthew W. Dunnigan**, Ali M. S. Zalzala*** Heriot-Watt University, Department of Computing & Electrical Engineering, Edinburgh, EH14 4AS, Scotland *
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ABSTRACT This paper describes how multimedia and the World Wide Web (WWW) have been put to use in enhancing an undergraduate course on Digital Control Systems in the Electrical and Electronic Engineering degree course at Heriot-Watt University.
1 INTRODUCTION Use of the internet and multimedia for education purposes is becoming increasingly popular in a wide range of fields, such as Physics (1), Chemistry (2), Biology (3), Veterinary Medicine (4) and the weather (5). As part of the undergraduate degree in Electrical and Electronic Engineering at Heriot-Watt University, one of the electives is a course in Digital Control Systems. This course had been taught in the traditional method using lectures, tutorials and recommended reading. In an effort to enhance the student's experience of this course, and improving their understanding, multimedia material has been created which the students have access to through the WWW.
2 DIGITAL CONTROL SYSTEMS The study of control systems is traditionally viewed by the majority of undergraduate students as a difficult course. This is primarily due to the significant mathematical content of such a course. Therefore it is a worthy objective to pursue methods that may aid understanding. The multimedia approach described in this paper offers many advantages. Additionally, the advent of packages such as MATLAB/SIMULINK, which can be used for control design/simulation purposes, has allowed a greater range of problems to be studied in undergraduate control classes (6). Before this the range of problems encountered through tutorials was generally confined to systems of third-order or lower. This is because in typical classical control problems the
task of manipulating and inverting Laplace or Z-transforms is onerous for high order systems. For the case of state-space systems, the manipulation and inversion of matrices is time consuming by hand for systems larger than third order. It should be stressed however that it is not being advocated that the traditional style of tutorial problem be removed. This plays an essential part in reinforcing the lecture material and allows practice and mastery of the analysis/design techniques studied. It is viewed that the longer case study based problems will run in parallel with the tutorials as an enhancement to the course. Most tutorial control problems involve applying a technique for analysis or design on a given dynamic system, be it open or closed loop. The problem is completely specified and a unique solution exists. While useful and necessary, the student may have the impression that this is a reflection of practical control system design. In practice, of course, control system specification is a difficult task, perhaps occupying most of the control design cycle, and requirements may be conflicting and/or lead to an underspecified design (7). This underspecification of design requirements is a feature of the inverted pendulum case study presented here and leads to a non-unique compensator design that satisfies the design requirements.
3 ADVANTAGES OF USING MULTIMEDIA AND THE WWW There are numerous reasons why one may choose to use multimedia and the WWW for educational purposes, from the ease of update, to global access. The reasons for choosing the WWW in this situation are mainly due to the ability to incorporate multimedia elements into an overall learning environment. Using multimedia over the WWW allows the incorporation of text, graphics, animations and interactions, and quizzes/self tests, as these can all be incorporated in a learning environment that can be viewed using a normal web browser. Further multimedia components, such as video and audio, can also be included to provide a rich environment for the students. The use of multimedia elements can stimulate the user and aid their understanding, as well as providing a variety of methods for the students to learn particular concepts. The provision of an environment such as this across the WWW allows students 24 hour access to lecture notes and additional, enhanced material. Due to the nature of the digital control course, the students are also required to use computers to utilise other pieces of software, such as MATLAB. Since they must be at a computer to do this, the ability to access further information, or look back at course notes, while they are using these tools proves extremely useful. This means that they do not need to have their notes, or access to the library, to find out the information necessary to continue with the task in hand.
4 COURSE MATERIAL The students access the material through the WWW, using a web browser. The material is presented in an environment called WebCT (http://about.webct.com/). This environment provides many of the standard features that enhance the learning environment, such as the communication tools, student management and assessment, as well as navigation tools. WebCT allows the designer to place material in the "course contents" in a linear fashion. This provides the students with a listing of the
"course notes" and assignments. Since the material has been created to enhance an existing lecture course, the lecture notes are available for the students to view and print. However, the notes have been enhanced with additional graphics, interactions, animations and links. The addition of sensible links within the course notes along with the "course contents" allows the user to take a non linear approach to learning the material if they wish.
5 INTERACTIONS The use of multimedia allows interaction to be built into the learning experience. The students understanding of many concepts can be enhanced by the use of interactive components. The interactive components provided in this course are embedded into the notes at the appropriate point, see Figure 1. All interactive elements are indicated by a mouse icon, Figure 3. This icon indicates that the user should be interacting with the corresponding element, but also opens the interactive element in a new window by itself when clicked upon, Figure 2. This allows users with smaller monitor sizes to view the interaction as a whole, whereas it may have been obscured in the environment shown in Figure 1.
Figure 1: Course notes for s-z plane equivalence
Figure 2: Interaction for s-z plane equivalence
Figure 3: Icon indicating interactive element The interaction in Figure 2 is used to demonstrate the equivalence between the s-plane and the zplane, a concept which is complex to illustrate through still images, or by drawing on the blackboard during a lecture. In this interaction the user is prompted to click on any of the shapes shown at the bottom of the simulation window. Initially, all the shapes in images of the s and z plane are grey. When the user clicks on one of the shapes they can see the path animate in colour in the s and z plane simultaneously. In this way the students can gain insight into how the mapping from one plane to another occurs. The student can choose the symbols in any order, and as many times as they wish until they have grasped the concept. In Figure 2 the user has just clicked on the cross symbol. This
shows that the locus of s-plane poles that lie on a line of constant damping ratio maps into a logarithmic spiral in the z-plane. Another typical interaction can be seen in Figure 4. Here the purpose of the interaction is to allow the students to view a signal as it goes through the processes of sampling, reconstruction by a zero-order hold operation, filtering by a transfer function block H(s) and a final sampling. The objective is to find the discrete zero-order equivalent, Hh0(z), of H(s). Instructions are presented to the student in a yellow box on the middle right of the interaction window. By clicking on any of the first three stages at the top of the interaction window they can see the signal as it changes with time, and how each process affects the signal. Figure 4 shows the signal after the sampling process, and Figure 5 shows the signal being drawn after the hold process.
Figure 4: Zero-order hold interaction after the sampling stage
Figure 5: Zero-order hold interaction after the hold stage
Once the students have grasped the concept of the zero-order hold, they can proceed to see how the discrete zero-order hold equivalent is derived. Again, an interaction has been created to reinforce this concept, Figure 6. As with the previous example, instructions and information throughout the interaction are presented to the student in a yellow box. Consistency such as this is important so that the students begin to learn how to use the interactions and are not frightened off by a new format. To see how the mathematical representation is derived the user must first choose a sample point. They then proceed through the steps to create the signal between that sample point and the next. They do this by reading the information in the boxes (bottom left), watching what is drawn on the screen on the right hand side, and clicking on the next button when they are ready to move onto the next step. Figure 6 shows the students view as they are progressing through the interaction. The student can start with any sample point they wish, and as they progress through the sample points they build up the signal on the left hand side. If they want to start again they simply press the clear button.
Figure 6: Building a mathematical representation of the signal after a zero-order hold process.
6 QUIZZES AND SURVEYS Throughout the course quizzes and surveys are made use of, both to gauge the students understanding and how it has been enhanced by the multimedia environment, and for the students to test their own knowledge and assess the areas which need further attention. Quizzes and surveys are extremely similar, except that a survey is anonymous and the information entered into it is not linked to the student. We have used this throughout the course to gauge the usefulness of the material and the students progress both before and after use of the multimedia environment. A typical quiz for this course is shown in Figure 7 where the student is presented with a series of randomly selected multiple choice questions. Once they have completed the series of questions they can have the quiz graded and obtain feedback. At present the student may retake a quiz as many times as they wish, as it is intended to help them gauge their knowledge, and not as an assessment exercise. Naturally assessment quizzes could also be included.
Figure 7: Screenshot of a course quiz
7 CASE STUDY - THE INVERTED PENDULDUM Increasing computer availability, power and software has enabled a wider variety of case studies, or investigations, to be presented to the student. Tools such as MATLAB and SIMULINK (MathWorks - http://www.mathworks.com/) have allowed more complicated case studies to be investigated, such as the inverted pendulum (8). The case study reinforces several key ideas in the course which are briefly summarised. The control objective is to keep the pendulum vertical (θ=0) by moving the cart. The students are asked to design a digital compensator, using the emulation design approach, to stabilise the inverted pendulum, which is a nonlinear system. The compensator design is best tackled intuitively with the aid of a root locus diagram which differs from the typical tutorial root locus problem. The selection of a suitable sample rate illustrates that a value far in excess of Nyquist's criterion has to be chosen for the responses produced by the continuous and discrete compensators to be similar. The limits of a linearisation approach is illustrated by the different control performance obtained when the deviation from the linearisation point is too large. This is only possible using a computer package capable of nonlinear simulation. The straightforward demonstration of aliasing and its effect in a digital control system is another advantage of using this approach. Since the students must be at a computer to use MATLAB and SIMULINK throughout this case study, it made sense to provide information and help in the multimedia environment to help them through the investigation. Figure 8 shows a screen shot of the description of the investigation, and an animation to demonstrate the problem. Animations and films are indicated by a film icon, Figure 10, in a similar manner to interactions. The animation is followed by a more detailed still image and text, Figure 9, describing the various mathematical symbols used in this problem, along with their meaning.
Figure 8: Description of the inverted pendulum case study including an animation demonstrating the problem. Figure 9: A section of the course notes giving more detailed view of the inverted pendulum problem.
Figure 10: Icon indicating a film element, i.e. a movie of animation As the student progresses through the case study, they are prompted to carry out various tasks using MATLAB and SIMULINK. If they have problems carrying out these tasks they can get hints by clicking on the help icon, Figure 11, which appears at the top of the screen when there are hints available. Two screen shots of examples of the hints provided are shown in Figure 12 and Figure 13. The hint in Figure 12 shows the student how to prove that the inverted pendulum is open-loop unstable by using the MATLAB command roots. Figure 13 shows how to use the MATLAB rootlocus command (rlocus) to prove that the system cannot be stabilised using proportional control alone.
Figure 11: Help icon
Figure 12: A screenshot of hint 2 in step 1 giving help on using MATLAB to find the roots of the system.
Figure 13: A screenshot of hint 2 in step 2 giving help on using MATLAB to plot the root locus. The expected plots are also shown.
8 CONCLUSION The increased availability of multimedia hardware and software has made it possible to create supplementary multimedia material for the undergraduate course in Digital Control Systems in the Department of Computing and Electrical Engineering at Heriot-Watt University. Text, graphics, animation, interactions and quizzes have all been combined to enhance the students learning
experience. This type of material also allows the student more freedom to study the material in the manner most suitable to them. Further work is being carried out on the material to improve the multimedia environment, mainly by adding more interactions, quizzes and case studies. Students are at present using the material as part of their course, and hopefully this will provide some useful feedback information.
ACKNOWLEDGEMENT The authors acknowledge the support of the European Commission under INCO grant DG96-1852 (GIPSECA, http://www.cee.hw.ac.uk/~ali/gipseca/).
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