Abstract. This distance learning course concerns fuzzy control of a ball balancer, an inverted pendulum problem. The ball balancer is simulated in Matlab (registered trademark of The MathWorks, Inc.). After the course you will be able to design a fuzzy controller and evaluate commercial tools for fuzzy logic. The work load is 60 hours, and it takes at least 8 weeks to complete the course. The course runs twice per year with a fixed end date, depending on the semester. The course is rated at 2.5 credit units in the European Credit Transfer System (ECTS). The course contents are: fuzzy set theory, fuzzy logic, cart-ball model, linear controller design, controller test, fuzzy linear controller, fuzzy nonlinear controller, and self-organising control.

 

Table of contents

1. Course description
2. Prerequisites
3. Fee
4. Textbook: Foundations Of Fuzzy Control
5. Software
6. Admission
7. Course lifecycle phases
8. Further information

Course description

 

You design and tune a controller, that balances a ball on a bridge by means of a moving cart. Figure 1 below is the ball balancing lab rig, also called the cart-ball rig. Figure 2 shows the Matlab simulator of the lab rig. The simulator is built from basic Matlab functions, and does not require any toolboxes.

 

 

Fig. 1. Cart-ball rig. The control objective is to balance the ball on the top, and at the same time position the cart on the middle of the track.

 

 

Fig. 2. Simulator in Matlab. Front panel showing animation and controller settings.

 

 

The course objective is: 

• to teach students how to design a fuzzy controller

The course runs on the Internet and uses Web technology for organizing the contents. The core means of communication is e-mail. The course resides in the socalled Learning Space environment (the Lotus Company, now IBM). The role of Learning Space is to organise the contents and the course schedule. You download the textbook material as well as the simulator, and you use it offline.

 

Students download assignments and return their answers by e-mail. The teaching principle is thus tutoring by e-mail.

 

For further details, see the official description in the course catalogue.

 

Prerequisites

 

In either of the following cases, you are eligible to sign up for the course.

1. You are a student enrolled at DTU.
2. You are a student enrolled in another university studying for a Bachelor or a Master´s degree or PhD.
3. You are a teacher or a professional from the industry.

In all three cases, a prerequisite is that you have taken an introductory course in automatic control.

 

Fees

 

Citizens of non-EU countries must pay a tuition fee plus course fee, totalling 5 525 Danish kroners (approximately 741 euro).

 

Citizens of EU countries, who enroll under Open University - Vacant Places, must pay a course fee, which amounts to 1 250 Danish kroners (approximately 168 euro). Participation does not require a residence permit, since the course is distance learning.

 

Guest students from Danish universities do not pay a fee at all.

 

Textbook: Foundations Of Fuzzy Control

 

The course uses the textbook

 

 Jan Jantzen: Foundations Of Fuzzy Control. Wiley, 2007.

 

A separate page describes the book contents and serves as a repository for files and notes. The book can be purchased from Wiley and Amazon.

 

Software

 

The course software is based on Matlab. The following is required:

1. Matlab Student Edition 4 (or a higher version), or Matlab version 4.2 (or a higher version);
2. your browser is Netscape Navigator 4.x / Microsoft Internet Explorer 4.x (or a higher version); and
3. you have an e-mail account.

You must use a browser to get access to the course material. If you are behind a firewall, it may create problems, but they are usually resolved.

 

Admission

 

The course runs twice a year,

 

Spring semester, February - June Autumn semester, September - December

 

Application deadlines are one month before the semester starts. Before you can start the course, you must be prepared to do a certain amount of administrative paper work, also in your home university; you are therefore advised to start the proces early.

 

Course lifecycle phases

 

You will go through four phases during the course:

1. Expression of interest by means of the file fuzzy00.txt
2. Registration
3. Active participation
4. Finished, but waiting for the certificate    

Phase 1

 

The first phase starts when you send Jan Jantzen an e-mail, based on the fuzzy00.txt text file.

 

It is a questionnaire by which you express your interest, and by which Jan Jantzen can judge whether you are eligible for the course.

1. Open the fuzzy00.txt file
2. Insert the file inside an e-mail massage (not as an attachment).
3. Write your answers directly into the e-mail, and send it to:  jj (at) oersted.dtu.dk

You will then receive a reply from Jan Jantzen within two working days.

 

Phase 2

 

The next phase is the registration phase where you will receive further instructions by e-mail communication. The goal is to produce a paper form, with a stamp and signature from your university, which certifies that you are actually enrolled as a student. The original paper must be sent to DTU by ordinary mail.

 

You must also send a document showing that your university accepts the credit transfer. This document is mandatory.

 

Phase 3

 

During the active phase you download material and work on the simulator. The main communication is by means of e-mail.

 

Phase 4

 

When you are finished with your assignments, and you have written a course evaluation, you must take an online multiple choice exam. There are about 15 questions, and you must get

• at least 50 % correct answers

in order to pass the course.

 

The instructor will send the paper work to the administrative staff at DTU, and they will issue a course certificate. Usually students will receive the certificate within a month after the end of the semester. 

 

Further information

 

Applicants for Open University are advised to read the DTU web page, the main entry point for foreigners.