Objectives
and Overview
Course
Materials Reference Materials
Assignments
and Exams Projects Grading
Pattern Course
Outline
This course is devoted to the study of topics in the area of Robust Control Theory. Robust control is defined as the control of uncertain plants - that is, systems with uncertain dynamics or unknown disturbance signals, using fixed deterministic controllers. This area in control theory flourished in the late 70's and is still very active in producing new results. The course deals with different transfer matrix, Nyquist and Nyquist-like techniques for robust control and several techniques and algorithms are compared. Seve ral MATLAB based problems are assigned to facilitate better understanding of the results developed in this course. These assignments also facilitate the learning of the powerful toolboxes of MATLAB: namely, control sytem, robust control and ?synthesis tool boxes. Robust control has wide applications in VLSI manufacturing technology, circuit design (the circuit elements have tolerances which we call uncertainties), automotive and aerospace appplications, chemical processing technology and several other control-centric application areas.
Introductory material is first presented on the sources of uncertainties in system modeling and particular motivation is given to the main classes of uncertainties encountered in the robust control literature as well as in general practice. The use of singular value techniques in the analysis of robust control system is then motivated and developed, first with reference to the general class of the so-called unstructured uncertainties and also with respect to a broad class of structured uncertainties. Using frequency response stability results of the Generalized Nyquist Criterion as a starting point, the effects of system uncertainties are incorporated as a perturbation about the nominal system description. The development provides a generalization of the Characteristic Locus Method for the case of uncertain systems via the E-contours and also gives a development of robustness analysis and design using the scaled singular values.
We also consider the question of real perturbations as these arise, for example, from a consideration of the uncertainties in the state space of both single-input single-output (SISO) and multi-input multi-output (MIMO) systems. It is shown that this problem may be cast as an equivalent frequency domain problem and is solved as such. The highly structured class of parametric uncertainties is introduced and the robust stability problem is solved by a new and elegant method called critical perturbation radius method, which is currently a main area of interest of the robust control group. A comparison of conservatism, computational burden, and efficiency with other techniques is also made, facilitating in-class interactions. Recent publications on these topics are discussed in the class, giving up-to-date information in the field and encouraging students to do a literature survey and even come up with their own research ideas in this field.
The final section of the course gives an introduction to optimal H-infinity, ?synthesis methods.
Stability and Performance Analysis of MIMO and SISO systems in the presence of Uncertainties.
An undergraduate course in Classical Control systems is required and some
exposure to state variable methods is also desirable
background for some of the material to be covered in the course. Specifically,
it would be helpful for students to have a sound grasp of transform
theory, elementary linear algebra and matrix theory.
Textbook: Frequency Response Methods for Uncertain Multivariable Systems,
Haniph A. Latchman, Course Notes.
Additional reading material
are listed below.
Electronic copies of the course syllabus, notes and other course information
will be accessible via the World Wide Web (WWW) at the following URL
http://latchman.list.ufl.edu. Select EEL 6619 from the FALL 2002 courses.
Course notes and problem solutions will be distributed in hardcopy format
in class and posted electronically as indicated above.
Grades are based on the following weights.
Homework and other assignments will be given periodically and will be due within
the first 5 minutes of class on the designated due-date.
FEEDS/NTU
students will have a one (1) week extension on all assignment due dates.Use regular-size paper,
staple the sheets together and put your name and homework
number at the
top. Late homework will be accepted only in exceptional circumstances which need
to be discussed with the Instructor for approval. Graded homework will be returned in class and/or placed
in the shelves near the elevators on the 4th floor of the New
Engineering Building.
The midterm exam and the final exam will be given in class and dates for these will be
announced in class. The final exam will be comprehensive, but with emphasis on
material covered since
the midterm exam. An announcement will be made to indicate whether the
examinations will be closed-book, open-book or limited-notes.
All students will be required to complete a final project or research
paper as part of the requirements of this course.
The project may take the form of a programming project, a simulation or
other quantitative experimental study, a critical review a relevant paper, or
some combination of these.
The project may be done individually or in
teams of two or more students, provided that the work is compartmentalized to
clearly identify the contribution of each participant. All projects must deal
with some aspect of robust control.
It is preferred that students select a project that is of interest to
them
and one that can be completed in a timely manner using readily available
resources. In some cases, the resources of the Laboratory for Information
Systems and Telecommunications (LIST) may be used, especially if the selected project
is relevant to on-going LIST research.
The project must be completed in the allotted time;
incomplete grades will not be given just to allow extra time to work on the
project. All
projects must be approved by the instructor. Each student or team must submit a brief
project proposal (about 1 page in length) that outlines project objectives, required
resources, work plan, and deliverables. Project proposals are due within the
first three weeks of classes.
You are encouraged to discuss project ideas with the instructor and
to submit
your proposal as early as possible.
If a student cannot find an appropriate topic, one will be assigned.
Course Materials
Grading
20% 30%Final Exam: 30%
20% 50%Participation 10%
Participation
In this class a formal grade will be assigned for active participation in
class-time and online activities. This will foster an active learning
mode as well as fruitful collaborative learning among students.
Details of the type of participation expected will be provided in class.
Final letter grades will be assigned at the end of the semester and will depend
on absolute and relative student and class performance.
Assignments
Exams
Final Project
Examples of Projects
Project Reports
Project reports should be presented in a professional manner. Students working
in teams may submit multiple reports or a single report as agreed with the
instructor on project approval.
All reports must be typed and neatly formatted. A cover page
that indicates project title, course, student name(s) and ID number(s) and date,
must be included. Final reports should be formatted according to
the standard IEEE Journal paper format. A sample will be provided.
Variations from this format must
be approved by the Instructor.
Neatness, spelling, grammar, writing style, presentation and
clarity will be considered in
grading. Any texts, papers, manuals, reports, or other sources must be acknowledged using
standard IEEE format. Neatly drawn figures and graphs should be used where
appropriate. Target lengths for the project report is about 15-20
pages. Please do not copy material directly from reference sources. Give proper
citations for all references and explictly identify the source of direct
quotations.