Robust Control

Prerequisite:

Theory of Dynamic Systems (X35TDS)

The course is a substitute for:

Robust Control (35ROR)

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

Robust control offers a suite of control design methods that take into consideration presence of modelling imprecissions and uncertainties. In this course, various mathematical modelling techniques for uncertainties will be introduced and design techniques will be presented that use such models. Main emphasis will be placed on design in frequency domain (modern optimization-based methods known as Hinf and mu-synthesis), but some intuitive graphical methods for design for real parametric uncertainties will be sketched. Included in this course will be an introduction to linear matrix inequalities and semidefinite programming, as these are the tools for solving numerous computational tasks in robust control design. Some advanced techniques for model and controller order reduction will also be covered.

Requirements:

Major concepts and tools from feedback control: feedback, stability, Bode frequency characteristics, Nyquist test of stability, expressing control specification in frequency domain using constraints on magnitude frequency characteristics. Roughly the scope covered by the courses SAM, SRI and TDS.

lBasic concepts and tools from matrix linear algebra: eigenvalues/eigenvectors, linear equations (overdetermined, underdetermined), Jordan canonical form, singular value decomposition (SVD).

Syllabus of lectures:

1.Modelling uncertainties in dynamic systems.

2.Analysis of robust stability and robust quality for unstructured uncertainties.

3.Analysis of robust stability and robust quality for structured uncertainties: mu analysis.

4.Limitations of achievable quality of control: SISO systems.

5.Limitations of achievable quality of control: MIMO systems.

6.Design of a robust controller for unstructured uncertainties using Hinf optimization.

7.Design of a robust controller for structured uncertainties using DK iteration (mu-synthesis).

8.Robust loopshaping using Hinf optimization.

9.Model and controller order reduction.

10.Linear matrix inequalities (LMI) and semidefinite programming.

11.Using LMI for analysis and design of robust control: computation of Hinf controller, quadratic stability of polytopic systems, linear parameter-varying systéms (LPV).

12.Analysis of robust stability for systems with uncertain real physical parameters.

13.-14. Design of a robust controller for systems with uncertain real physical parameters.

Syllabus of tutorials:

1.Modelování neurčitostí v dynamických systémech.

2.Modelling uncertainties in dynamic systems.

3.Analysis of robust stability and robust quality for unstructured uncertainties.

4.Analysis of robust stability and robust quality for structured uncertainties: mu analysis.

5.Limitations of achievable quality of control: SISO systems.

6.Limitations of achievable quality of control: MIMO systems.

7.Design of a robust controller for unstructured uncertainties using Hinf optimization.

8.Design of a robust controller for structured uncertainties using DK iteration (mu-synthesis).

9.Robust loopshaping using Hinf optimization.

10.Model and controller order reduction.

11.Linear matrix inequalities (LMI) and semidefinite programming.

12.Using LMI for analysis and design of robust control: computation of Hinf controller, quadratic stability of polytopic systems, linear parameter-varying systéms (LPV).

13.Analysis of robust stability for systems with uncertain real physical parameters.

14.Design of a robust controller for systems with uncertain real physical parameters.

Study Objective:

Study materials:

Lecture notes (continuously updated) [pdf files downloadable at http://dce.felk.cvut.cz/ror ]

Professor Michael Sebek's slides for his course in 1998-2004 [pdf files downloadable at http://dce.felk.cvut.cz/ror/prednasky_sebek.html]

Some other lecture notes freela available for download:

O. H. Bosgra, H. Kwakernaak, G. Meinsma. Design Methods for Control Systems: Lecture notes for DISC course, 2005. More then 300 pages downloadable at http://wwwhome.math.utwente.nl/~meinsmag/courses/dmcs/

J. Doyle, B. Francis, A. Tannenbaum. Feedback Control Theory. Macmillan Publishing, 1990. Whole book downloadable at http://www.control.utoronto.ca/people/profs/francis/dft.html

C. Scherer, S. Weiland. Linear Matrix Inequalities in Control: Lecture notes for DISC course, 1999. More then 200 pages downloadable at http://www.cs.ele.tue.nl/sweiland/lmi.html

S. Skogestad, I. Postlethwaite. Multivariable Feedback Control: Analysis and Design. John Wiley & Sons, 2nd ed., 2005. The first three pages downloadable at http://www.nt.ntnu.no/users/skoge/book/

Some other printed books:

S. Skogestad, I. Postlethwaite. Multivariable Feedback Control: Analysis and Design. John Wiley & Sons, 2nd ed., 2005. This is the book on which this major part of this course is built.

J. Ackermann. Robust Control: The Parameter Space Approach. Springer-Verlag London,2002.

S. P. Bhattacharyya, H. Chapellat, L. H. Keel. Robust Control: The Parametric Approach. Prentice-Hall, 1996.

R. B. Barmish. New Tools for Robustness of Linear Systems. MacMillan, 1994.

S. Boyd, C. H. Barratt. Linear Controller Design: Limits of Performance. Prentice-Hall, 1991.

J. B. Burl. Linear Optimal Control: H2 and Hinfinity Methods. Addison Wesley Longman, 1999.

M. A. Dahleh, I. J. Diaz-Bobillo. Control of Uncertain Systems: A Linear Programming Approach. Prentice-Hall, 1995.

K. Zhou, J. C. Doyle, K. Glover. Robust and Optimal Control. Prentice-Hall, 1996.

K. Zhou, J. C. Doyle. Essentials of Robust Control. Prentice-Hall, 1997.

G. E. Dullerud, F. Paganini. A Course in Robust Control Theory. Springer-Verlag, 2000.

M. Morari, E. Zafiriou. Robust Process Control. Prentice-Hall, 1989.

C.H. Houpis, S.J. Rasmussen. Quantitative Feedback Theory: Fundamentals and Applications. Marcel Dekker, 1999.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory elective course)
• Cybernetics and Measurements - Artificial Intelligence- structured studies (compulsory elective course)
• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory elective course)
• Cybernetics and Measurements - Aeronautical Engineering and Control Systems- structured studies (compulsory elective course)