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Course Postgraduate
Semester Electives
Subject Code AVC 623
Subject Title Robust Control Design

Syllabus

Basics: Control system representations, System stabilities, Coprime factorization and stabilizing controllers, Signals and system norms

Modelling of uncertain systems: Unstructured Uncertainties, Parametric uncertainty, Linear fractional transformation, Structured uncertainties.

Robust design specifications: Small gain theorem and robust stabilization, Performance considerations, Structured singular values.

Design: Mixed sensitivity optimization, 2-Degree of freedom design, Sub-optimal solutions, Formulae for discrete time cases.

Loop- shaping design procedures: Robust stabilization against Normalized coprime factor perturbation, Loop shaping design procedures, Formulae for discrete time cases.
m- Analysis and Synthesis: Consideration of robust performance, m-synthesis: D-K iteration method, m-synthesis: m -K iteration method.

Lower-order controllers: Absolute error approximation methods like Balanced truncation, Singular perturbation approximation and Hankel-norm approximation, Reduction via fractional factors, Relative error approximation and frequency weighted approximation methods.

Design case studies: Robust Control of a mass damper spring system, A triple inverted pendulum control system, Robust control of a hard disk drive.

Linear Matrix Inequalities: Some standard LMI problems – eigen-value problems,generaliszed eigen-value problems; Algorithms to solve LMI problems – Ellipsoid algorithm, interior point methods.

Text Books
References

1. D.-W.Gu, P.Hr.Petkov and M.M.Konstantinov, Robust Control Design with MATLAB, Springer, 2005.
2. Alok Sinha, Linear Systems- Optimal and Robust Controls, CRC Press, 2007.
3. S. Skogestad and Ian Postlethwaite, Multivariable feedback control,John Wiley & Sons, Ltd, 2005.
4. G.E. Dullerud, F. Paganini, A course in Robust control theory- A convex approach, Springer, 2000.
5. Kemin Zhou with J.C. Doyle and K. Glover, Robust and Optimal control, Prentice Hall, 1996.
6. G Balsa, R.Y. Chiang, A.K.Packard and M.G.Safonov, Robust Control Toolbox (Ver. 3.0) User’s
7. Guide. Natick, MA: The Mathworks, 2005. http://www.mathworks.com/access/helpdesk/hellp/toolbox/robust
8. Kemin Zhou, John Comstock Doyle, Keith Glover, Robust and optimal control, Prentice Hall, 1996.
9. Kemin Zhou, John Comstock Doyle, Essentials of robust control, Prentice Hall, 1998.
10. Stephen Boyd, Laurent El Ghaoul, Eric Feron, Linear Matrix Inequalities in System and ControlTheory, SIAM, 1994.
11. "Robust Control"- Bhattacharya, Chapellat, Keel, Prentice Hall, 1995