JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Control Systems

Course Objectives:

• To understand the concepts of optimal and robust control,
• To enable to analyze and design a robust Control System.

Course Outcomes

Upon the completion of this course, the student will be able to

• Have knowledge on Parametric Optimization
• Acquire knowledge of Calculus of variations, Pontryegans Max/min Principle, learn Dynamic Programming in Continuous and Discrete Time
• Apply iterative methods of optimization,
• Analyze and design a robust Control System.

UNIT - I

Overview and Preliminaries: Overview on Robust control, Basics from Matrix Algebra, Norms of signals and systems (L2, H2, L∞, H∞). Convex Optimization: Convexity, Convex sets, Affine function, Linear matrix inequality (LMI), Projection lemma, S-procedure, Semi-definite programming, Feasibility problem, Minimization problem, Generalized eigen value problem, Programming in MATLAB.

UNIT - II

System properties and stability: Well-posedness, Causality, Passivity, Bounded-realness, Positive- realness, Internal stability, Bounded-Input-Bounded-Output stability, Finite-gain stability.

UNIT - III

Robust performance and Linear Fractional Transformation: Robust performance and limitations due to physical constraints, Linear Fractional Transformation (LFT), Uncertainties, Riccati equation and inequality. Useful Lemmas and Theorems in Robust Control: KYP Lemma, Bounded-real lemma, Positive-real lemma, Small-gain theorem, Passivity theorem.

UNIT - IV

H-infinity controller synthesis: Generalized H-infinity controller synthesis problem, Controller design via LMI approach. H-infinity Loopshaping Design: Four-block problem, Loopshaping concept, Weight selection, Controller synthesis via LMI.

UNIT - V

Mu Analysis and Synthesis: Robust stability and performance problems, structured singular value, D- scaling problem, D-K Iteration.

TEXT BOOKS:

• 1. Da-Wei Gu Petko Petkov, Mihali M Konstantinov, Robust Control Design with MATLAB, Springer – 2013.
• 2. Sigurd Skogestad, Ian Postlethwaite, Multivariable Feedback Control: Analysis and Design, John Wiley, 2005.
• 3. Kemin Zhou, John Constock Doyle, Kith Glovr, Robust and Optimal Control, PH Inc., 1996

REFERENCES:

• 1. Michael Green, David J.N. Limebeer, Linear Robust Control, PH Inc., 1995.
• 2. Uwe Mackenroth, Robust Control Systems : Theory and Case Studies, Springer, 2013.
• 3. S.O. Reza Moheimani, Perspective in Robust Control, Sprinter, 2001. M. Tech – I Year – II Sem. (Control Engg. / Control Sys.)