Course Overview

ROBUST CONTROL COURSE

Introduction
Industrial examples (automotive and electromechanical applications).
1 Tools
Hinf norm: how to dene the gain of a MIMO system ?
Singular values of a transfer matrix, introduction to H2 and H1 norms.
Example of a mass/srping/damper system.
Internal stability: Notion of well-posedness, Small Gain theorem
2 Performance analysis
 Denition of the sensitivity functions
 frequency-domain performance indices (sensitivity functions, stability and robustness margins, bandwidth, SISO and MIMO cases)
3 Hinf control design
Performance Specications: selection of weighting functions.
Loop-shaping Mixed sensitivity problem.
Solving the Hinf control problem:  Obtaining the General control conguration
 Hinf controller structure (state feedback, dynamic output feedback)
 Problem solution using Riccati equations or LMIs -Bounded Real Lemma)
 Illustrative examples
4 Uncertainty and robustness
Representing uncertainties: unmodelled dynamics, frequency forms, unstructured uncertainties
Parametric uncertainties, LFT forms, structured uncertainties
Robust stability analysis: M
structure, small gain theorem
Robust stability for unstructured uncertainties.
Robust performance analysis: A simplied Hinf criterion,
Introduction to mu-analysis - structured uncertainties

5 Introduction to LMIs
What is an Linear Matrix Inequality ? Brief optimisa-
tion background, Denition
Stability issue: From Lyapunov equation to LMIs
Control design: problem formulation: Example on
State feedback
6 Short introduction to LPV systems
Denition of Linear Parameter Varying systems, stability issue, control design
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http://ense3.grenoble-inp.fr/en/academics/non-linear-and-robust-controls-5eus5cnl

Learning Achievement

Ability for design and analysis of Hinfinity controlllers, robustness analysis, and the limits of the linearization, the analytical tools for nonlinear stability, and the basic principles of feedback control nonlinear state.

Competence

Ability for design and analysis of Hinfinity controlllers, robustness analysis, and the limits of the linearization, the analytical tools for nonlinear stability, and the basic principles of feedback control nonlinear state.

Course prerequisites

Linear Systems, Transfer and state space approach, frequency and time-domain analysis

Grading Philosophy

Exam
Homework
Project reports
Individual evaluation in Matlab tutorials

Course schedule

Course type

Lecture

Online Course Requirement

Instructor

Olivier Sename

Other information

Course content can evolve at any time before the start of the course. It is strongly recommended to discuss with the course contact about the detailed program.

Please consider the following deadlines for inbound mobility to Grenoble:
- April 1st, 2020 for Full Year (September to June) and Fall Semester (September to January) intake ;
- September 1st, 2020 for Spring Semester intake (February – June).

Site for Inquiry