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Analysis and control of nonlinear systems - 5AMAC551

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  • Number of hours

    • Lectures : 12.0
    • Tutorials : 6.0
    • Laboratory works : 9.0
    • Projects : -
    • Internship : -
    • Written tests : -
    ECTS : 2.5
  • Officials : Eduardo MENDES

Goals

This course is an introduction to the many methods of analysis and control of nonlinear systems. Given the extent of existing methods and approaches, this course is not intended to be exhaustive. At the end of the course, students will have the foundation necessary to address the best way and the most appropriate, analysis and control of nonlinear systems.

Content

Part 1: Analysis Methods of NonLinear Systems

  • Properties of differential equations and linearization
  • Controllability and Observability
  • Elements of the Lyapunov theory of stability
    - Lyapunov stability theorems
    - LaSalle invariance theorem - Barbalat Lemma
    - Ultimate Uniform Boundedness
  • Input-Output stability analysis Methods
    - Small gain theorem
    - Criterion circle
    - Stability Analysis by the passivity theorem
  • Describing Method Analysis (first harmonic method)
    Part 2: Methods of control of NonLinear Systems
  • Methods based on Lyapunov stability
    - Direct Method of Lyapunov
    - Adaptive nonlinear control based on Lyapunov analysis
    - Backstepping Method
  • Exact input-output Linearization method
  • Flatness based control
  • Sliding mode control
  • Passivity based control

Practical work:
Analysis and control of nonlinear systems (e.g. turbojet motor, DC-DC "Boost" converter, ball and beam, magnetic levitation system...). Nonlinear adaptive control. Observers and nonlinear estimation of parameters.

The job is mainly done by simulation.

Prerequisites

Linear algebra, complex numbers, Norms, elementary topology in Rn, elementary differential geometry.
Analysis and control of linear systems in continuous-time, transfer function modelling, state space modelling.

Tests

Session 1 :
E1 : Written final Exam of 2h30mn, all course documents allowed, Simple calculator allowed.
CC : Written class-work of 1h30mn, all course documents allowed, Simple calculator allowed.
TP : Average of notes of practical reports
Session 2:
E2 : Written final Exam of 2h30mn, all course documents allowed, Simple calculator allowed.

Calendar

The course exists in the following branches:

    see the course schedule for 2020-2021

    Additional Information

    Course ID : 5AMAC551
    Course language(s): FR

    You can find this course among all other courses.

    Bibliography

    H.K. Khalil, Nonlinear Systems, 1996, Prentice Hall.
    J.J.E. Slotine, et W. Li, Applied Nonlinear Control, 1991, Prentice-Hall.
    A.J. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, 2000, Springer-Verlag.
    A. Isidori, Nonlinear Control Systems, 1989, Springer-Verlag.
    B. d’Andréa-Novel et M. Cohen de Lara, Commande linéaire des systèmes dynamiques, 1994, Masson.
    H. Bülher, Réglage par mode de glissement, 1986, Presses Polytechniques Romandes.

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    Date of update June 25, 2015

    Université Grenoble Alpes