Undergraduate Teaching 2024-25

Engineering Tripos Part IIB, 4F2: Robust & Nonlinear Systems & Control, 2019-20

Engineering Tripos Part IIB, 4F2: Robust & Nonlinear Systems & Control, 2019-20

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Module Leader

Prof RJCPM Sepulchre

Lecturers

Prof RJCPM Sepulchre and Dr I Lestas

Timing and Structure

Lent term. 14 lectures + 2 examples classes. Assessment: Exam only

Prerequisites

3F2 assumed.

Aims

The aims of the course are to:

  • introduce fundamental concepts from nonlinear dynamic systems
  • introduce techniques for the analysis and control of nonlinear and multivariable systems.

Objectives

As specific objectives, by the end of the course students should be able to:

  • apply standard analysis and design tools to multivariable and nonlinear feedback systems.
  • appreciate the diversity of phenomena in nonlinear systems.

Content

PART 1: MULTIVARIABLE FEEDBACK SYSTEMS (7L + 1 example class, Prof R. Sepulchre)

  • Performance measures for multi-input/multi-output systems.
  • Stabilization: stability conditions, all stabilizing controllers, small gain theorem.
  • Models for uncertain systems.
  • Robust stability and performance. Loop shaping design.
  • Design of multivariable systems.

PART 2: NONLINEAR SYSTEMS (7L + 1 example class, Dr I Lestas)

  • Linear and Nonlinear systems; feedback circuits.
  • Differential equations and trajectories.
  • Multiple equilibria, limit cycles, chaos and other phenomena.
  • Examples from biology and mechanics.
  • State space stability analysis:
  • The theorems of Lyapunov, LaSalle invariance principle.
  • Stability of nonlinear circuits and neural behaviors.
  • State-space tools for robustness analysis.
  • Input/output stability analysis:
  • Describing functions
  • Small gain theorems, circle and Popov criteria, passivity.

Further notes

ASSESSMENT

Lecture Syllabus/Written exam  (1.5 hours) - Start of Easter Term/100%

Booklists

Please see the Booklist for Group F Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 19/09/2019 10:14

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