Undergraduate Teaching 2024-25

Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2024-25

Engineering Tripos Part IIB, 4F2: Robust and Nonlinear Control, 2024-25

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Module Leader

Prof F Forni

Lecturer

Prof F Forni

Timing and Structure

Lent term. 14 lectures + 2 computer lab sessions. Assessment: 100% coursework

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 I. ROBUST CONTROL (7L + 1 Computer Lab session, Prof F Forni)

1. Uncertainty and Nonlinearity in control systems: simple models.

2. Signal spaces and system gains.

3. The small-gain theorem and the passivity theorem. Phase versus gain uncertainties

4. Dissipativity theory

5. Robust stability and performance. Stability margins.

6. An introduction to H-infty control. 

7. Gap metrics

PART 2: NONLINEAR SYSTEMS (7L + 1 computer lab session, Prof F Forni)

1. Small and large signal analysis. Contractive systems. Fading memory operators.

2. State-space analysis and Nyquist. Differential stability. Differential dissipativity. Differential circle criterion.

3. Feedback systems: simple models.

4. Phase portrait analysis.

5. Analysis and design of switches and clocks. Robust differential control.

6. Monotone systems. Scale relative graphs (SRGs). Applications in biology.

7. Describing function analysis.

Further notes

ASSESSMENT

Coursework only.

Coursework

Coursework Format

Due date

& marks

[Coursework activity #1  Robust control of haptic interfaces

Coursework 1 brief description

Learning objective:

  • Learn how to model uncertainty in an engineering application
  • Design a robust controller in Matlab

Individual Report 

  anonymously marked

 

28 February 2025

[30/60]

[Coursework activity #2  Feedback oscillations control ]

Coursework 2 brief description

Learning objective:

  • Learn how to model and analyse nonlinear oscillations in feedback systems
  • Design a nonlinear oscillator in a biologically motivated appication

Individual Report

anonymously marked

  28 March 2025

[30/60]

 

Booklists

Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.

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: 19/01/2025 18:26

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