
Module Leader
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