ENGINEERING TRIPOS PART IIB – 2012/2013

Module 4F2 - Robust and Nonlinear Systems and Control

AIMS

The aims of this module are to introduce fundamental concepts from nonlinear dynamic systems and to introduce techniques for the analysis and control of nonlinear and multivariable systems.

LECTURE SYLLABUS

PART 1: MULTIVARIABLE FEEDBACK SYSTEMS (7L + 1 example class, Prof. M.C. Smith)

• 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, Prof. J. M. Maciejowski)

• Dynamical systems:
• Differential equations and trajectories.
• 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 networks.
• Stability of predictive control.
• State-space tools for robustness analysis.
• Input/output stability analysis:
• Describing functions
• Small gain theorems, circle and Popov criteria, passivity.

OBJECTIVES

On completion of the module, 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.

REFERENCES

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

Last updated: July 2012