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ENGINEERING TRIPOS PART IIB – 2009/2010

Module 4F3 - Nonlinear and Predictive Control

Leader:	Prof J M Maciejowski (jmm@eng)
Timing:	Lent Term
Prerequisites:	3F1 and 3F2 useful
Structure:	14 lectures + 2 examples classes
Assessment:	*Material / Format / Timing / Marks* Lecture Syllabus / Written exam (1.5 hours) / Start of Easter Term / 100 %

AIMS

Introduce fundamental concepts from nonlinear dynamic systems. Study general methods for investigating properties such as stability of nonlinear systems. Introduce predictive control as a technology of increasing importance. Apply methods from the nonlinear systems part of the course to analyse predictive control systems.

LECTURE SYLLABUS

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

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.

Input/output stability analysis:

Describing functions
Small gain theorems, circle and Popov criteria, passivity

PART 2: PREDICTIVE CONTROL (7L + 1 examples class, Prof J.M. Maciejowski)

What is predictive control? Importance of constraints. Flexibility of specifications. Typical applications.
Introduction to multivariable linear discrete-time state-space systems.
Basic formulation of predictive control problem without constraints. The receding horizon concept. Analytical derivation of optimal multivariable control law. Comparison with unconstrained LQR.
Including constraints in the problem formulation.
Guaranteeing offset-free control in the presence of constant disturbances.
Predictive control case study by industrial speaker (Dr P.C. Austin).

OBJECTIVES

On completion of the course, students should:

Appreciate the diversity of phenomena in nonlinear systems
Be able to use state space and input/output methods to study the stability of nonlinear systems
Be familiar with main ideas, applications and techniques of predictive control

REFERENCES

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

Last updated: September 2009

teaching-office@eng.cam.ac.uk