Nonlinear Control - 2021 entry

Whilst linear systems are better understood from a mathematical perspective (often yielding analytic solutions) and have been extensively studied and used as a platform for the design of a wide range of linear control strategies, many real engineering systems are nonlinear and cannot be approximated well by linear ones (except around limited operational points). In this module, you will look at methods to analyse nonlinear systems and will introduce some state-of-the-art techniques for developing practical nonlinear control strategies for such systems.

In this module, you will learn why some Engineering systems are better modelled as nonlinear equations. The module will look at some of the popular methods to analyse nonlinear systems and will introduce some state-of-the-art techniques for developing practical nonlinear control strategies for such systems.

1: Motivation examples: electric motors, Euler Lagrange (mechanical systems);

2: The phase plane analysis method (to including a discussion of limit cycles);

3: Describing function analysis;

4: The fundamentals of Lyapunov theory;

5: Jacobian linearization;

6: L’ure systems;

7: Popov and Circle Criteria;

8: Passivity theory;

9: An introduction to feedback linearization: 10: Sliding mode control theory;

11: Simple direct adaptive control;

11: Adaptive model reference control;

12: Control Lyapunov functions;

13: Lyapunov design methods (the "back stepping" procedure): 14: The L_2 gain and the Small Gain Theorem;

15: Hamilton-Jacobi-Bellman equation.

As the module is assessed by the examination and coursework, the ref/def assessment will be by examination. The candidates will be awarded the ref/def examination mark combined with the original coursework mark.

Reading list for this module: