Nonlinear Control - 2023 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.
 

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge M1,M2,M3,M17

1. Create nonlinear models of multivariable physical systems - including electrical and mechanical systems (M1,M2,M3)
2. Understand Lyapunov theory and how it underpins many/most of the modern nonlinear control design methods (M1,M2,M3)
3. Be familiar with 'hard nonlinearities' and their impact on closed-loop performance (M1,M2,M3,M17)
4. Recognise when engineering systems can be modelled as L’ure systems and the advantages of this approach (M1,M2,M3,M17)
5. Reflect on the differences/advantages/disadvantages of nonlinear control design methods compared to the linear control methods taught earlier in the degree programme (M1,M2,M3)

Discipline Specific Skills and Knowledge M1,M2,M3,M17

Personal and Key Transferable / Employment Skills and Knowledge M1,M2,M3,M4,M17

9. Demonstrate enhanced ability to formulate and analyse real physical problems using a variety of tools (M1,M2,M3)

10. Show enhanced modelling, problem-solving and computing skills (M1,M2,M3,M4)

 11. Improved communication skills (M17).

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 and Energy Shaping

9: Euler Lagrange Systems

10: An introduction to feedback linearization

11: Finite time control

12: Adaptive control

13: Control Lyapunov functions

14: Lyapunov design methods (the "back stepping" procedure)

15: The L_2 gain and the Small Gain Theorem

16: Hamilton-Jacobi-Bellman equation
 

Reassessment will be by a single written exam only worth 100% of the module. For deferred candidates, the mark will be uncapped. For referred candidates, the mark will be capped at 50%.

1. J.-J E.Slotine & W.Li, Applied Nonlinear Control, Pearson International edition (1998)
2. Khalil, HK,Nonlinear systems, Prentice Hall
3. Edwards, C and Spurgeon, SK Sliding mode control: theory and application,  Taylor & Francis

Reading list for this module: