ENGM018 | 2024 | University of Exeter

MODULE TITLE	Nonlinear Control	CREDIT VALUE	15
MODULE CODE	ENGM018	MODULE CONVENER	Prof Christopher Edwards (Coordinator)

DURATION: TERM	1	2	3
DURATION: WEEKS		11

Number of Students Taking Module (anticipated)	20

DESCRIPTION - summary of the module content

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.

AIMS - intentions of the module

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.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

Programmes that are accredited by the Engineering Council are required to meet Accreditation of Higher Education Programmes (AHEP4) Learning Outcomes.

The following Engineering Council AHEP4 Learning Outcomes are covered on this module (shown in brackets):

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

Module Specific Skills and Knowledge:

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:

6. Show an improved ability to interpret data in terms of mathematical models (M1,M2,M3)

7. Translate a physical problem into an appropriate (nonlinear) mathematical system (M1,M2,M3)

8. Interpret solutions of these equations in physical terms (M1,M2,M3)

Personal and Key Transferable/ Employment Skills and Knowledge:

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)

SYLLABUS PLAN - summary of the structure and academic content of the module

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 (sliding modes)

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

LEARNING AND TEACHING

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching Activities	35	Guided Independent Study	115	Placement / Study Abroad

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS

Category	Hours of study time	Description
Scheduled learning and teaching activities	25	Lectures
Scheduled learning and teaching activities	5	Tutorials (alternate weeks)
Scheduled learning and teaching activities	5	Laboratory classes
Guided independent study	115	Private Study

ASSESSMENT

FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade

SUMMATIVE ASSESSMENT (% of credit)

Coursework	20	Written Exams	80	Practical Exams

DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment	% of Credit	Size of Assessment (e.g. duration/length)	ILOs Assessed	Feedback Method
Written exam	80	2 hours	1-3 (M1,M2,M3,M17)	Exam mark
Coursework	20	2 hours	1 -11 (M1,M2,M3,M4, M17)	Return of annotated scripts

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)

Original Form of Assessment	Form of Re-assessment	ILOs Re-assessed	Time Scale for Re-reassessment
All above	Written exam (100%, 2 hours)	1-11 (M1,M2,M3,M4,M17)	Referral/Deferral Period

RE-ASSESSMENT NOTES

Deferrals: Reassessment will be by coursework and/or exam in the deferred element only. For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module. As it is a referral, the mark will be capped at 50%.

RESOURCES

INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

J.-J E.Slotine & W.Li, Applied Nonlinear Control, Pearson International edition (1988), 10:0130408905 [Library]
Khalil, HK, Nonlinear systems, Prentice Hall
Edwards, C and Spurgeon, SK, Sliding mode control: theory and application, Taylor & Francis

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE	15	ECTS VALUE	7.5

PRE-REQUISITE MODULES	None
CO-REQUISITE MODULES	None

NQF LEVEL (FHEQ)	7	AVAILABLE AS DISTANCE LEARNING	No
ORIGIN DATE	Friday 22nd March 2024	LAST REVISION DATE	Tuesday 1st October 2024

KEY WORDS SEARCH	None Defined

Nonlinear Control - 2024 entry