ENGM018 - Nonlinear Control (2023)

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MODULE TITLENonlinear Control CREDIT VALUE15
MODULE CODEENGM018 MODULE CONVENERProf Christopher Edwards (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated)
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)

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

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 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).

 

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

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 35.00 Guided Independent Study 115.00 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  

 

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 Exam mark
Coursework  20 20 hours 1-12 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) 1-12 Referral/dedferral period

 

RE-ASSESSMENT NOTES

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%.

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
  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:

Type Author Title Edition Publisher Year ISBN Search
Set Slotine, JJ and Li, W Applied Nonlinear Control Pearson 1988 [Library]
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 27 January 2023 LAST REVISION DATE Thursday 15 February 2024
KEY WORDS SEARCH None Defined