Mathematics (Penryn)

ECM3907 - Dynamical Systems and Control (2018)

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MODULE TITLEDynamical Systems and Control CREDIT VALUE15
MODULE CODEECM3907 MODULE CONVENERDr Tim Hughes (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
Number of Students Taking Module (anticipated) 16
DESCRIPTION - summary of the module content

The field of dynamical systems and control aims towards a fundamental understanding of interconnected dynamical systems (technological, biological, socioeconomic, etc), and the use of feedback to improve their performance. Feedback is a ubiquitous technology, universally applicable to situations where an outcome is desired in the presence of uncertainty. For example, central heating systems use feedback to maintain a comfortable temperature inside a building irrespective of the external temperature; blood sugar levels are tightly regulated even during periods of heavy exercise by using negative feedback in a process known as glucose homeostasis. This module will introduce a number of key concepts and techniques from dynamical systems and control, building on material covered in ECM1906 (Dynamics) and ECM2906 (Data, Signals and Systems). The material will be illuminated by practical examples while being treated with mathematical rigour. Classical methods of linear systems analysis and control design will be introduced, such as the stability tests of Routh Hurwitz and Nyquist; notions of observability (whether you can infer the state of the system from your observations) and controllability (whether you can control the state of the system); and also methods of linear feedback design. This will be complemented with material on nonlinear systems, notably Lyapunov’s methods of stability analysis. The appreciation of the theoretical material will be reinforced through practical sessions and computational examples which use Matlab Simulink for control system design.

Prerequisite modules: “Vector and Matrices” (ECM1902), “Dynamics” (ECM1906), “Linear Algebra” (ECM2901), “Data, Signals and Systems” (ECM2906), and familiarity with Matlab.

 

AIMS - intentions of the module

The intention of the module is to provide an introduction to several tools and techniques in Dynamical Systems and Control; an appreciation and understanding of the underlying mathematics; hands-on experience with practical control system design using state of the art software; and an awareness of the relevance and importance of control to a diverse range of disciplines.

 

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

1 Demonstrate a sound understanding of the mathematics underlying dynamical systems and control;

2 Develop familiarity with the representation and manipulation of interconnected dynamical systems described by differential equations, difference equations, state space equations or transfer functions; and a range of techniques for their analysis and control;

3 Develop a basic understanding of feedback control and how to apply designs to simple example models motivated by scientific and engineering questions;

 

Discipline Specific Skills and Knowledge

4 Demonstrate competence in the application of various techniques in dynamical systems and control, an awareness of their relevance to different disciplines, and a thorough understanding of the underlying mathematics;

5 Synthesize a range of mathematical and computational techniques in MATLAB and Simulink for the analysis of dynamical systems and the design of control systems;

 

Personal and Key Transferable / Employment Skills and Knowledge

6 Formulate and solve problems;

7 Communicate reasoning and solutions effectively in writing;

8 Demonstrate appropriate use of learning resources;

9 Demonstrate self-management and time-management skills.

 

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

- Dynamical systems preliminaries: differential equations and continuous time dynamical systems; difference equations and discrete time dynamical systems; state space; linear systems; linearization of nonlinear systems; numerical and analytical solution of differential and difference equations; impulse response; Laplace transforms; z transforms; transfer functions; equilibria; stability [7 hours];

- Linear single-input single-output systems: Routh Hurwitz stability condition; block diagram algebra; closed loop transfer functions; steady state and frequency response; Bode and Nyquist diagrams; Nyquist stability condition; proportional and integral control [7 hours]:

- Linear input-state-output systems: variation of the constants formula; state feedback; controllability; stabilizability; pole placement; observability; detectability; observers; state space isomorphism theory; formulation of optimal control problems [6 hours];

- Nonlinear systems: phase portraits; linearization and Lyapunov’s indirect method; invariant sets, equilibria and limit cycles; Poincaré Bendixson theorem; Lyapunov’s direct method; LaSalle’s invariance principle [7 hours];

- Systems analysis and controller design using Matlab and Simulink: representations of continuous and discrete time dynamical systems using Matlab’s Control systems toolbox; block diagrams in Simulink; simulation; linearization; control system design [6 hours].

 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33.00 Guided Independent Study 117.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled Learning & Teaching activities 16 Formal lectures of new material
Scheduled Learning & Teaching activities 6 MAtlab Simulink computing sessions
Scheduled Learning & Teaching activities 11 Tutorials for individual and group support
Guided Independent Study 117 Lecture & assessment preparation, wider reading

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Four example sheets 4 x 2.5 hours 1-4, 6-9 Written and oral
One computing exercise 1 x 3 hours 1-9 Written and oral

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 40 Written Exams 60 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Control design in Matlab Simulink 40 16 hours 1-9 Written and oral
Written exam - closed book 60 2 hours 1-4, 6-7, 9 Written/verbal on request

 

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-assessment
All above Written exam (100%) All August Ref/Def period

 

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment. If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

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

Basic reading:

ELE: http://vle.exeter.ac.uk

 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Luenberger D.G. Introduction to Dynamic Systems: Theory, Models & Applications 1st John Wiley & Sons 1979 978-0471025948 [Library]
Set Åström K.J. and Murray R.M. Feedback Systems: An Introduction for Scientists and Engineers 2nd Princeton University Press 2016 0691135762 [Library]
Set Khalil H.K. Nonlinear Systems 3rd Prentice Hall 2002 0130673897 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM1902, ECM1906, ECM2901, ECM2906
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 6 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 07 May 2015 LAST REVISION DATE Thursday 13 December 2018
KEY WORDS SEARCH Dynamical systems, differential equations, stability, state space, feedback, control, controllability, observability, Matlab simulink.