ECM3907 | 2020 | University of Exeter

MODULE TITLE	Dynamical Systems and Control	CREDIT VALUE	15
MODULE CODE	ECM3907	MODULE CONVENER	Dr Tim Hughes (Coordinator)

DURATION: TERM	1	2	3
DURATION: WEEKS	11	0	0

Number of Students Taking Module (anticipated)	18

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; and 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: “Vectors and Matrices” (ECM1902), “Dynamics” (ECM1906), and familiarity with MATLAB.

Note: The module will also touch on concepts from 'Linear Algebra' (ECM2902), 'Differential Equations' (ECM2903), and 'Data, Signals and Systems' (ECM2906), although these are not essential prerequisites.

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 [3 hours];

- Linear single-input single-output systems: Routh Hurwitz stability condition; block diagram algebra; closed loop transfer functions; steady state and frequency response; Nyquist stability condition; proportional and integral control [9 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 [9 hours];

- Nonlinear systems: linearization and Lyapunov’s indirect method; invariant sets, equilibria and limit cycles; Poincaré Bendixson theorem; Lyapunov’s direct method; LaSalle’s invariance principle [6 hours];

- Systems analysis and controller design using MATLAB and Simulink: representations of continuous and discrete time dynamical systems using MATLAB and Simulink; block diagrams in Simulink; simulation; linearization; control system design [8 hours].

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	0

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS

Category	Hours of study time	Description
Scheduled Learning & Teaching activities	27	Formal lectures of new material and tutorials for individual and group support
Scheduled Learning & Teaching activities	8	MATLAB Simulink computing sessions
Guided Independent Study	115	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

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	8 hours computing sessions, plus guided independent study	1-9	Written and oral
Examination	60	Approx. 2 hours	1-4, 6-9	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	Examination (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
Set	Luenberger, D.G.	Introduction to Dynamic Systems: Theory, Models & Applications	1st	John Wiley & Sons	1979	978-0471025948
Set	Astrom, K.J. and Murray, R.M.	Feedback Systems: An Introduction for Scientists and Engineers	2nd	Princeton University Press	2016	0691135762
Set	Khalil, H.K.	Nonlinear Systems	3rd	Prentice Hall	2002	0130673897

CREDIT VALUE	15	ECTS VALUE	7.5

PRE-REQUISITE MODULES	ECM1902, ECM1906
CO-REQUISITE MODULES

NQF LEVEL (FHEQ)	6	AVAILABLE AS DISTANCE LEARNING	No
ORIGIN DATE	Thursday 13th December 2018	LAST REVISION DATE	Wednesday 29th July 2020

KEY WORDS SEARCH	Dynamical systems; differential equations; stability; state space; feedback; control; controllability; observability; MATLAB Simulink

Dynamical Systems and Control - 2020 entry