# Engineering

## ECM2119 - Mathematical Modelling and Control Engineering (2019)

MODULE TITLE CREDIT VALUE Mathematical Modelling and Control Engineering 15 ECM2119 Dr Halim Alwi (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 15
DESCRIPTION - summary of the module content

You will be exposed to standard methods of systems analysis using differential equation modelling and transform methods, in both continuous and discrete variable form. Topics will include: system synthesis and design, “s plane” pole zero system specification, transfer function and frequency response functions, feedback and stability. This will cover general linear constant coefficient systems with first and second order systems as illustrations. Practical design method studied will be: block diagram synthesis, pole-zero distribution/frequency response design and time-step specification for discrete systems.

Prerequisite module: ECM1102, ECM1107 or equivalent

AIMS - intentions of the module

The aims of the module are for students to:

Understand why a systems approach is useful for the engineering profession

Gain skills in building differential equation and block diagram descriptions of real physicals entities

Appreciate the advantages of and gain skills in Laplace and Z transform theory

Gain skills in block diagram synthesis of transfer functions

Understand key ideas and concepts: dynamics and feedback

Appreciate the relevant mathematical theory

Be able to analyse existing systems and realise simple designs from dynamical specifications

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

This is a constituent module of one or more degree programmes which are accredited by a professional engineering institution under licence from the Engineering Council. The learning outcomes for this module have been mapped to the output standards required for an accredited programme, as listed in the current version of the Engineering Council’s ‘Accreditation of Higher Education Programmes’ document (AHEP-V3).

This module contributes to learning outcomes: SM1p SM2m, SM3m, SM4m, SM5m, EA1p, EA2p, EA3m, EA4p, EA6m, D4p, D7p, G2p, G3p

A full list of the referenced outcomes is provided online: http://intranet.exeter.ac.uk/emps/subjects/engineering/accreditation/

The AHEP document can be viewed in full on the Engineering Council’s website, at http://www.engc.org.uk/

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

Module Specific Skills and Knowledge:

1 demonstrate awareness and skills in the following techniques: time domain evaluation of system output in terms of input (diff., equ., and impulse response), Laplace transforms, use of LT’s to obtain time domain solutions;
2 demonstrate, through analytical and simulation work, knowledge and understanding of the power and limitations of feedback systems; techniques;
3 derive simple performance specifications for systems and analyse simple examples using analytic tools;
4 with limited guidance, use analytic tools to design and analyse high linear order systems.

Discipline Specific Skills and Knowledge:

5 demonstrate skill in quantitatively analysing engineering problems;
6 demonstrate an awareness of the interrelationship between design and analysis;
7 demonstrate an understanding of the relationship between a real system and a model.

Personal and Key Transferable/ Employment Skills and  Knowledge:

8 analyse problems clearly and formally;
9 demonstrate an awareness of the many approaches to the same problem and to be able to assess their relative merits;
10 express your problem solving intentions clearly and systematically in written form.

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

- generic modelling of engineering systems as networks;

- electromechanical, thermal and fluid systems examples;

- SISO and MIMO systems;

- system block diagrams;

- Laplace transforms;

- transfer functions;

- block diagram algebra, systems;

- open and closed-loop systems;

- block diagram manipulation and transfer function synthesis;

- “S Plane pole-zero descriptions”;

- stability (pole and bounded input, bounded output);

- explicit time responses;

- impulse response;

- frequency response;

- discretisation;

- recurrence relations;

- sampling theorem;

- time step selection;

- “Z Transforms”;

- discrete frequency response.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 57 93 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 27 Lectures (27 Term 1) Scheduled learning and teaching activities 30 Tutorials Guided independent study 93 Lecture and assessment preparation; private study

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

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 15 85
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 85 2 hours in January All Via problem class and revision sessions
Coursework – assessment using exam style questions 15 Two full examination papers to be completed over the Christmas vacation All Post course feedback lecture session

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%) 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

ELE: http://vle.exeter.ac.uk

Web based and Electronic Resources:

Other Resources: