# Engineering

## ECM2119 - Mathematical Modelling and Control Engineering (2010)

MODULE TITLE CREDIT VALUE Mathematical Modelling and Control Engineering 15 ECM2119 Prof Mike Belmont (Coordinator), Dr Mustafa Aziz
DURATION: TERM 1 2 3
DURATION: WEEKS
DESCRIPTION - summary of the module content
AIMS - intentions of the module
To introduce students to mathematical models of engineering systems. To expose them to standard methods of systems analysis using transform methods in both continuous and discrete variable form.To introduce them to the concepts of feedback and stability, and standard control concepts via a detailed analysis of proportional, integral and derivative controls for first and second order systems.
INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
Note: List A comprises core outcomes that will be covered fully in lectures and must be achieved by all students to meet the minimum university requirement for progression. List B comprises outcomes that are EITHER more difficult to achieve OR are to be achieved by private study (or both). All outcomes will be assessed, and coverage of List B outcomes is essential for both BEng and MEng students. A: THRESHOLD LEVEL System modelling. Motivational examples of real physical systems and their behaviour (sourced by student experience), spring mass damper, RLC networks, heated reservoir, liquid tanks with capillary pipes. Input/output relationships, the lumped parameter element concept, linearity, constant and time varying, reciprocity, non-linearity. Linear time-invariant reciprocal lumped parameter, (LT) approximations to real elements. Storage elements, dissipative elements. Approximations to real first and second order systems by building up connected networks of LT elements, need for extra system elements (signed summer, constant coefficient multiplier). Description of network as single system block with single input, single output. Derivation of system differential equation. System order and relationship to number of storage elements and physical link to number of initial conditions. Coupled systems, 3rd order and above, multi-input, multi-output systems. B: GOOD TO EXCELLENT System modelling. Direct derivation of system differential equation from first principles. Time-varying, non-reciprocal and non-linear elements and systems incorporating them, dependence of non-linear system behaviour on initial conditions. Linearisation techniques. Vector and matrix description of multi-input multi-output systems, introduction to distributed systems.
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. Laplace systems (Mustafa) Open and Closed-Loop Control Systems Sensitivity of Control Systems to Parameter Variation Disturbance Rejection Transient Response Steady-State Error Case Study -- Speed Control of a DC Motor The Stability of Linear Feedback Systems Three-Term PID Controller Control of First-Order Systems Proportional (P) Control of First-Order Systems Integral (I) Control of First-Order Systems PI Control of First-Order Systems Derivative (D) Control PD Control of Second-Order Systems PID Control
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 30 70
DETAILS OF SUMMATIVE ASSESSMENT
DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
RE-ASSESSMENT NOTES
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

Type Author Title Edition Publisher Year ISBN Search
Set Dorf, Richard C Modern Control Systems 11(5th or later) Reading, Mass; Wokingham: Addison-Wesley 2008 978-0132451925 [Library]
Set Nise, Norman S Control Systems Engineering: MATLAB tutorial update to version 6 3rd or later New York: John Wiley and Sons 2002 0471250910 [Library]
Set Ogata, Katsuhiko Modern Control Engineering 4/e (2nd or later) 2010 0130609072 [Library]
Set Franklin G.F., Powell J.D. and Emami-Naeini A. Feedback Control of Dynamic Systems Pearson 2008 978-0135001509 [Library]
Set Wilke, J; Johnson, M and Katebi, R Control Engineering: an Introductory Course Basingstoke: Palgrave 2001 [Library]
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES ECM1102, ECM1107
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 2 No Thursday 15 December 2011 Thursday 15 December 2011
KEY WORDS SEARCH None Defined