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Last Updated S022023

DEng 603

Unit Name Applied Mathematical Modelling and Simulation
Unit Code DENG603
Unit Duration 12 weeks
Award

 

Doctor of Engineering

Duration 3 years
Year Level One
Unit Coordinator / Lecturer  Dr Milind Siddhpura / Dr Ali Marzoughi 

  

 

Core/Sub-Discipline: Core
Pre/Co-requisites N/A 
Credit Points

 

4

 

Total Program Credit Points 120
Mode of Delivery Online or on-campus. 
Unit Workload

10 hours per week:

Lecture - 1 hour

Tutorial - 1 hour

Assessments / Practical / Lab - 1 hour (where applicable)

Personal Study recommended - 7 hours (guided and unguided)

Unit Description and General Aims

This unit is a graduate level foundation unit for any engineering discipline.  The unit aims to apply mathematical modelling and simulation as well as a multidisciplinary approach to analysing engineering problems. 

A systems approach is thus the identification of inherent relationships and building a useful model to analyse engineering systems. Systems thinking is a way of thinking about, and a language for describing and understanding, the forces and interrelationships that shape the behaviour of systems. This helps us to see how to change systems more effectively, and to act more in tune with the processes of the natural and economic world. (ref: http://www.thwink.org/sustain/glossary/SystemsThinking.htm ). 

 

Advanced studies in Engineering will focus on characterising systems and the application of relevant mathematical methods to bring forth underlying relationships.

 

Learning Outcomes

 

On successful completion of this Unit, students are expected to be able to:

  1. Design and identify systems

Bloom’s Level 6

  1. Produce a structured thought process to engineering solutions

Bloom’s Level 6

  1. Recommend relevant mathematical methods towards systems’ definition

Bloom’s Level 5

  1. Evaluate and apply relevant software tools

Bloom’s Level 5

  1. Hypothesise, consolidate, present and apply models and simulations

Bloom’s Level 6

Student assessment

Assessment Type When assessed Weighting (% of total unit marks) Learning Outcomes Assessed

Assessment 1

Type: System Definition

Word length: 1000 to 2000

Consider an engineering system – for example a saucepan containing water at room temperature.  This water is to be heated to 90oC.  What are the various processes occurring that describe the system completely?  Complement your answer with a mind map (free tools are available on the net).  What are the mathematical equations?  What assumptions have been built in and what are the system boundaries? Consider both steady and dynamic states.

 After topic 4 20% 1, 2,3

Assessment 2

 

Type: Engineering Application (Mid-project) + Presentation

Word length: 2000 + code + working program

Consider a complex engineering problem in consultation with your facilitator. In your report detail the development of the equations. What were the underlying assumptions, how did you identify the system boundaries?  How did you solve your equations? Provide numerical details as well as code that can be run in an available software package.  What conclusions can you draw and what are the limitations of what you have done?		 Due after Topic 8 30% 3,4,5

Assessment 3

 

Type: Engineering Application (Final Project) + Presentation 

Word length: 2500 + code + working program

In consultation with your facilitator consider a sufficiently complex engineering or other problem where deterministic relationships are not that evident.  Using some of the stochastic methods discussed identify underlying relationships.  Compare and contrast the deterministic versus stochastic approach and identify where you would use one over the other		 Final week  50% 3,4

Prescribed and Recommended Readings

Required Textbook(s)

KLUEVER, C. A., Dynamic systems: modelling, simulation, and control, 2nd Edition, 2019, Wiley, ISBN 978-1-119-60186-7.  

 

Recommended Textbook(s):

Kreyszig, E., Advanced Engineering Mathematics, 10th Edition, August 2011, Wiley, ISBN 978-1-118-26670-0

Polya, G., How to Solve It: A new aspect of mathematical method, Second Edition, Princeton University press, ISBN 9780691164076  

 

Reference Materials

As advised during the class.  

Software Reference Material

Mendeley or EndNoteTM software for constructing reference lists, bibliography (www.endnote.com), (www.Mendeley.com)

MATLAB

SIMULINK

Microsoft Excel

Other tools as advised

 

Unit Content

Topic 1 

Introduction to dynamic systems

This topic focuses on systems definition and analysis through problem solving process. To assist in the understanding, relatively simple but fundamental systems will be chosen to discuss following key concepts:

  1. Different types of engineering systems: Distributed, Lumped, Continues, Discrete-time, Time varying, Time invariant and Nonlinear systems.
  2. How to model dynamic systems (Mechanical Systems). In this topic, students learn the fundamental engineering mathematical model of some practical mechanical systems. They will learn how to use mathematical model of simple mechanical systems to solve the complex systems in practice.

Topic 2

How to model dynamic systems

  1. Mathematical modelling of Electrical and Electromechanical systems. 
  2. Mathematical modelling of Fluid and Thermal systems.
  3. Mathematical modelling for fundamental engineering systems such as electrical and electromechanical, fluid and hydraulic systems will be continued in this section. This is essential for the engineers at this level to know how to model different types of equipment which is used in the industry.

 

Topic 3

Standard mathematical models for dynamic systems

  1. State-Space representation
  2. Linearization
  3. Transfer function and block diagrams
  4. Standard I/O functions

Topic 4

On linear dynamic systems and their analytical solutions

  1. Ordinary Differential Equations. 
  2. First-order, Second order, and Higher-order systems.
  3. Eigenvalues and State-space representation. 
  4. Simplified model.

 

Topic 5

Dynamic system analysis

  1. Laplace transformation
  2. Inverse Laplace transformation
  3. Application of Laplace Transformation on Analysis Dynamic Systems
  4. MATLAB and SIMULINK

Topic 6 

System Response

  1. Transient Response and steady-state response for first-order and second-order systems. 
  2. Frequency response 
  3. Analytical solution of the state equation.
  4. Response to non-linear systems

 

Topic 7

Introduction to control systems

  1. Feedback control systems and type of controllers
  2. Time-domain performance specifications
  3. Frequency-domain performance specifications
  4. System identification based on transfer function

 

Topic 8

Mathematical model and control of physical systems (Case Study1)

  1. Vibration Isolation System for a Commercial Vehicle

Topic 9

Mathematical model and control of physical systems (Case Study2)

  1. Mathematical model and feedback control design for a hydraulic servomechanism control

 

Topic 10

Mathematical model and control of physical systems (Case Study3)

  1. Armature controlled DC motor

 

Topics 11 and 12

These remaining topics will revisit the software tools and address any pending concerns. Key areas to be addressed during this period:

  1. An example of a non-deterministic simulation technique (e.g., Mont Carlo Simulation, ...)
  2. The use of tools such as MATLAB/SIMULINK

 

Software/Hardware Used

Software

  • Software: MATLAB, SIMULINK
  • Version: N/A
  • Instructions: N/A 
  • Additional resources or files: N/A

Hardware

  • N/A

Unit Changes Based on Student Feedback

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