Last Updated | S022020 |

**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 Creator / Reviewer | Dr. Srinivas Shastri & 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:

- Design and identify systems

*Bloom’s Level 6*

- Produce a structured thought process to engineering solutions

*Bloom’s Level 6*

- Recommend relevant mathematical methods towards systems’ definition

*Bloom’s Level 5*

- Evaluate and apply relevant software tools

*Bloom’s Level 5*

- Hypothesise, consolidate, present and apply models and simulations

*Bloom’s Level 6*

**Bloom’s Taxonomy**

The cognitive domain levels of Bloom’s Taxonomy:

Bloom's level | Bloom's category | Description |

1 | Remember | Retrieve relevant knowledge from long-term memory by recognising, identifying, recalling and retrieving |

2 | Understand | Construct meaning from instructional messages by interpreting, classifying, summarising, inferring, comparing, contrasting, mapping and explaining. |

3 | Apply | Carrying out or using a procedure in a given situation by executing, implementing, operating, developing, illustrating, practicing and demonstrating. |

4 | Analyse | Deconstruct material and determine how the parts relate to one another and to an overall structure or purpose by differentiating, organising and attributing. |

5 | Evaluate | Make judgments based on criteria and standards by checking, coordinating, evaluating, recommending, validating, testing, critiquing and judging. |

6 | Create | Put elements together to form a coherent pattern or functional whole by generating, hypothesising, designing, planning, producing and constructing. |

## Student assessment

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

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 90 |
After topic 4 | 20% | 1, 2,3 |

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 |

Type: Engineering Application (Final Project) 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.

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

**Recommended Textbook(s):**

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 EndNote^{TM} 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:

- Different types of engineering systems: Distributed, Lumped, Continues, Discrete-time, Time varying, Time invariant and Nonlinear systems.
- 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*

- Mathematical modelling of Electrical and Electromechanical systems.
- Mathematical modelling of Fluid and Thermal systems.
- 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*

- State-Space representation
- Linearization
- Transfer function and block diagrams
- Standard I/O functions

#### Topic 4

*On linear dynamic systems and their analytical solutions*

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

#### Topic 5

*Dynamic system analysis*

- Laplace transformation
- Inverse Laplace transformation
- Application of Laplace Transformation on Analysis Dynamic Systems
- MATLAB and SIMULINK

#### Topic 6

*System Response *

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

#### Topic 7

*Introduction to control systems*

- Feedback control systems and type of controllers
- Time-domain performance specifications
- Frequency-domain performance specifications
- System identification based on transfer function

#### Topic 8

*Mathematical model and control of physical systems (Case Study1)*

- Vibration Isolation System for a Commercial Vehicle

#### Topic 9

*Mathematical model and control of physical systems (Case Study2)*

- Mathematical model and feedback control design for a hydraulic servomechanism control

#### Topic 10

*Mathematical model and control of physical systems (Case Study3)*

- 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:

- An example of a non-deterministic simulation technique (e.g., Mont Carlo Simulation, ...)
- 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