Modelling and behaviour
This chapter is on the theme of linear models. For example:
A d3x/dt3 + B d2x/dt2 + C dx/dt + D x = K u
where x(t) is the state, u(t) the input and A, B, C, D, K are model parameters.
Core skills are things such as:
How do I find a mathematical model representation of a real physical system?
How do such systems behave and how does the behaviour link to the model parameters?
Are there generic analysis tools that help with understanding?
It is implicit that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace.
Relatively quick overview videos and summary notes which introduce the core topics.
Sections in chapter two
Section one: Modelling principles
How do we do physical modelling? Are there common concepts we can exploit? What are the analogies between different disciplines? Derive models for example scenarios.
Section two: Modelling first order systems
Define a number of engineering scenarios which lead to first order models. Demonstrate the modelling from first principles and illustrate analogies.
Section three: Responses of first order systems
How do first order systems behave? Are there efficient and insightful ways of defining and illustrating behaviour? How do we choose system parameters to achieve the desired behaviour?
Section four: Modelling second order systems
Define a number of engineering scenarios which lead to second order models. Demonstrate the modelling from first principles and illustrate analogies.
Section five: Responses of second order systems
How do second order systems behave? Are there efficient and insightful ways of defining and illustrating behaviour? How do we choose system parameters to achieve the desired behaviour?
Section six: Behaviour characterisation for any order systems
Discussion of how to characterise behaviour in general, including for higher order systems.
Section seven: Case studies on modelling and behaviours
Examples of a variety of engineering scenarios and modelling from first principles, leading to models with different orders and attributes.
Section eight: Linearisation of nonlinear models
Most real models included nonlinear components and relationships. However, they can be approximated well enough locally by a linear model.