# Chapter two

Modelling and behaviour

## Section one: Modelling Principles

This chapter is on the theme of linear models. For example:
A d
3x/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.

This section focuses on the following principles:

• How do I model core engineering components?

• Are there analogies between different components?

• Are there analogies between similar arrangements of different components?

The sections on first and second order modelling will develop the principles and analogies further to illustrate how we create models of dynamic behaviour.

### 1. Concepts and components

Approaches and concepts in first principles modelling. What are the common physical components and how are these modelled?

View notes (PDF, 847KB).

### 2. Systems of springs

How do we model a system comprising of a number of springs linked together? How would this extend to capacitors?

Springs in parallel video and notes (PDF, 655KB).

Springs in series video and notes (PDF, 555KB).

### 3. Systems of resistors

How do we model a system comprising of a number of resistors linked together? How would this extend to dampers?

Resistors in series video and notes (PDF, 740KB).

Resistors in parallel video and notes (PDF, 722KB).

### 4. Systems of pipes

Modelling a system comprising of a number of pipes linked together and extensions to systems of heat conductors.

Pipes in series and parallel video and notes (PDF, 688KB).

Heat conductors in series video and notes (PDF, 467KB).

### 5. Analogous arrangements

Simple analogies between arrangements across different disciplines.

Analogies discussion and summary notes (PDF, 980KB).

Analogies in brief notes (PDF, 577KB).

Pipes and conductors in parallel video.

Analogies summary video.

### 6. Linearity and non-linear systems

A concise introduction to superposition, linearity and what to do with non-linear models.

Two talk through videos are on YouTube (video one, video two).