# Chapter two

Modelling and behaviour

## Section seven: Case studies on Modelling and Behaviours

This chapter is on the theme of linear models. For example:

A d^{3}x/dt^{3} + B d^{2}x/dt^{2} + 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 collates several case studies to demonstrate the relevance of the learning.

### 1. First order examples

A good test of understanding is to ask how these concepts and analogies might be extended and/or applied to each engineering discipline.

Mixing tank (PDF, 772KB)

House temperature (PDF, 654KB)

Mass-damper (PDF, 770KB)

Tank level (PDF, 624KB)

Pain relief (PDF, 263KB)

Thermal system (PDF, 612KB)

Electrical system (PDF, 666KB)

Heat exchanger (PDF, 652KB)

DC servo (PDF, 307KB)

Savings and debt models (PDF, 166KB)

### 2. Second order examples

It is noted that many examples are electro-mechanical. Therefore, they are relevant across all engineering disciplines.

Mass spring damper (PDF, 439KB)

Diabetes (PDF, 184KB)

DC servo (PDF, 331KB)

Car velocity (PDF, 248KB)

House temperature (PDF, 195KB)

Tank level (PDF, 770KB)

Aeroplane roll (PDF, 224KB)

Pulleys (PDF, 535KB)

Gears (PDF, 361KB)

Electrical circuits (PDF, 262KB)

### 3. Collations, analogies and comparisons

An interesting piece of coursework would be to form some collations of your own, relevant to your own studies.

Biology examples (PDF, 263KB)

Heat exchanger examples (PDF, 374KB)

Mixing examples (PDF, 401KB)

### 4. Impact of feedback and under damping

A lot of real life examples lead to over damped second order models. However, the necessary introduction of feedback often makes these become under damped.

Cruise control (PDF, 252KB)

Heat exchanger examples (PDF, 344KB)

DC servo (PDF, 345KB)