Chapter two

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.

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)