1. Simple Electrical Circuits:
Use of Kirchoff's voltage law (voltage balance) and component equations to derive 2nd order models for simple series electrical circuits.
i. Resistor-inductor-capacitor modelling.
ii. Video on RLC circuit modelling.
2. Simple linear mechanical systems:
Modelling a system of mechanical components arranged in parallel using force balance across components.
ii. Mass-spring-damper with a pulley.
iii. Car suspension system.
iv. Video mass-spring-damper modelling.
v. Video on mass-spring-damper + gears.
Real systems often combine components from multiple disciplines, electro-mechanical being very common.
i. DC servo with a flexible shaft.
ii. DC servo with simple dynamics.
iii. DC servo with gears.
iv. Video on DC servo modelling.
v. Video on DC servo with modifications.
4. Fluid systems:
In a manufacturing system, there may be multiple tanks which are interconnected and this can lead to higher order dynamics.
i. Multiple tank systems.
ii. Video on modelling a two tank system.
5. Miscellaneous case studies:
A number of examples exploiting first principles modelling to derive models of various orders.
i. Speed of a car
ii. House temperature with radiator dynamics.
iii. Aeroplane roll.
iv. Diabetes and blood sugar levels.