Modelling, dynamics and control by Anthony Rossiter

Section on modelling 2nd order systems

This section is part of the chapter 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 focuses on applying core modelling principles to a variety of both 2nd and higher order systems.
1. How do I model simple electrical and mechanical systems and are there analogies between similar arrangements of different components?
2. What systems from a broader range of disciplines can also be described by a 2nd order model?
The sections on system responses will develop the principles and analogies futher to illustrate how we create models of dynamic behaviour, including systems beyond 2nd order.

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.
i. Mass-spring-damper.
ii. Mass-spring-damper with a pulley.
iii. Car suspension system.
iv. Video mass-spring-damper modelling.
v. Video on mass-spring-damper + gears.

3. Electro-mechanical: 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.

## MATLAB RESOURCES

Use the main MATLAB page to see all resources. Topic relevant resources are referenced directly as used in the sections.
To use these files in MATLAB, save the files into your own folder and then open, for example from the command window write: "open filename" .
More precise instructions for function files are provided where required.