Modelling, dynamics and control by Anthony Rossiter

Section on modelling 1st 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 1st 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 1st order model?
The sections on 1st order responses will develop the principles and analogies futher to illustrate how we create models of dynamic behaviour.

1. Simple Electrical Circuits: Use of Kirchoff's voltage law (voltage balance) and component equations to derive 1st order models for simple series circuits.
i. Resistor-capacitor pdf file.
ii. Resistor-inductor pdf file.
iii. Video on resistor-capacitor modelling.
iv. Video on resistor-inductor modelling.

2. Simple mechanical systems: Modelling a system of mechanical components arranged in parallel using force balance across components.
i. Spring-damper pdf file.
ii. Mass-damper pdf file.
iii. Video on spring-damper modelling.
iv. Video on mass-damper modelling.

3a. Fluid systems: Fluid systems are driven by pressure differences across pipes/orifices causing flow, and storage components such as tanks. Balance is done with respect to volumes and/or molar quantities.
i. General fluid systems pdf file.
ii. Tank-level systems pdf file.
iii. Mixing tanks pdf file.
iv. Mixing tank with reaction pdf file.

4. Thermal systems: This could be a heat exchanger in manufacturing or as simple as domestic heating.
i. Heat exchanger pdf file.
ii. House temperature pdf file.
iii. Video on thermal system modelling.
iv. Video on heat exchanger modelling.
iv. Heat exchanger modelling tutorial video.

5. Analogous arrangements: It is always useful to summarise the analogies between systems from different disciplines as this can help understand behaviours and support design.
i. Analogous 1st order systems pdf file.
ii. Video on modelling analogies and time constant form.
iii. Analogies with savings models.

## 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.