Modelling and behaviour
Section two: modelling first order systems
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 focuses on applying core modelling principles to a variety of 1st order systems.
How do I model simple electrical and mechanical systems and are there analogies between similar arrangements of different components?
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 further 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 first order models for simple series circuits.
2. Simple mechanical systems
Modelling a system of mechanical components arranged in parallel using force balance across components.
3. 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.
General fluid systems notes (PDF, 718 KB).
Tank-level systems notes (PDF, 624 KB).
Pipes and tanks modelling video.
Tank level modelling video.
Tank system modelling tutorial video.
Mixing tank tutorial video.
4. Thermal systems
This could be a heat exchanger in manufacturing or as simple as domestic heating.
House temperature notes (PDF, 654 KB).
Thermal system modelling video.
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.
Analogous first order systems notes (PDF, 903 KB).
Modelling analogies and time constant form video.
Analogies with savings models notes (PDF, 166 KB).