Modelling and control by Anthony Rossiter

# SECOND ORDER SYSTEM MODELLING

This is the first chapter in the theme on modelling and simulation of linear models. Use the left hand toolbar to access the other chapters and themes.

 It is implicit in several of these chapters that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace. More information on these can be found in the Mathematics theme on the left hand toobar.

This chapter contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

## Second order modelling 1 - mass-spring-damper

Extends the 1st order modelling videos to show how the derivation of a model for a simple 2nd order mechanical systems comprising parallel arrangement of a mass, spring and a damper is straightforward. Includes a brief discussion of quarter car models which include mass-spring-damper components.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Second order modelling 2 - resistor-inductor-capacitor

Extends the 1st order modelling videos to show the derivation of a model for a simple 2nd order electrical circuit comprising resistor, inductor and capacitor. Reiterates messages on analogies with mechanical systems.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Second order modelling 3 - mass-spring-damper and gears

Pulleys and gears are widely used in mechanical systems and thus an understanding of basic modellng techniques is invaluable. Develops models for a basic mas-spring-damper system working through a pulley (or gear). Has a discussion of gears in general, mostly based around a simple bicycle example.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Second order modelling 4 - DC servo

DC servos are one of the most common systems in use in the world today. This video gives a keep overview of how these might be modelled and how typical assumptions lead to 2nd order dynamics. Gives the modelling steps in detail.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Second order modelling 5 - DC servo and gears

Considers scenarios where the DC servo is driving a load throuugh a system of gears and shows how, with simplifying assumptions, this still results in a 2nd order model. Also shows that a typical DC servo assumptions leads to 1st order dynamics being representative of many DC servo applications.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Second order modelling 6 - two tank systems

Shows how different arrangments of two tanks leads to models with different characteristics. Indicates the need for more involved modelling approaches to deal with complex systems.