Control Systems

Appendix A

Differential equations

As will be evident from the models discussed in Chapter 2, many systems have input-output relationships which have to be described by differential equations. A differential equation is an equation involving derivatives of a function, i.e. terms such as dy/dt and d²y/dt². Thus:

is a differential equation. The term ordinary differential equation is used when there are only derivatives of one variable, e.g. we only have terms such as dy/dt and d²y/dt² and not additionally dx/dt or dx²/dt². The order of a differential equation is equal to the order of the highest derivative that appears in the equation. For example, ...