Appendix B

Laplace transform

Control systems tend to have input-output relationships which are described by differential equations. The differential equations describe how the output varies with time for an input. We can determine the output for a system with some particular input by solving the differential equation. However, the Laplace transform is a way of transforming differential equations into more convenient forms for determining outputs.

A quantity which is a function of time can be represented as f(t) and is said to be in the time domain, e.g. if we have a voltage v which is a function of time we can write as v(t) to show that it is. In discussing control systems we are only concerned with values of time greater than or equal to 0, ...

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