Instrumentation and Control Systems, 3rd Edition

Appendix C

Laplace Transform

Abstract

This appendix looks at the mathematics behind the Laplace transform.

Keywords

Laplace transform

C.1 The Laplace Transform

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, i.e. t≥0, and so to obtain the Laplace transform of f(t) function we multiply it by e^−st and then integrate with respect to time from zero to infinity; s is a constant with the unit of 1/time. The result is then said to be in the s-domain. The Laplace transform of the function of time f(t), which ...