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Control Systems Engineering, 3rd Edition by S. K. Bhattacharya

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Appendix 1

Laplace Transform

A1.1  INTRODUCTION

For a proper understanding of the behaviour of a system, one has to represent the system in the form of mathematical relations. The voltage equation in algebraic form or a differential equation of an electrical circuit are a few such mathematical relations.

The Laplace transformation offers a very simple and elegant method of solving linear or linearised differential equations which result from the mathematical modelling of a process or a system. The Laplace transform also allows us to develop input-process-output models which are very useful for the study of control systems. It is because of the above reasons that the Laplace transform is used extensively in control engineering.

A1.2  DEFINITION ...

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