November 2025
Intermediate to advanced
352 pages
12h 30m
English
Content preview from Optical Beam Control
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Chapter 3Feedback Control
Feedback control system analysis begins with mathematical models, typically based on small perturbations around an operating point and described by ordinary differential equations. Direct manipulation of these equations can be cumbersome. To address this, systematic methods such as the Laplace transform, state-space, and optimal control are employed to simplify analysis and design. The following chapters will explore each of these methods, providing an introductory overview of their applications in control system design. The emphasis will be on concepts and practical usage, while detailed derivations will not be covered. Interested readers are encouraged to consult the references provided for a deeper understanding of mathematical foundations and advanced techniques.
3.1 Foundations of Classical Control
3.1.1 The Laplace Transform
The Laplace transform converts linear differential equations into the complex frequency or Laplace domain, simplifying integration into algebraic manipulations. The basic Laplace transform of a time signal 
is
or more compactly
(3.1)
It is assumed that is zero for all times before . Here, represents the complex frequency. ...
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