We introduce the Laplace transform as a method of converting differential equations in time into algebraic equations in a complex variable. Afterward, we present the concepts of transfer function and block diagram as a means to represent linear time-invariant (LTI) dynamical systems.

Chapter Contents:

• 1.1 Fundamentals
• 1.1.1 List of symbols
• 1.1.2 Laplace transform and Laplace domain
• 1.1.3 Transfer function
• 1.1.4 Block diagram
• 1.1.5 Block diagram algebra
• 1.1.5.1 Mason rule
• 1.2 Worked examples
• 1.3 Proposed exercises
• 1.4 Block diagram analysis using computer packages
• 1.4.1 MATLAB
• 1.4.2 SCILAB
• 1.4.3 OCTAVE

Inspec keywords: transfer functions; diagrams; Laplace transforms; algebra; differential equations; linear systems

Other keywords: system transfer function; differential equation; linear time-invariant dynamical system; block diagram algebra; LTI dynamical system; Laplace transform

Subjects: Integral transforms; Control system analysis and synthesis methods; Algebra; Mathematical analysis; Linear control systems