Block Diagrams: Formal Graphical Description of Linear Systems

The first part of the book focuses on the mathematical foundations of linear feedback control systems. This chapter, together with most of the subsequent chapters, add to the design engineer’s toolbox for control systems. Many analysis and design problems can be treated by following specific recipes, much like a cookbook. In this chapter, the formal description of linear systems with block diagrams is covered. Block diagrams represent a linear system as a block with a transfer function, an input and an output signal. In the Laplace- and z z -domains, the output signal is obtained by multiplying the input signal with the transfer function. Linear systems, including feedback control systems, can be represented by block diagrams, much like an electronic circuit diagram. As an alternative to the algebraic solution, rules for block diagram manipulation and simplification are introduced in this chapter. Signal flow graphs, which are a parallel representation, are also briefly introduced.