Bode diagrams for frequency domain analysis and design

Abstract

The classical methods known as frequency domain techniques have their origin with electrical engineers, who rely extensively on representations of signals as sums of sinusoids in their modelling and analysis. It has seemed natural for them to carry such ideas with them into control systems analysis and synthesis, often with considerable success. Less successful has been the direct use of the methods for sampled data control systems (although indirect use characterized by conversion of continuous system designs is possible). This has been for several reasons: the approximations that allow sketching do not always apply, the compensators of most common use are not so relevant for digital control systems, and well established relationships between step responses, pole locations, and frequency responses seem to hold only roughly for sampled data systems. Nevertheless having at least some knowledge of frequency domain methods is fundamental, and for that reason we review them here.