Author: Richard F. Whitbeck

Publisher:

Published: 1978

Total Pages: 238

ISBN-13:

Revisitation and extension of classical sampled data approaches for the analysis of discretely controlled continuous systems is the focus of this report. A review of basic linear analysis topics required to support later developments is given. These topics include Laplace, z- and advanced z-transform facts; partial fraction expansion; data holds and the switch decomposition technique. Extension of switch decomposition for the vector signal case is given. The w'-domain is defined by a bilinear transformation of the z-domain. Properties of the w'-domain are developed. A new direct transform domain approach for analyzing two-rate sampled systems is developed This approach also applies for multi-rate sampled systems in restricted circumstances. Utility of this approach resides in its operator notation and conventions for manipulation in connection with vector block diagram algebra. This, in turn, expedites development of pulse transfer functions and of response recursion relations for multivariable, closed-loop systems. This is accomplished without resorting to the more complicated switch decomposition method. Multi-rate sampling analysis procedures are used to sharpen the concept of frequency response for discretely excited, continuous systems. Frequency response, in this case, pertains to steady-state responses at the input frequency and its positive aliases. All methods of analysis presented in this report are closed-form and exact in that no approximation is required in the mathematical development of any result.