Frequency Domain Analysis of Sampled-data Control Systems
Julio H. Braslavsky
185 pages, with index, 115 references
ISBN 7259 0905 6
Department of Electrical and Computer Engineering
The University of Newcastle, 1995.
PDF 1.5M
Postscript 681K (zip-compressed)
Abstract:
This thesis is aimed at analysis of sampled-data feedback systems. Our
approach is in the frequency-domain, and stresses the study of
sensitivity and complementary sensitivity operators. Frequency-domain
methods have proven very successful in the analysis and design of
linear time-invariant control systems, for which the importance and
utility of sensitivity operators is well-recognized. The extension of
these methods to sampled-data systems, however, is not
straightforward, since they are inherently time-varying due to the
intrinsic sample and hold operations.
In this thesis we present a systematic frequency-domain framework to
describe sampled-data systems considering full-time information. Using
this framework, we develop a theory of design limitations for
sampled-data systems. This theory allows us to quantify the essential
constraints in design imposed by inherent open-loop characteristics of
the analog plant. Our results show that: (i) sampled-data systems
inherit the difficulty imposed upon analog feedback design by the
plant's non-minimum phase zeros, unstable poles, and time-delays,
independently of the type of hold used; (ii) sampled-data systems are
subject to additional design limitations imposed by potential
non-minimum phase zeros of the hold device; and (iii) sampled-data
systems, unlike analog systems, are subject to limits upon the ability
of high compensator gain to achieve disturbance rejection. As an
application, we quantitatively analyze the sensitivity and robustness
characteristics of digital control schemes that rely on the use of
generalized sampled-data hold functions, whose frequency-response
properties we describe in detail.
In addition, we derive closed-form expressions to compute the
L2-induced norms of the sampled-data sensitivity and complementary
sensitivity operators. These expressions are important both in
analysis and design, particularly when uncertainty in the model of the
plant is considered. Our methods provide some interesting
interpretations in terms of signal spaces, and admit straightforward
implementation in a numerically reliable fashion.
Keywords:
Sampled-data systems, Frequency response, Performance limitations,
Sensitivity analysis, Generalized sampled-data holds.
Production notes: This thesis was typeset by the author on a
DEC station 3100 using
LaTeX and
Emacs. Typeset chapters were translated into Postscript files
using DVIPS. The typeface used for the main text is Palatino and the
Mathematics font is Euler, by Hermann Zapf. The layout, styles used,
etc, of this thesis are available in its LaTeX master file (9K).
Julio Braslavsky
Last modified: Fri Aug 30 11:05:30 EST 2002