NDLI: Relative stability of closed-loop systems

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Relative stability of closed-loop systems

Content Provider	IEEE Xplore Digital Library
Author	Kirby, M. J. Beaumariage, D. C.
Copyright Year	2012
Abstract	Frequency response plots have long been used to predict transient as well as steady-state responses of closed loop linear systems, avoiding the exact and laborious solution of differential equations. This paper considers the relations between specific properties of frequency response plots and the corresponding properties of the early portions of the time responses. It is shown that the common output/input transfer function plots are in reality plots of the Laplace transform of the impulse (transient) response. The Laplace transform of a time function is a real integral in which an exponential kernal is multiplied by the time function, and the product summed from time zero to infinity. This process amounts to a mechanism by which the kernal scans the time function as the frequency is varied. This paper gives a method for interpreting Laplace transform plots and extending their use, and presents a method for estimating the size, frequency, damping, and phase of oscillations in the corresponding time response. ¿Standard¿ plots are included to aid in estimating particular properties. The method is relatively quick in application, and makes use of functions and techniques already familiar in Laplace transform analysis. In addition, it is not limited to the responses of systems having rational transforms, or to responses to impulses or step inputs, but can be used to estimate the response to almost any desired input, and is applicable to systems having time-varying elements.
Starting Page	22
Ending Page	43
Page Count	22
File Size	1369759
File Format	PDF
ISSN	00972185
Volume Number	72
Issue Number	1
Language	English
Publisher	American Institute of Electrical Engineers
Publisher Date	1953-03-01
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Transforms Laplace equations Transfer functions Transient analysis Servomotors Stability criteria
Content Type	Text
Resource Type	Article

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