"Transient response plays an important role in servomechanism, electronic and electrical circuits. A time response of a linear system is the intuitive and immediately comprehensible description of the system performance. The utility of the system performance in television and high speed computer circuits can be determined by its transient characteristics. By locating certain points on the transient response curve the designer is enabled to predict the shape of the response with some precision. The choice of the overall transfer function (or location of the system singularities on the s-plane plot) is decided by speed, accuracy and stability of the response required by the specifications. When the test signals, such as impulse, step or ramp, are applied to the input of the system, the characteristics of the system are obtained. The Laplace transformation technique is a desirable approach for the determination of the transient response.
The complex poles or repeated poles in the overall transfer function often have a predominant effect on the transient response of the system. Simple poles and zeros which are far from the imaginary axis have negligible effect. Among the important characteristics of transient response influenced by the position of poles and zeros are the initial value and the time and amplitude of the maximum value. For instance, quick acting relays will discriminate between transient impulses solely according to the height of the first current crest; their satisfactory operation therefore depends on a setting that is determined from the maximum current wave.
In this thesis a quick prediction method based on the ratio of residues is developed for determining the initial and the maximum value of the transient responses associated with either repeated or complex poles. The residue ratio can be evaluated promptly from the transfer function by root locus methods. The residue ratio is used with a normalized standard plot to indicate the initial value and the characteristic response of the transfer function to a unit impulse input. The standard plot for the complex poles or the repeated poles can be defined as a transient response which has a maximum value at the time equal to one second"--Introduction, pages 1-2.
Chenoweth, Robert D.
Nelson, John August
Richards, Earl F., 1923-
Faucett, T. R.
Electrical and Computer Engineering
M.S. in Electrical Engineering
Missouri School of Mines and Metallurgy
vi, 52 pages
© 1962 Ramesh S. Patel, All rights reserved.
Thesis - Open Access
Transients (Electricity) -- Mathematical models
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Patel, Rameshchandra Shankerbhai, "Predicted transient response of complex poles by means of a residue ratio" (1962). Masters Theses. 2902.