A generalized procedure for determining transient response of third order systems.
Harrison, Joe P.
Strum, Robert D.
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For any system whose input-output relationship may be described by a ratio of polynomials in S (the complex number ѵ±jw), one of the measures of the system performance is its transient response to a step input. For systems of order greater than second the determination of the parameters of this transient response has always been a difficult process. In this thesis a new procedure is developed which allows the rapid and accurate determination of the transient parameters of any system up to and including third order with one zero. The procedure consists of developing the response equation in terms of angles at the singularities rather than the magnitudes. The resulting equation is utilized to develop expressions for times of extremals, magnitudes of extremals, and a form of rise time. A simple but accurate graphical method is demonstrated for solving the resulting transcendental equations. It is shown that the expression for times of extremals is a function of only two variables and may therefore be displayed on a two-dimensional plot. The times determined from this plot are utilized in computing the magnitudes of extremals. Various curves are presented to provide a means for general analysis.
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