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A Study on Integral Equalities Related to a Laplace Transformable Function and its Applications

Byung-Moon Kwon/Hee-Seob Ryu/Oh-Kyu Kwon
International Journal of Control, Automation, and Systems, vol. 1, no. 1, pp.76-82, 2003

Abstract : This paper establishes some integral equalities formulated by zeros located in the convergence region of a Laplace transformable function. Using the definition of the Laplace transform, it shows that Laplace transformable functions have to satisfy the integral equalities in the time-domain, which can be applied to the understanding of the fundamental limitations on the control system represented by the transfer function. In the unity-feedback control scheme, another integral equality is derived on the output response of the system with open-loop poles located in the convergence region of the output function. From these integral equalities, two sufficient conditions related to undershoot and overshoot phenomena in the step response, respectively, are investigated.

Keyword : Laplace transform, fundamental limitation, unity-feedback control, undershoot, overshoot.

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