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In control systems, a way to evaluate the stability of a system is to determine the magnitude and phase of the open loop system transfer function in the frequency domain. But due to the nature of the phase expression, practice and theory are not aligned. Some problems arise when the phase is determined, caused by the properties of the arctan function. This paper analyses these phase problems for a third order lag system and a third order lag with time delay system. It also presents modifications to obtain the analytically correct phase values from the computed values.
Sourdille, Pauline and O'Dwyer, Aidan : Determination of the phase of a transfer function: theory versus practice. Proceedings of the 13th European Conference on Mathematics for Industry (ECMI 2004), Eindhoven, Netherlands, June.