A new Nyquist test for the stability of control systems

Abstract

The Nyquist plot, which maps the loop transfer function along a Nyquist contour, has been used for studying the stability of control systems. However, if a controller with an integral mode is used or if the process transfer function contains purely imaginary poles, a closed Nyquist plot can only be constructed by using some asymptotical properties of the system loop transfer function. This fact makes it difficult to apply the Nyquist plot to MIMO systems, where such asymptotic properties are not readily clear and readable. In such cases justification of stability based on the Nyquist plot of the original loop transfer function is not easy. In order to resolve this difficulty, this paper describes a new Nyquist test. This test is characterized by its use of a normalized Nyquist plot, which facilitates determining encirclements of the plot around the critical point.