Investigation of Popov’s Lines’ Limiting Position to Ensure the Process Control Systems’ Absolute Stability

This paper presents a study of the nonlinear systems stability. One of the most well-known stability criteria is the Popov criterion, which can be used to investigate the absolute stability. The problem the nonlinear control systems absolute stability studying arises due to the fact that in some cases the nonlinear characteristic is unstable and can only be characterized by a certain area. The limiting position of Popov’s line, which ensures the absolute stability of nonlinear systems, had been studied. With a given linear part of the system, the maximum angle of the sector was determined, which should belong to the static characteristics of the systems nonlinear elements with an absolutely stable equilibrium point.