Contributions to the application of Popov and circle criterion for stability analysis

Abstract

Many nonlinear control systems can be represented as a feedback connection of a linear dynamical system and nonlinear element. Popov and circle criterion use the frequency response of the linear system, which builds on classical control tools like Nyquist plot and Nyquist criterion. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The tables include frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically. When we allow the nonlinearity to become time varying, the Popov criterion is no longer applicabled. The circle criterion gives us a tool to analyse absolute stability for a time varying nonlinearity. Results the criterion applies to a specific system with a well-defined nonlinearity for which much more is known about than its sector bounds.