Open and closed logarithmic Nyquist plots

The Nyquist plot is a fundamental tool in the investigation of the stability of control systems. Usually Nyquist polar diagrams are plotted in a linear scale and often, in particular when poles at the origin are present, the diagrams need different levels of magnification in order to inspect the behavior of the frequency response in the areas very close to or very far from the origin of the complex plane. In this paper a new logarithmic Nyquist plot is proposed where the amplitude is in a logarithmic scale and the diagram is entirely contained and shown in a circle of finite radius. This method does not need to zoom in or zoom out the plot. All the considerations made by Nyquist stability criterion can be done with this plot which maintains all the properties of polar plots such as gain and phase margins, intersection points with the real axis, encirclements of the critical point. The design of first order lead and lag compensators can be done on this diagram in a simple way. The proposed new Nyquist plot is implemented in a Matlab function available to users.