P-Map: An Intuitive Plot to Visualize, Understand, and Compare Variable-Gain PI Controllers

This paper introduces P-map, an intuitive plot to visualize, understand and compare variable-gain PI controllers. The idea is to represent the difference between a target controller and a baseline controller (or a second controller for comparison) by an equivalent proportional controller. By visualizing the value of the proportional gain and examining how it changes with inputs, it is possible to qualitatively understand the characteristics of a complex variable-gain PI controller. Examples demonstrate that P-map gives more useful information than control surface for variable-gain PI controllers. So, it can be used to supplement or even replace the control surface.