A new approach to control design : variable gain plots

Abstract: "This report proposes a new graphical representation and perspective on the Evans root locus, a well known controls design technique for stability and performance evaluation. The visualization is based on the adjustment of a proportional control gain in the same fashion that is employed in constructing the root locus. The result is a set of Variable Gain Plots (VGPs) that depict the polar coordinates, i.e., magnitude and angle, of each closed loop system eigenvalue in the complex plane as a function of the gain. The VGPs consist of two graphs: (i) magnitude of system eigenvalues vs. gain, and (ii) argument of system eigenvalues vs. gain.The VGPs impart significant insight for determining the values of gain that render a closed-loop system either stable or unstable. By exposing the correspondence of gain values to specific eigenvalues, the VGPs are useful tools for identifying closed-loop designs meeting performance specifications. An additional advantage of the VGPs is their ability to reveal by inspection information about closed-loop sensitivity to gain variations. Finally, the VGPs are applicable to both single-input, single-output (SISO) and multiple-input, multiple-output (MIMO) closed- loop feedback systems. For both cases, the VGPs present eigenvalue trajectories in an informative and unambiguous manner, and serve as a powerful new design paradigm."