A new approach to control design : variable gain plots
journal contributionposted on 01.01.1991 by Thomas R. Kurfess, Mark L. Nagurka, Carnegie Mellon University.Engineering Design Research Center.
Any type of content formally published in an academic journal, usually following a peer-review process.
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."