New design paradigms for SISO control system synthesis

Abstract: "This paper proposes a new graphical representation and perspective on the Evans root locus, a well known controls 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 Gain Plots (GPs) depicting the root loci in polar coordinates, i.e., magnitude and angle, of each closed loop system eigenvalue in the complex plane as a function of the gain. The GPs 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 GPs are a useful pole-placement tool for identifying closed-loop designs meeting performance specifications. An additional advantage of the GPs is their ability to reveal by inspection information about the gain sensitivity of closed-loop eigenvalues. This paper develops the concept of GPs and applies them to single-input, single-output (SISO) systems. A companion paper (Nagurka and Kurfess, 1991a) extends the concepts to multivariable closed-loop feedback systems. For both cases, the GPs present eigenvalue trajectories in an informative and unambiguous manner."