New design paradigms for MIMO control system synthesis

Abstract: "This report examines the use of Gain Plots (GPs), a new graphical representation and perspective on the Evans root locus, for analysis and design of multivariable feedback control systems. The development is based on the adjustment of a scalar, forward loop, proportional control gain cascaded with a square multi-input, multi-output (MIMO) plant employed in an output feedback configuration. By tracking the closed-loop eigenvalues as an explicit function of gain, it is possible to visualize the MIMO root loci in a set of plots, the GPs, depicting the polar coordinates of each eigenvalue in the complex plane. The GPs consist of two graphs: (i) magnitude of system eigenvalues vs. gain, and (ii) argument (angle) of system eigenvalues vs. gain.The concept of GPs is developed in detail in a companion report focusing on single-input, single-output systems (Kurfess and Nagurka, 1991a). By identifying closed-loop eigenvalue trajectories, the GPs impart significant insight for determining the values of scalar gain that render a MIMO closed-loop system either stable or unstable. Furthermore, by exposing the correspondence of gain values to specific eigenvalueangles and magnitudes, the GPs are useful for evaluating the migration of closed- loop eigenvalues toward finite and infinite transmission zeros. The GPs reveal MIMO eigenvalue information unambiguously in a new and precise manner, that is not available in a standard MIMO root locus plot.Thus, GPs significantly enhance the control engineer's multivariable systems toolbox."