TheV-transform: A tool for analysis of control systems robustness with respect to disturbance model uncertainty

摘要

This work is motivated by the need forr tools for the analysis of disturbance model uncertainty in feedback control systems. Such tools are developed in this paper for the case where the disturbance is modeled as the output of a first-order filter which is driven by white noise and whose bandwidth,ωd, and gain,K, are uncertain. An analytical expression for the steady-state output variance as a function ofωdis derived: This function is referred to as aV-transform, and is denoted byV(G)(ωd), whereG(s)is the closed-loop transfer function from disturbance to output. Properties ofV-transforms are investigated and the notions ofdisturbance gain marginanddisturbance bandwidth margin, both measures of robustness with respect to disturbance model uncertainty, are introduced. Using these new tools, it is shown that there is a fundamental robustness performance limitation if the plant has nonminimum-phase zeros, but no such limitation in the minimum-phase case.