IMPROVING CONTROL DESIGN FOR NONLINEAR PARAMETRIC UNCERTAINTY

Models developed from first principles often contain coefficients that are nonlinear functions of design parameters, which themselves are ge nerally only known within some tolerance. Analysis and design of contr ollers for such models (plants) are often expedited through the use of an overbounding interval plant representation of the original plant. However, such representations are known to introduce conservativeness. As an alternative, we provide an algorithm for synthesizing a frequen cy-dependent convex hull approximation of an uncertain plant with nonl inear coefficients, which we refer to as a minimized plant. We develop several theorems that demonstrate reduced conservativeness through th e use of minimized plants. In particular, the use of these plants to d etermine robust stability margins results in an improvement over the u se of overbounding interval plants. We also illustrate in an example h ow a constant coefficient compensator and minimized plant meet a given set of design specifications, but the same compensator fails to meet specifications when analysed using an interval plant. As reduced conse rvativeness simplifies the design process, the convex hull synthesis a lgorithm and associated theorems provided in this paper facilitate rob ust controller analysis and design.