Robustness with respect to Disturbance Models Uncertainties

Professor Pierre T. Kabamba

Department of Aerospace Engineering

University of Michigan

In contrast to the case of robustness with respect to plant model uncertainty, the control system community has paid relatively little attention to the issue of robustness with respect to disturbance model uncertainty. However, disturbance model uncertainty is of significance in many practical problems, including, for example, aircraft control (where the disturbance is turbulence), ship control (where the disturbances are wind and waves), and active suspension control problems (where the disturbance is road roughness). Motivated, in particular, by turbulence model uncertainty, this talk considers the analysis and design of linear time-invariant controllers that are robust with respect to uncertainty in the disturbance intensity and bandwidth, where disturbance attenuation is measured by the output variance. Five aspects of the robust disturbance attenuation problem are considered. First, an expression for the output variance in terms of the uncertain disturbance parameters is derived. This expression is written in terms of an operator called the V-transform. Second, the notions of disturbance gain margin and disturbance bandwidth margin are introduced as quantitative measures of robustness with respect to uncertainty in the disturbance gain and disturbance bandwidth, respectively. Third, lower bounds on the achievable output variance are found under constraints of practical importance, e.g., constraints on bandwidth and stability robustness. The lower bounds are used to show that, in almost every practical situation, there is a limitation on both the achievable nominal performance and achievable robustness margins. Fourth, tradeoffs between nominal performance and robust performance are investigated. The main result is that good nominal and good robust performance are neither incompatible nor equivalent. Fifth, a design procedure to achieve a prescribed level of robustness is proposed; the principal idea is to reduce the robust performance design problem to one or more appropriately formulated nominal performance design problem. Throughout the talk, an aircraft autopilot system is used to illustrate the theoretical results.

This is joint work with Daniel E. Davison and Semyon M. Meerkov

Friday, March 9, 2001

3:30 - 5:00 p.m.

1500 EECS