Mathematical Problems in Engineering
Volume 6 (2000), Issue 2-3, Pages 267-304

Robustness with respect to disturbance model uncertainty: Theory and application to autopilot performance analysis

Daniel E. Davison,1,2 Pierre T. Kabamba,1 and Semyon M. Meerkov1

1Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Avenue, Ann Arbor 48109-2122, MI, USA
2Cambridge University Engineering Department, Trumpington Street, Cambridge CB2 1PZ, UK

Received 10 September 1999

Copyright © 2000 Daniel E. Davison et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the notion of disturbance model uncertainty. The disturbance is modeled as the output of a first-order filter which is driven by white noise and whose bandwidth and gain are uncertain. An analytical expression for the steady-state output variance as a function of the uncertain bandwidth and gain is derived, and several properties of this variance function are analyzed. Two notions, those of disturbance bandwidth margin and disturbance gain margin are also introduced. These tools are then applied to the analysis of a simple altitude-hold autopilot system in the presence of turbulence where the turbulence scale is treated as an uncertain parameter. It is shown that the autopilot, which is satisfactory for nominal turbulence scale, may be inadequate when the uncertainty is taken into account. Moreover, it is proven that, in order to obtain a design that provides robust performance in the face of turbulence scale uncertainty, it is necessary to substantially increase the controller bandwidth, even if one is willing to sacrifice the autopilot's holding ability and stability robustness.