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

This paper deals with the notion of disturbance model uncertainty. The dist urbance 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 expr ession for the steady-state output variance as a function of the uncertain bandwidth and gain is derived, and several properties of this variance func tion are analyzed. Two notions, those of disturbance bandwidth margin and d isturbance gain margin, are also introduced. These tools are then applied t o the analysis of a simple altitude-hold autopilot system in the presence o f turbulence where the turbulence scale is treated as an uncertain paramete r. It is shown that the autopilot, which is satisfactory for nominal turbul ence scale, may be inadequate when the uncertainty is taken into account. M oreover, it is proven that, in order to obtain a design that provides robus t 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.