Robust Stability Analysis of an Uncertain Aircraft Model with Scalar Parametric Uncertainty

TL;DR

This paper compares various robustness criteria for analyzing the stability of an uncertain aircraft model, demonstrating that Popov analysis provides less conservative bounds than traditional small gain methods.

Contribution

It introduces a graphical approach to compare robustness tests and highlights the effectiveness of Popov analysis for constant parametric uncertainties.

Findings

Popov analysis yields less conservative stability bounds.

Small gain analysis is the most conservative.

Graphical approach simplifies robustness testing.

Abstract

A robust controller is specified, and the stability bounds of the uncertain closed-loop system are determined using the small gain, circle, positive real, and Popov criteria. A graphical approach is employed in order to demonstrate the ease with which the above robustness tests can be carried out on a problem of practical interest. A significant improvement in stability bounds is observed as the analysis moves from the small gain test to the circle, positive real, and Popov tests. In particular, small gain analysis results in the most conservative robust stability bounds, while Popov analysis yields significantly less conservative bounds. This is because traditional small gain type tests allow the uncertainty to be arbitrarily time-varying, whereas Popov analysis restricts the uncertainty to be constant, real parametric uncertainty. Therefore, the results reported here indicate the conservatism associated with small gain analysis, and the effectiveness of Popov analysis, in gauging robust stability in the presence of constant, real parametric uncertainty.