Literal singular-value-based flight control system design techniques

Recent control system research has resulted in new methods for assessing stability and performance robustness with respect to plant and controller uncertainty. The emphasis has been on using frequency domain matrix singular values for multi-input/multi-output systems. Problems originating from aircraft flight control systems have been an important motivation for these developments, and applications are currently being carried out at government research centers and in industry. These new robustness methods are, however, only slowly becoming part of the working flight control designer's practical tools. Before becoming routine, means must be provided for better physical insight. This paper presents a distinctly different interpretation based on literal (symbolic) formulations of singular values. This approach is an outgrowth of and is related to classical multivariable control systems methods based on coupling numerators. A lateral-directional flight control system design for an advanced fighter is used as an example. Robustness of stability with respect to input uncertainties is first assessed using standard numerical techniques. Literal approximations are then given for openand closed-loop singular values. The literal approximations are consistent with the numerical results. More importantly, they provide a means for decomposing and diagnosing robustness problems by providing explicit connections to critical aircraft and controller parameters. Both unstructured and structured uncertainties are treated, using respectively literal approximations of regular and structured singular values.