Introduction

Traditionally, airplanes employ three controls: ailerons, elevator, and rudder, for control about their three axes (the roll, pitch, and yaw axes, respectively.) Modern, high-performace fighter airplanes often come with many more than the traditional three controls; however, the requirement for control about three axes remains the same. The control systems of such aircraft often include a control allocation system, also called a control mixer, operating inside the feedback loop.

The damage that these same modern, high-performance fighters are apt sustain as part of their mission can cause signifant changes to their dynamics. This can be a serious problem, especially for airplanes that are inherently unstable, as modern fighters often are. Consequently, these aircraft employ adaptive flight control systems

The major problem with adaptive flight control is what happens when the airplane is not manuevering. Airplanes spend much time cruising, with all states and controls more or less constant. Such long periods have adverse effects on the parameter identification.

This report will investigate a simple nonlinear self-tuning control system. The airplane dynamics are modeled by a global nonlinear polynomial model of an F-16 [1]. I shall investigate longitudinal motion only (that is, motion in the plane of symmetry about the pitch axis). The controlled variable is the angular velocity about the pitch axis, $q$. We use only one control, the elevator deflection, $\delta_e$ (although it seems, and probably is, silly to use control allocation for just one control). The parameter identification scheme is sequential least squares with a forgetting factor.