Effect of Control Saturation on the Tracking of Longitudinal States of an Aircraft

This paper addresses the effect of elevator saturation on asymptotically stable tracking of a desired flight path angle of an aircraft. The desired reference trajectory is computed using a non-linear kino-dynamic model of the longitudinal states of the aircraft incorporating control bounds. Next, based on a linearised model about the reference states, a state-feedback controller is designed to track the reference trajectory in the presence of deviations. Using results from the polytopic approach, which indicate that in the presence of control saturation, the magnitudes of the allowable deviations reduce as the eigenvalues of the open-loop system move from the left to the right of the complex plane. By estimating the volumes of these so-called regions of asymptotic stability, which is based on solving a set of Linear Matrix Inequalities, the results presented in this paper aid in the selection of appropriate trajectories that enable asymptotically stable tracking in the presence of deviations and control saturation. Simulation results are used to illustrate this concept.