Two-time-scale longitudinal control of airplanes using singular perturbation

Abstract

The singular perturbation approach to the analysis and design of two-time-scale systems is applied to the longitudinal motion of airplanes. Linearized models of longitudinal dynamics have a well known, two-time-scale structure, characterized by the presence of a slow (phugoid) mode and a fast (short-period) mode. Such linearized models are represented in the singularly perturbed form via scaling of state and output variables. The singular perturbation approach is then used to obtain lower-order slow and fast models. The accuracy of these models in approximating eigenvalues is demonstrated using typical numerical data for stable as well as unstable airplanes. The slow and fast models are employed in a sequential design procedure to design a two-time-scale compensator for an unstable transport airplane. In this procedure, a fast compensator is designed first using the fast model; then a slow compensator is designed using a modified slow model. The results of the slow and fast designs are shown to be reasonably recovered when the two-time-scale compensator is applied to the full model.