On the Specification of the Damping Ratio and the Characteristic Frequency for the Longitudinal Control of Airplanes

The Singular Perturbation Approach

Abstract

The singular perturbation approach is applied to the longitudinal motion of airplanes, whose linearlized model has well known two-time scale structure in the presence of a slow (phugoid) mode and a fast (short-period) mode. Such a linearlized model is transformed into the singularly perturbed form via scaling of the state. First the flight control systems are separately designed for each mode via state feedback. Then the slow and fast designs are composed, and are applied to the full model. The composite flight control systems are shown to guarantee the damping ratio and the characteristic frequency specified by JIS W 0402.