Using Bifurcation Methods to Aid Nonlinear Dynamic Inversion Control Law Design

Abstract

The use of bifurcation analysis as an aid to nonlinear control law design and analysis is demonstrated by application to a hypothetical, high-angle-of-attack combat aircraft. Bifurcation analysis determines the equilibrium flight conditions of the unaugmented aircraft as a function of the elevator with all lateral controls set at zero. These results are used to identify instabilities that cause aircraft departure into spin regions. The removal of these departures, and hence the onset of spins, is achieved using a nonlinear dynamic inversion-based control law until the lateral control surfaces saturate, thus extending the stable, decoupled flight envelope. The work illustrates how bifurcation analysis may be used to formulate control law specifications for an unaugmented aircraft and to validate the control law by analyzing the resulting augmented aircraft model. The results also indicate the global stabilization properties of nonlinear dynamic inversion. b