Application of continuation and bifurcation methods to the design of control systems

Abstract

The use of nonlinear dynamics theory for the analysis of aircraft motion and the assessment of aircraft control systems is well known. In this paper the continuation and bifurcation methods are applied to aircraft nonlinear control design problems. The search for the recovery control from spin regimes is based on the minimization of an energy-like scalar function constrained by the aircraft's equilibria conditions. The design of a global stability augmentation system in the case of severe wing-rock motion is performed using bifurcation diagrams for equilibrium and periodical modes. The nonlinear control law, which totally suppresses wing-rock motion, is derived, taking into account both local stability characteristics of aircraft equilibrium states and domains of attraction, along with the requirement that all other attractors be eliminated.