Computation of controllability regions for unstable aircraft dynamics.

An active control approach to air vehicle design can significantly expand the flight envelope and improve vehicle performance characteristics. In some cases it can be attained by implementing the aerodynamically unstable configuration or expanding operation at flight regimes with dynamic instability, which are then purposely stabilized by the flight control system. An important issue in stabilization of unstable dynamics is connected with the size of the controllability region, which is the set of all states of the aircraft dynamics that can be stabilized by some realizable control action. This region is bounded because of nonlinear actuator constraints, and its size can be considered as a measure for allowable level of external disturbances. In this paper an algorithm based on convex optimization technique is proposed for computation of the controllability region of an unstable linear system under amplitude and rate control constraints. Examples of the controllability region analysis for an aeroservoelastic airfoil system and unstable aircraft dynamics are presented to illustrate the capabilities of the proposed algorithm.