Aircraft Multi-Constrained Generalized Dynamic Inversion Control

The new and evolving paradigm of generalized dynamic inversion (GDI) is applied to aircraft maneuvering control design, through the development of a new multiple constraint formulation. The flexibility of GDI in utilizing nullspace of the controls coefficient matrix is exploited to eliminate the problems of excessive control effort and limited performance that are associated with classical dynamic inversion. Scalar deviation functions of the aircraft state error variables are differentiated along the aircraft mathematical model solution trajectories, and linear time varying stable dynamics in these deviation functions are manipulated to obtain linear algebraic constraint equations in the control vector. The constraint equations are inverted using the Greville formula, resulting in the control law. The particular part of the control law drives the states to their desired values, and the auxiliary part acts to stabilize the vehicles inner dynamics by means of the null-control vector. The null-control vector is constructed via a novel class of positive semidefinite Lyapunov functions and nullprojected Lyapunov equations. The closed loop control system is assessed by performing a fully coordinated simultaneous heading-velocity change maneuver. The new type of GDI control laws shows to require low control effort, in addition to providing excellent transient response and reasonable steady-state tracking accuracy.