On the internal stability of non-linear dynamic inversion: application to flight control

Aircraft are highly non-linear systems, but flight control laws are traditionally designed from a set of linearised models. Due to the application of linear control laws on a non-linear system, the real performance ability of the aircraft is not fully utilised. In addition, in adverse situations like near stall, the aircraft develops significant non-linearities, and linear control laws do not perform well. This study therefore considers the design of a longitudinal flight controller for a fixed-wing aircraft using non-linear dynamic inversion technique or, in terms of control theory, partial exact feedback linearisation. A novel contribution of this study is the proposed combination of three different automatic flight controllers that provide complete 3-DOF longitudinal control. A detailed analysis of the internal dynamics for each controller is also presented. It has been shown that for each controller the internal dynamics are stable. This makes the controller suitable for various flight conditions. The aims of these flight controllers are threefold. First, to provide control of the flight path angle by tracking the pitch angle and the angle of attack. Second, to provide high attitude (pitch up or down) manoeuvrability. Finally, to provide automatic adverse attitude recovery of the aircraft in situations like stall, the switching strategy between the controllers are also discussed. A simulation carried out on a non-linear model of a multi-role fighter aircraft verified the proposed theoretical results confirming the suitability of the controllers.