Differential Dynamic Programming to Critical-Engine-Inoperative Takeoff Certification Analysis

Abstract

Critical-engine-inoperative (CEI) takeoff is a required flight test in transport aircraft type certification. Due to the limited excess power following engine failure, this flight test is potentially dangerous and highly sensitive to the flight controls. To enhance the flight safety in CEI takeoff, an optimal longitudinal control sequence is necessary for the flight test. On the other hand, to reduce the cost associated with type certification process, it is desired to incorporate certification analysis in early design phases. Since the certification regulations pose requirements on aircraft dynamic responses, the point-mass based method used in most of the takeoff analyses for aircraft early design is not suitable. To incorporate flight dynamics in takeoff analysis, a robust longitudinal control law is needed for takeoff performance prediction. This paper proposes to use Differential Dynamic Programming (DDP) for the optimization of elevator control for CEI takeoff certification analysis. To evaluate the method, two test cases are performed on the CEI takeoff of a small single-aisle aircraft model with different initial conditions. The results of two cases suggests that the DDP algorithm is able to optimize the trajectory in terms of minimizing takeoff distance, maximizing the rate of climb, and improving the compliance with respect to takeoff certification constraints. The optimized trajectory is sensitive to the initial control sequence given to the algorithm and the cost function settings.