Facilitating aircraft optimal control based on numerical nonlinear dynamic inversion

摘要

This paper investigates a novel method for high fidelity aircraft trajectory optimization based on numeric nonlinear dynamic inversion (NDI). The problem formulation exploits the fact that NDI yields a nonlinear feedback strategy such that the resulting closed loop dynamics show a linear input-output relation. By means of linear reference models for the different dynamic levels of the aircraft dynamics we are then free to choose the aircraft's dynamic behavior within the physical limits. Due to the reduced nonlinearity when choosing linear reference models, the solution of the direct optimal control problem is facilitated compared to the fully nonlinear case. The main contribution of this paper is a constraint formulation suitable for optimal control problem problems, which inverts the dynamic equations numerically. This fact makes the approach not specific to certain model equations but applicable for a wide class of aircraft dynamics. The approach is illustrated by the trajectory optimization for an air race track utilizing a highly agile aircraft model. For this example we use the fully nonlinear rigid body aircraft model including second order actuator dynamics for the primary control surfaces. The approach show good performance and despite the altered model dynamics the numeric NDI assisted controller yields close to optimal lap times compared to the direct solution of the optimal control problem.