连续下降进近（CDA）航迹的 Gauss 伪谱优化方法

摘要

Aiming at optimizing trajectory problems of linear continuous descent approach (CDA)of the aircrafts with a constant gliding angle,a Bolza optimal control problem (OCP)is converted into a nonlinear programming problem by the Gauss pseudospectral method under different flap states of aircrafts,resulting in an optimized time of CDA trajec-tories.A dynamic model of CDA is established,where state variables of flight position and control variables of trajectory angle are determined,and performance measure of minimizing landing time is proposed.B737-800 aircrafts are selected for a case study.GPOPS algorithm is used to optimize trajectory via the Gauss pseudospectral method,within the landing areas and flying areas and the position of top of descent (TOD)and the curve of speed control are determined.Compared with other algorithms for computing CDA trajectory,the Gauss pseudospectral method has several advantages.This stud-y analyzes the approaching state of 1 7 CDA trajectories and 1 traditional trajectory in landing areas.The results show that compared with traditional stepped approaching trajectory,the landing time of CDA trajectory computed by Gauss pseudospectral method decreases by 1 6.67%.Simulation results verified that the CDA trajectory optimized by Gauss pseudospectral method can reduce landing time and improve accuracy of track forecast and efficiency of flight control sys-tems.%针对优化恒定下滑角的直线连续下降进近(CDA)飞行航迹问题，采用高斯伪谱法将 Bolza型最优控制问题(OCP)转化成飞行器不同襟翼状态下的非线性规划问题，得出时间优化连续下降进近飞行航迹.对连续下降进近的飞行器建立动力学模型，确定飞行位置的状态变量及航迹角的控制变量，提出时间最小化性能指标.选取 B737-800机型，在终端区和飞行状态限制条件下利用 GPOPS工具仿真高斯伪谱法时间优化航迹，确定 TOD 位置和飞行速度控制曲线.并与其它 CDA 航迹算法进行比较研究.对比分析终端区17条 CDA 航迹及1条传统阶梯式进近航迹的进近状态，结果显示，采用高斯伪谱法获得的 CDA 航迹相比于传统进近航迹的下降时间缩短了16．67％，且优于其它算法获得的 CDA 航迹.验证使用高斯伪谱法优化 CDA 航迹可节省下降时间，提高航迹预测的精度和飞行控制系统的计算效率.