连续下降进近(CDA)航迹的Gauss伪谱优化方法

Trajectory Optimization of Continuous Descent Approach(CDA)by a Gauss Pseudospectral Method

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。

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 trajectories. A dynamic model of CDA is established？ where state variables of flight position and control variables of trajectory angle arc determined 〉 and performance measure of minimizing landing time is proposed. B737-800 aircrafts arc selected for a ease 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 arc determined. Compared with other algorithms for computing CDA trajectory, the Gauss pseudospectral method has several advantages. This stud-y analyzes the approaching state of 17 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 16.67%. Simulation results verified that the CD八 trajectory optimized by Gauss pseudospectral method can reduce landing time and improve accuracy of track forecast and efficiency of flight control systems.