建立了直升机单发失效后增广的纵向三维刚体飞行动力学模型,通过选择合适的目标函数、路径约束和边界约束,将自转着陆问题表示成非线性最优控制问题,使用非线性规划方法求解得到自转着陆的最优轨迹和操纵。以UH-60直升机为例,首先计算了自转着陆距离最短的最优解,并与二维点质量模型进行对比。结果表明三维刚体模型在旋翼转速、旋翼拉力系数和下降率的时间历程与二维点质量模型一致的情况下,能提供直升机自转过程中的姿态变化,且纵向操纵更符合实际。然后考虑驾驶员反应滞后的实际情况,研究了自转着陆速度最小的最优轨迹和操纵,发现可以获得更小的下降率和更柔和的操纵,而着陆所需的末端时间和自转着陆距离会明显增加。
This paper studies the trajectory optimization of helicopter autorotation landing in the event of one engine failure by applying the nonlinear optimal control theory. An augmented longitudinal three-dimensional rigid-body flight dynamic model of a helicopter is first presented. By selecting the appropriate objective function, path constraints and boundary constraints, the trajectory optimization problem of helicopter autorotation landing is then formulated into a nonlinear optimal control problem, which is further transcribed into a discrete nonlinear programming problem. Finally, the optimal trajectories and controls are obtained by solving the nonlinear programming problem. Using helicopter UH-60 as the sample helicopter, the optimal solutions are calculated to minimize autorotation landing distance, and these solutions are compared with those obtained using a two-dimensional point-mass model. It is found that the time histories of rotor speed, thrust coefficient and sink-rate using the two different models show great correlation, and that the optimal solutions obtained using the three-dimensional rigid-body model furthermore include pitch rate, pitch attitude, and more realistic longitudinal cyclic pitch control. Then the trajectory optimization problem of helicopter autorotation landing is solved to minimize the velocity at touchdown with 1 second constant-control pilot delay. The resulting optimal trajectories and controls show safer sink-rate and slower pitch control rates while the final time and autorotation landing distance also increase considerably.
[1] Jhemi A A. Optimal flight a helicopter in engine failure. Minneapolis, Minnesota: Department of Aerospace Engineering and Mechanics, University of Minnesota, 1999.
[2] Johnson W. Helicopter optimal descent and landing after power loss. NASA TM-73244, 1977.
[3] Lee A Y, Bryson A E, Hindson W S. Optimal landing of a helicopter in autorotation[J]. Journal of Guidance, Control, and Dynamics, 1988, 11(1): 7-12.
[4] Chen R T N, Zhao Y. Optimal trajectories for the helicopter in one-engine-inoperative terminal-area operations. NASA TM-110400, 1996.
[5] Okuno Y, Keiji K, Akira A. Analytical prediction of height-velocity diagram of a helicopter using optimal theory[J]. Journal of Guidance, Control, and Dynamics, 1991, 14(2): 453-459.
[6] 张余华. 直升机自转着陆过程的最优控制. 南京: 南京航空航天大学航空宇航学院, 2004. Zhang Yuhua. Optimal control for helicopter autorotational landing. Nanjing: College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 2004. (in Chinese)
[7] 曾洁. 发动机失效后直升机轨迹优化研究. 南京: 南京航空航天大学航空宇航学院, 2007. Zeng Jie. Investigation on helicopter flight trajectory optimization after engine failure. Nanjing: College of Aero-space Engineering, Nanjing University of Aeronautics and Astronautics, 2007. (in Chinese)
[8] Hilbert K B. A mathematical model of the UH-60 helicopter. NASA TM-85890, 1984.
[9] 席华彬. 直升机单台发动机停车后的飞行轨迹优化. 南京: 南京航空航天大学航空宇航学院, 2006. Xi Huabin. Research on optimization of helicopter flight following one-engine failure. Nanjing: College of Aero-space Engineering, Nanjing University of Aeronautics and Astronautics, 2006. (in Chinese)
[10] Johnson W. Helicopter theory[M]. Princeton: Princeton University Press, 1980: 146-198.
[11] 高正, 陈仁良. 直升机飞行动力学[M]. 北京: 科学出版社, 2003: 54-65. Gao Zheng, Chen Renliang. Helicopter flight dynamics[M]. Beijing: Science Press, 2003: 54-65. (in Chinese)
[12] Bottasso C L, Croce A, Leonello D, et al. Optimization of critical trajectories for rotorcraft vehicles[J]. Journal of the American Helicopter Society, 2005, 50(2): 165-177.
[13] Bryson A E. Aerospace trajectory optimization using direct transcription and collocation. (2009-05-07) . http://www.cdeagle.com/freeware/.
[14] John T B. Practical methods for optimal control using nonlinear programming[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2001: 37-132.
[15] John T B. Survey of numerical methods for trajectory optimization[J]. Journal of Guidance, Control, and Dyna-mics, 1998, 2(2): 193-207.
[16] Lee A Y.Optimal autorotational descent of a helicopter with control and state inequality constraints [J]. Journal of Guidance, Control, and Dynamics, 1990, 13(5): 922-924.
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