# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020180
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## Energy management method for an unpowered landing

 School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

* Corresponding author: Yingjing Shi (shiyingjing@uestc.edu.cn)

Received  June 2020 Revised  September 2020 Early access December 2020

Fund Project: This work is supported in part by the National Natural Science Foundation of China under grant (No. 61973055), the Fundamental Research Funds for the Central Universities (No. ZYGX2019J062) and a grant from the applied basic research programs of Sichuan province (No. 2019YJ0206).

The unpowered landing of unmanned aerial vehicle (UAV) is a critical stage, which affects the safety of flight. To solve the problem of the unpowered landing of UAV, an energy management scheme is proposed. After the cruise is over, the aircraft shuts down the engine and begins to land. When the aircraft is in the high altitude, the dynamic pressure is too large, and it is difficult to open the speed brake. When the aircraft is in the low altitude, it is close to the runway. The method of S-turn may make the aircraft veer off the runway and may be unable to land. So two different schemes of high altitude and low altitude are designed to control energy. In the high altitude, when the energy is too high, it takes the S-turn scheme to consume excess energy. At the same time, the availability and reasonability of the S-turn scheme is demonstrated. In the low altitude, the open angle of speed brake is controlled to adjust the energy consumption. Finally, the simulation results are given to illustrate the availability of energy management.

Citation: Xiaoxiao Li, Yingjing Shi, Rui Li, Shida Cao. Energy management method for an unpowered landing. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020180
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##### References:
The full ground track of S-turn scheme
Flow chart of terminal energy management at various phase
The prediction of range in acquisition phase
The prediction of range in HAC-Turn phase
Track angle of aircraft
The judgment nominal line of aircraft in pre-approach phase
The force direction of the aircraft
The high energy change of the S-turning scheme
The range of the S-turning scheme at high energy
The low energy change of the S-turning scheme
The range of the S-turning scheme at low energy
The angle of speed brake in the nominal case
The angle of speed brake at high energy
The angle of speed brake at low energy
The resistance of closed speed brake and opened speed brake
 h(m) $\rho(kg/m^3)$ $\alpha (^\circ)$ $D_c$(N) $D_o$(N) 4500 0.7768 4.86 5541 7565 4000 0.8191 4.74 5643 7782 3500 0.8632 4.46 5769 8028 3000 0.9091 4.36 5913 8296 2500 0.9569 4.12 6071 8558 2000 1.0065 3.76 11760 14290 1500 1.0580 3.60 12290 14950 1000 1.1116 3.44 12840 15630
 h(m) $\rho(kg/m^3)$ $\alpha (^\circ)$ $D_c$(N) $D_o$(N) 4500 0.7768 4.86 5541 7565 4000 0.8191 4.74 5643 7782 3500 0.8632 4.46 5769 8028 3000 0.9091 4.36 5913 8296 2500 0.9569 4.12 6071 8558 2000 1.0065 3.76 11760 14290 1500 1.0580 3.60 12290 14950 1000 1.1116 3.44 12840 15630
The control effect of the speed brake
 Speed brake Glide angle (high/low) Touchdown velocity Closed $-9^{\circ}/-15^{\circ}/-19^{\circ}$ 293.4km/h Fully opened $-29^{\circ}/-15^{\circ}/-19^{\circ}$ 290.2km/h
 Speed brake Glide angle (high/low) Touchdown velocity Closed $-9^{\circ}/-15^{\circ}/-19^{\circ}$ 293.4km/h Fully opened $-29^{\circ}/-15^{\circ}/-19^{\circ}$ 290.2km/h
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