Optimization of Geostationary Orbit Transfers via Combined Chemical–Electric Propulsion
Abstract
:1. Introduction
2. Materials and Methods
2.1. Dynamic Model
2.2. Optimal Control Theory
2.3. Steps of Solving Hybrid Transfer Problem
- Apply the ICEA algorithm to search the approximate solutions of the initial costate vector , the timing and magnitude of impulsive burn and numerical Lagrange multipliers to the high-thrust short-duration transfer problem .
- Take the approximate solutions of step 1 as the initial guess to provide the accurate solution of the high-thrust short-duration transfer problem . Go back to step 1 if it does not converge.
- Set and begin the thrust continuation process. Reduce the thrust by , i.e., . Employ the solution of the previous problem as an initial guess to solve the new problem . If it does not converge, reduce and repeat this step. Let if it converges.
- When , set and begin the transfer time continuation process. Increase the transfer time by , i.e., . Employ the solution of the previous problem as an initial guess to solve the new problem . If it does not converge, reduce and repeat this step. Let if it converges.
- When , output the desired solutions of the hybrid transfer problem .
3. Results
3.1. Solution of Hybrid Minimum-Fuel Hybrid Transfer
3.2. Performance of Hybrid Transfer with Various Low-Thrust Maximum Magnitude and Specific Impulse
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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() | e | ||||
---|---|---|---|---|---|
3.82 | 0.731 | 27 | 0 | 0 | 0 |
(Days) | (Days) | MinPack-1 | Hybrid | Discrete Newton | Broyden |
---|---|---|---|---|---|
40 | 42 | 1.8 s 257.22 kg | 1.2 s 257.22 kg | 4.7 s 257.22 kg | 1.4 s 257.22 kg |
70 | 72 | 4.9 s 182.28 kg | 3.0 s 182.28 kg | 8.6 s 182.28 kg | 2.7 s 182.28 kg |
100 | 105 | 6.9 s 96.59 kg | 5.2 s 96.59 kg | 19.5 s 96.59 kg | 8.6 s 96.59 kg |
−3.99577 | 0.03540 | −0.70065 | −0.98333 | −0.65100 |
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Yang, S.; Xu, B.; Li, X. Optimization of Geostationary Orbit Transfers via Combined Chemical–Electric Propulsion. Aerospace 2022, 9, 200. https://doi.org/10.3390/aerospace9040200
Yang S, Xu B, Li X. Optimization of Geostationary Orbit Transfers via Combined Chemical–Electric Propulsion. Aerospace. 2022; 9(4):200. https://doi.org/10.3390/aerospace9040200
Chicago/Turabian StyleYang, Shihai, Bo Xu, and Xin Li. 2022. "Optimization of Geostationary Orbit Transfers via Combined Chemical–Electric Propulsion" Aerospace 9, no. 4: 200. https://doi.org/10.3390/aerospace9040200
APA StyleYang, S., Xu, B., & Li, X. (2022). Optimization of Geostationary Orbit Transfers via Combined Chemical–Electric Propulsion. Aerospace, 9(4), 200. https://doi.org/10.3390/aerospace9040200