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2024 | OriginalPaper | Chapter

5. A Unified Hybrid Control Approach to Maximum Endurance of Aircraft

Authors : Emily Oelberg, Luis Rodrigues

Published in: Control of Autonomous Aerial Vehicles

Publisher: Springer Nature Switzerland

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Abstract

Unmanned air vehicles and urban air mobility have driven the need for the development of new algorithms for flight management systems. However, for certification, there is a strong desire to compare the new algorithms with the ones used for more conventional aircraft such as turbofan fixed-wing vehicles. With this need in mind, the main contribution of this chapter is to propose a unified approach for the maximum endurance of turbojet, turboprop, turbofan, and all-electric aircraft. This chapter details the two main steps to achieve this goal. First, a unified model of energy-depletion dynamics encompassing both fuel-burning and all-electric aircraft is developed. Next, using the unified energy model, the problem of maximum cruise endurance is formulated in a unified framework for all aircraft configurations and for a flight with three phases: climb, cruise, and descent. The problem is formulated and solved using hybrid optimal control in conjunction with the unified energy model. The general solution is then applied to turbojet, turbofan, turboprop, and all-electric aircraft. Simulation results are provided for a turbofan and a turboprop aircraft. Conclusions compare the results and summarize the most important findings.

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Literature
2.
go back to reference Tomic T, Schmid K, Lutz P, Domel A, Kassecker M, Mair E, Grixa IL, Ruess F, Suppa M, Burschka D (2012) Toward a fully autonomous uav: Research platform for indoor and outdoor urban search and rescue. IEEE Robot Autom Mag 19(3):46–56CrossRef Tomic T, Schmid K, Lutz P, Domel A, Kassecker M, Mair E, Grixa IL, Ruess F, Suppa M, Burschka D (2012) Toward a fully autonomous uav: Research platform for indoor and outdoor urban search and rescue. IEEE Robot Autom Mag 19(3):46–56CrossRef
5.
go back to reference Reinecke M, Prinsloo T (2017) The influence of drone monitoring on crop health and harvest size. In: Conference on next generation computing applications (NextComp). IEEE, pp 5–10 Reinecke M, Prinsloo T (2017) The influence of drone monitoring on crop health and harvest size. In: Conference on next generation computing applications (NextComp). IEEE, pp 5–10
7.
go back to reference Bryson AE, Ho Y-C (1975) Applied optimal control: optimization, estimation, and control. Taylor & Francis, New York, NY Bryson AE, Ho Y-C (1975) Applied optimal control: optimization, estimation, and control. Taylor & Francis, New York, NY
8.
go back to reference Stengel RF (1994) Optimal control and estimation. Dover, New York, NYMATH Stengel RF (1994) Optimal control and estimation. Dover, New York, NYMATH
9.
go back to reference Liberzon D (2012) Calculus of variations and optimal control theory: a concise introduction. Princeton University Press, Princeton, NJCrossRefMATH Liberzon D (2012) Calculus of variations and optimal control theory: a concise introduction. Princeton University Press, Princeton, NJCrossRefMATH
10.
go back to reference Athans M, Falb PL (1966) Optimal control: an introduction to the theory and its applications. McGraw-Hill, Mineola, NYMATH Athans M, Falb PL (1966) Optimal control: an introduction to the theory and its applications. McGraw-Hill, Mineola, NYMATH
11.
go back to reference Sussman HJ, Willems JC (1997) 300 years of optimal control: From the brachystoschrone to the maximum principle. IEEE Control Syst 17(3):32–44CrossRef Sussman HJ, Willems JC (1997) 300 years of optimal control: From the brachystoschrone to the maximum principle. IEEE Control Syst 17(3):32–44CrossRef
12.
go back to reference Miele A (1963) A survey of the problem of optimizing flight paths of aircraft and missiles. University of California Press, Berkeley, CA, pp 3–32MATH Miele A (1963) A survey of the problem of optimizing flight paths of aircraft and missiles. University of California Press, Berkeley, CA, pp 3–32MATH
13.
go back to reference Miele A (1962) The calculus of variations in applied aerodynamics and flight mechanics. In: Leitmann G (ed) Optimization techniques, ser. Mathematics in science and engineering, vol 5. Elsevier, pp 99–170 Miele A (1962) The calculus of variations in applied aerodynamics and flight mechanics. In: Leitmann G (ed) Optimization techniques, ser. Mathematics in science and engineering, vol 5. Elsevier, pp 99–170
14.
go back to reference Pakniyat A (2016) Optimal control of deterministic and stochastic hybrid systems: Theory and applications. Ph.D. dissertation, McGill University, Montreal, Quebec, Canada Pakniyat A (2016) Optimal control of deterministic and stochastic hybrid systems: Theory and applications. Ph.D. dissertation, McGill University, Montreal, Quebec, Canada
15.
go back to reference Sorensen JA, Morello SA, Erzberger H (1979) Application of trajectory optimization principles to minimize aircraft operating costs. IEEE conference on decision and control 2:415–421 Sorensen JA, Morello SA, Erzberger H (1979) Application of trajectory optimization principles to minimize aircraft operating costs. IEEE conference on decision and control 2:415–421
16.
go back to reference Burrows JW (1983) Fuel-optimal aircraft trajectories with fixed arrival times. J Guidance Control Dyn 6(1):14–19CrossRef Burrows JW (1983) Fuel-optimal aircraft trajectories with fixed arrival times. J Guidance Control Dyn 6(1):14–19CrossRef
17.
go back to reference Vilardaga S, Prats X (2015) Operating cost sensitivity to required time of arrival commands to ensure separation in optimal aircraft 4D trajectories. Transp Res Part C-Emer Technol 61:75–86CrossRef Vilardaga S, Prats X (2015) Operating cost sensitivity to required time of arrival commands to ensure separation in optimal aircraft 4D trajectories. Transp Res Part C-Emer Technol 61:75–86CrossRef
18.
go back to reference Villarroel J, Rodrigues L (2016) Optimal control framework for cruise economy mode of flight management systems. J Guidance Control Dyn 39(5):1022–1033CrossRef Villarroel J, Rodrigues L (2016) Optimal control framework for cruise economy mode of flight management systems. J Guidance Control Dyn 39(5):1022–1033CrossRef
19.
go back to reference Botros A (2017) Minimizing direct operating cost for turbojet and turboprop aircraft in cruise. Master’s thesis, Concordia University, Montreal, Quebec, Canada Botros A (2017) Minimizing direct operating cost for turbojet and turboprop aircraft in cruise. Master’s thesis, Concordia University, Montreal, Quebec, Canada
20.
go back to reference García-Heras J, Soler M, Sáez FJ (2014) A comparison of optimal control methods for minimum fuel cruise at constant altitude and course with fixed arrival time. In: Procedia engineering, vol 80, pp 231–244. International Symposium on Aircraft Airworthiness García-Heras J, Soler M, Sáez FJ (2014) A comparison of optimal control methods for minimum fuel cruise at constant altitude and course with fixed arrival time. In: Procedia engineering, vol 80, pp 231–244. International Symposium on Aircraft Airworthiness
21.
go back to reference Kim N, Cha S, Peng H (2011) Optimal control of hybrid electric vehicles based on Pontryagin’s minimum principle. IEEE Trans Control Syst Technol 19(5):1279–1287CrossRef Kim N, Cha S, Peng H (2011) Optimal control of hybrid electric vehicles based on Pontryagin’s minimum principle. IEEE Trans Control Syst Technol 19(5):1279–1287CrossRef
22.
go back to reference Bert CW (1999) Range and endurance of turboprop, turbofan, or piston-propeller aircraft having wings with or without camber. Aircraft Design 2(4):183–190CrossRef Bert CW (1999) Range and endurance of turboprop, turbofan, or piston-propeller aircraft having wings with or without camber. Aircraft Design 2(4):183–190CrossRef
23.
go back to reference Raymer DP (2004) Approximate method of deriving loiter time from range. J Aircraft 41(4):938–940CrossRef Raymer DP (2004) Approximate method of deriving loiter time from range. J Aircraft 41(4):938–940CrossRef
24.
go back to reference Villarroel J (2015) An optimal control framework for flight management systems. Master’s thesis, Concordia University, Montreal, Canada Villarroel J (2015) An optimal control framework for flight management systems. Master’s thesis, Concordia University, Montreal, Canada
25.
go back to reference Kaptsov M (2017) An energy efficient optimal control framework for general purpose flight management systems. Master’s thesis, Concordia University, Montreal, Canada Kaptsov M (2017) An energy efficient optimal control framework for general purpose flight management systems. Master’s thesis, Concordia University, Montreal, Canada
26.
go back to reference Kaptsov M, Rodrigues L (2018) Electric aircraft flight management systems: Economy mode and maximum endurance. J Guidance Control Dyn 41(1):288–293CrossRef Kaptsov M, Rodrigues L (2018) Electric aircraft flight management systems: Economy mode and maximum endurance. J Guidance Control Dyn 41(1):288–293CrossRef
27.
go back to reference Bert CW (1981) Prediction of range and endurance of jet aircraft at constant altitude. J Aircraft 18(10):890–892CrossRef Bert CW (1981) Prediction of range and endurance of jet aircraft at constant altitude. J Aircraft 18(10):890–892CrossRef
28.
go back to reference Pakniyat A, Caines PE (2017) Hybrid optimal control of an electric vehicle with a dual-planetary transmission. Nonlinear Anal: Hybrid Syst 25:263–282MathSciNetMATH Pakniyat A, Caines PE (2017) Hybrid optimal control of an electric vehicle with a dual-planetary transmission. Nonlinear Anal: Hybrid Syst 25:263–282MathSciNetMATH
29.
go back to reference Ross IM, D’Souza CN (2005) Hybrid optimal control framework for mission planning. J Guidance Control Dyn 28(4):686–697CrossRef Ross IM, D’Souza CN (2005) Hybrid optimal control framework for mission planning. J Guidance Control Dyn 28(4):686–697CrossRef
30.
go back to reference Soler M, Olivares A, Staffetti E (2010) Hybrid optimal control approach to commercial aircraft trajectory planning. Journal of Guidance, Control Dyn 33(3):985–991CrossRef Soler M, Olivares A, Staffetti E (2010) Hybrid optimal control approach to commercial aircraft trajectory planning. Journal of Guidance, Control Dyn 33(3):985–991CrossRef
31.
go back to reference Franco A, Rivas D (2015) Optimization of multiphase aircraft trajectories using hybrid optimal control. J Guidance Control Dyn 38(3):452–467CrossRef Franco A, Rivas D (2015) Optimization of multiphase aircraft trajectories using hybrid optimal control. J Guidance Control Dyn 38(3):452–467CrossRef
32.
go back to reference Soler M, Olivares A, Staffetti E, Zapata D (2012) Framework for aircraft trajectory planning toward an efficient air traffic management. J Aircraft 49(1):341–348CrossRef Soler M, Olivares A, Staffetti E, Zapata D (2012) Framework for aircraft trajectory planning toward an efficient air traffic management. J Aircraft 49(1):341–348CrossRef
33.
go back to reference Sachs G, Christodoulou T (1986) Endurance increase by cyclic control. J Guidance Control Dyn 9(1):58–63CrossRefMATH Sachs G, Christodoulou T (1986) Endurance increase by cyclic control. J Guidance Control Dyn 9(1):58–63CrossRefMATH
34.
go back to reference Menon PK, Sweriduk GD, Bowers AH (2007) Study of near-optimal endurance-maximizing periodic cruise trajectories. J Aircraft 44(2):393–398CrossRef Menon PK, Sweriduk GD, Bowers AH (2007) Study of near-optimal endurance-maximizing periodic cruise trajectories. J Aircraft 44(2):393–398CrossRef
35.
go back to reference Villarroel J, Rodrigues L (2016) An optimal control framework for the climb and descent economy modes of flight management systems. IEEE Trans Aerosp Electron Syst 52(3):1227–1240CrossRef Villarroel J, Rodrigues L (2016) An optimal control framework for the climb and descent economy modes of flight management systems. IEEE Trans Aerosp Electron Syst 52(3):1227–1240CrossRef
36.
go back to reference Zhao Y, Tsiotras P (2013) Analysis of energy-optimal aircraft landing operation trajectories. J Guidance Control Dyn 36(3):833–845CrossRef Zhao Y, Tsiotras P (2013) Analysis of energy-optimal aircraft landing operation trajectories. J Guidance Control Dyn 36(3):833–845CrossRef
37.
go back to reference Stell L (2011) Prediction of top of descent location for idle-thrust descents. In: USA/Europe air traffic management R &D seminar, Berlin, Germany Stell L (2011) Prediction of top of descent location for idle-thrust descents. In: USA/Europe air traffic management R &D seminar, Berlin, Germany
38.
go back to reference Rodrigues L (2018) A unified optimal control approach for maximum endurance and maximum range. IEEE Trans Aerosp Electron Syst 54(1):385–391MathSciNetCrossRef Rodrigues L (2018) A unified optimal control approach for maximum endurance and maximum range. IEEE Trans Aerosp Electron Syst 54(1):385–391MathSciNetCrossRef
39.
go back to reference Erzberger H, Lee H (1980) Constrained optimum trajectories with specified range. J Guidance Control 3(1):78–85CrossRef Erzberger H, Lee H (1980) Constrained optimum trajectories with specified range. J Guidance Control 3(1):78–85CrossRef
40.
go back to reference Patron RSF, Botez RM, Labour D (2014) Flight trajectory optimization through genetic algorithms coupling vertical and lateral profiles. In: International mechanical engineering congress and exposition Patron RSF, Botez RM, Labour D (2014) Flight trajectory optimization through genetic algorithms coupling vertical and lateral profiles. In: International mechanical engineering congress and exposition
41.
go back to reference Franco A, Rivas D (2011) Minimum-cost cruise at constant altitude of commercial aircraft including wind effects. J Guidance Control Dyn 34(4):1253–1260CrossRef Franco A, Rivas D (2011) Minimum-cost cruise at constant altitude of commercial aircraft including wind effects. J Guidance Control Dyn 34(4):1253–1260CrossRef
42.
go back to reference Randle WE, Hall CA, Vera-Morales M (2011) Improved range equation based on aircraft flight data. J Aircraft 48(4):1291–1298CrossRef Randle WE, Hall CA, Vera-Morales M (2011) Improved range equation based on aircraft flight data. J Aircraft 48(4):1291–1298CrossRef
43.
go back to reference Chakravarty A (1985) Four-dimensional fuel-optimal guidance in the presence of winds. J Guidance Control Dyn 8(1):16–22CrossRef Chakravarty A (1985) Four-dimensional fuel-optimal guidance in the presence of winds. J Guidance Control Dyn 8(1):16–22CrossRef
44.
go back to reference Hale FJ, Steiger AR (1979) Effects of wind on aircraft cruise performance. J Aircraft 16(6):382–387CrossRef Hale FJ, Steiger AR (1979) Effects of wind on aircraft cruise performance. J Aircraft 16(6):382–387CrossRef
45.
go back to reference El-Sayed A (2016) Fundamentals of aircraft and rocket propulsion. Springer, London, UKCrossRef El-Sayed A (2016) Fundamentals of aircraft and rocket propulsion. Springer, London, UKCrossRef
46.
go back to reference Longmuir M, Ahmed NA (2009) Commercial aircraft exterior cleaning optimization. J Aircraft 46(1):284–290CrossRef Longmuir M, Ahmed NA (2009) Commercial aircraft exterior cleaning optimization. J Aircraft 46(1):284–290CrossRef
48.
go back to reference FAA (2016) Pilot’s handbook of aeronautical knowledge (FAA-H-8083-25B). Aircraft Performance FAA (2016) Pilot’s handbook of aeronautical knowledge (FAA-H-8083-25B). Aircraft Performance
Metadata
Title
A Unified Hybrid Control Approach to Maximum Endurance of Aircraft
Authors
Emily Oelberg
Luis Rodrigues
Copyright Year
2024
DOI
https://doi.org/10.1007/978-3-031-39767-7_5

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