Four-Dimensional Generalized AMS Optimization Considering Critical Engine Inoperative for an eVTOL
Abstract
:1. Introduction
1.1. Background
1.2. Literature Review
1.3. Motivation and Objective
2. Preliminaries and Definitions
3. Optimization Setup
3.1. Problem Definition
given a fixed RMS , search for an optimal set of effector-related parameters within their constraint limits, to maximize the margin between and .
3.2. Optimization Formulation
- is the total number of vertices on RMS;
- is the margin factor of the RMS vertex;
- is the vector of variables to optimize, with and its lower and upper limits;
- is the vector of additional constraints, e.g., structural or spatial restriction;
- is the upper limits of .
3.3. Optimization to Account for Critical Engine Failure
- is the total number of inputs;
- is the margin factor of the RMS vertex of index i to the AMS given the failure of the input of index j.
3.4. Solving for
3.5. Solving the Optimization
4. Test Implementation
4.1. Airframe Under Consideration
- are the orientations of rotors around the longitudinal axis, positive is defined by the right-hand rule;
- is the generalized moments vector of rotational accelerations and vertical load factor in the body-fixed axis;
- is the effectiveness matrix [29], as a function of ;
- and are the rotational speed of the propellers and their upper limit.
4.2. Assumptions
4.3. Test Setup
- Two-variable failure-free test as Equation (2), with
- Two-variable failure-free test as Equation (2), with
- Same grouping as Test 1, including critical OEI according to Equation (3);
- Same grouping as Test 2, including critical OEI according to Equation (3).
5. Optimization Results
5.1. Optimization Results—Failure-Free Cases
5.2. Optimization Results—Critical Failure Case
5.3. Validation and Comparison of Optimization Results
6. Closed-Loop Verification
6.1. Closed-Loop Simulation Framework
6.2. Initial Configuration: Failure-Free Simulation
6.3. Initial Configuration: Simulation with Injected Failure
6.4. Failure-Free Optimized Configuration: Simulation with Injected Failure
6.5. Critical-Failure-Optimized Layout Simulation with Injected Failure
6.6. Summary of Simulation Results
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Durham, W.C. Constrained control allocation. J. Guid. Control Dyn. 1993, 16, 717–725. [Google Scholar] [CrossRef]
- Durham, W.C. Constrained control allocation—Three-moment problem. J. Guid. Control Dyn. 1994, 17, 330–336. [Google Scholar] [CrossRef]
- Johansen, T.A.; Fossen, T.I. Control allocation—A Survey. Automatica 2013, 49, 1087–1103. [Google Scholar] [CrossRef]
- Durham, W.C. Attainable moments for the constrained control allocation problem. J. Guid. Control Dyn. 1994, 17, 1371–1373. [Google Scholar] [CrossRef]
- Varriale, C.; Voskuijl, M.; Veldhuis, L.L. Trim for Maximum Control Authority using the Attainable Moment Set. In Proceedings of the AIAA Scitech 2020 Forum, Orlando, FL, USA, 6–10 January 2020; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2020. ISBN 9781624105951. [Google Scholar]
- Ma, T.; Wang, X.; Qiao, N.; Zhang, Z.; Fu, J.; Bao, M. A Conceptual Design and Optimization Approach for Distributed Electric Propulsion eVTOL Aircraft Based on Ducted-Fan Wing Unit. Aerospace 2022, 9, 690. [Google Scholar] [CrossRef]
- Suiçmez, E.C. Full Envelope Nonlinear Controller Design for a Novel Electric VTOL(eVTOL) Air-taxi via INDI Approach Combined with CA. Ph.D. Thesis, Middle East Technical University, Ankara, Turkey, 2021. [Google Scholar]
- Moore, K.R.; Ning, A. Distributed Electric Propulsion Effects on Existing Aircraft Through Multidisciplinary Optimization. In Proceedings of the 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, FL, USA, 8–12 January 2018; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2018; ISBN 978-1-62410-532-6. [Google Scholar]
- Fard, M.T.; He, J.; Huang, H.; Cao, Y. Aircraft Distributed Electric Propulsion Technologies—A Review. IEEE Trans. Transp. Electrific. 2022, 8, 4067–4090. [Google Scholar] [CrossRef]
- Bacchini, A.; Cestino, E. Electric VTOL Configurations Comparison. Aerospace 2019, 6, 26. [Google Scholar] [CrossRef]
- Akash, A.; Raj, V.S.J.; Sushmitha, R.; Prateek, B.; Aditya, S.; Sreehari, V.M. Design and Analysis of VTOL Operated Intercity Electrical Vehicle for Urban Air Mobility. Electronics 2022, 11, 20. [Google Scholar] [CrossRef]
- Piccinini, R.; Tugnoli, M.; Zanotti, A. Numerical Investigation of the Rotor-Rotor Aerodynamic Interaction for eVTOL Aircraft Configurations. Energies 2020, 13, 5995. [Google Scholar] [CrossRef]
- Tumuluru Ramesh, N.; Pandurangi, P.V. A Flight Performance Based Optimization Model for eVTOL Vehicles. Eng. Arch. 2022, preprint. [Google Scholar]
- Cook, J. A Strip Theory Approach to Dynamic Modeling of eVTOL Aircraft. In Proceedings of the AIAA Scitech 2021 Forum, Virtual, 11–21 January 2021; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2021. [Google Scholar]
- Stokkermans, T.C.A.; Usai, D.; Sinnige, T.; Veldhuis, L.L.M. Aerodynamic Interaction Effects Between Propellers in Typical eVTOL Vehicle Configurations. J. Aircr. 2021, 58, 815–833. [Google Scholar] [CrossRef]
- EASA. Special Condition for Small-Category VTOL-Capable Aircraft. Available online: https://www.easa.europa.eu/en/downloads/139946/en (accessed on 28 October 2024).
- EASA. Means of Compliance with the Special Condition VTOL—MOC SC-VTOL Issue 2. Available online: https://www.easa.europa.eu/en/downloads/127717/en (accessed on 28 October 2024).
- Eric, N.V.; Pierre, T.; Joël, J.; Daniel, A.; Philippe, P.; Carsten, D. Reduction of Vertical Tail Using Differential Thrust: Influence on Flight Control and Certification. In Proceedings of the Advanced Aircraft Efficiency in a Global Air Transport System (AEGATS’18), Toulouse, France, 23–25 October 2018; pp. 1–8. [Google Scholar]
- Van, E.N.; Alazard, D.; Döll, C.; Pastor, P. Co-design of aircraft vertical tail and control laws using distributed electric propulsion. IFAC-PapersOnLine 2019, 52, 514–519. [Google Scholar] [CrossRef]
- Moore, K.R.; Ning, A. Takeoff and Performance Trade-Offs of Retrofit Distributed Electric Propulsion for Urban Transport. J. Aircr. 2019, 56, 1880–1892. [Google Scholar] [CrossRef]
- Pei, J.; Bassett, G.; Grisham, J.; Finch, P.; Toniolo, M.; Miller, L.; Bandu, P. Generic Control Allocation Toolbox for Preliminary Vehicle Design. In Proceedings of the 2018 Modeling and Simulation Technologies Conference, Reston, VA, USA, 25–29 June 2018; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2018. ISBN 9781624105517. [Google Scholar]
- Varriale, C.; Voskuijl, M. A trim problem formulation for maximum control authority using the Attainable Moment Set geometry. CEAS Aeronaut J. 2022, 13, 251–266. [Google Scholar] [CrossRef]
- Söpper, M.; Zhang, J.; Holzapfel, F. Required Moment Sets: Enhanced Controllability Analysis for Nonlinear Aircraft Models. (submitted). Appl. Sci. 2021, 11, 3456. [Google Scholar] [CrossRef]
- Zhang, J.; Söpper, M.; Holzapfel, F. Attainable Moment Set Optimization to Support Configuration Design: A Required Moment Set Based Approach. Appl. Sci. 2021, 11, 3685. [Google Scholar] [CrossRef]
- Lu, Z.; Hong, H.; Schweighofer, F.; Holzapfel, F. Controllability Evaluation for VTOL Aircraft in Velocity Envelope: A Distance-Based Metric. J. Guid. Control Dyn. 2024, 47, 1–14. [Google Scholar] [CrossRef]
- MathWorks. MATLAB Version: 9.8.0.1451342 (R2021a); MathWorks: Natick, MA, USA, 2021. [Google Scholar]
- Gupta, G.; Abdallah, S. Propeller Force-Constant Modeling for Multirotor UAVs from Experimental Estimation of Inflow Velocity. Int. J. Aerosp. Eng. 2018, 2018, 1–10. [Google Scholar] [CrossRef]
- MIT. Performance of Propellers. Available online: https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html (accessed on 28 October 2024).
- Du, G.-X.; Quan, Q.; Yang, B.; Cai, K.-Y. Controllability Analysis for Multirotor Helicopter Rotor Degradation and Failure. J. Guid. Control Dyn. 2015, 38, 978–985. [Google Scholar] [CrossRef]
- Di Francesco, G.; Mattei, M. Modeling and Incremental Nonlinear Dynamic Inversion Control of a Novel Unmanned Tiltrotor. J. Aircr. 2016, 53, 73–86. [Google Scholar] [CrossRef]
- Wang, X.; van Kampen, E.-J.; Chu, Q.; Lu, P. Stability Analysis for Incremental Nonlinear Dynamic Inversion Control. J. Guid. Control Dyn. 2019, 42, 1116–1129. [Google Scholar] [CrossRef]
- Lu, P.; van Kampen, E.-J.; Visser, C.d.; Chu, Q. Aircraft fault-tolerant trajectory control using Incremental Nonlinear Dynamic Inversion. Control Eng. Pract. 2016, 57, 126–141. [Google Scholar] [CrossRef]
- Smeur, E.J.J.; Chu, Q.; Croon, G.C.H.E.d. Adaptive Incremental Nonlinear Dynamic Inversion for Attitude Control of Micro Air Vehicles. J. Guid. Control Dyn. 2016, 39, 450–461. [Google Scholar] [CrossRef]
- Bodson, M. Evaluation of Optimization Methods for Control Allocation. J. Guid. Control Dyn. 2002, 25, 703–711. [Google Scholar] [CrossRef]
- Zhang, J.; Bhardwaj, P.; Raab, S.A.; Saboo, S.; Holzapfel, F. Control Allocation Framework for a Tilt-rotor Vertical Take-off and Landing Transition Aircraft Configuration. In Proceedings of the 2018 Applied Aerodynamics Conference, Atlanta, GA, USA, 25–29 June 2018; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2018. ISBN 978-1-62410-559-3. [Google Scholar]
- Raab, S.A.; Zhang, J.; Bhardwaj, P.; Holzapfel, F. Proposal of a Unified Control Strategy for Vertical Take-off and Landing Transition Aircraft Configurations. In Proceedings of the 2018 Applied Aerodynamics Conference, Atlanta, GA, USA, 25–29 June 2018; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2018. ISBN 978-1-62410-559-3. [Google Scholar]
- Bhardwaj, P.; Raab, S.A.; Zhang, J.; Holzapfel, F. Integrated Reference Model for a Tilt-rotor Vertical Take-off and Landing Transition UAV. In Proceedings of the 2018 Applied Aerodynamics Conference, Atlanta, GA, USA, 25–29 June 2018; American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2018. [Google Scholar]
- Sieberling, S.; Chu, Q.P.; Mulder, J.A. Robust Flight Control Using Incremental Nonlinear Dynamic Inversion and Angular Acceleration Prediction. J. Guid. Control Dyn. 2010, 33, 1732–1742. [Google Scholar] [CrossRef]
Preliminary Design Parameters | Values |
---|---|
Take-off Weight | 250 kg |
Wingspan | 10 m |
Motor Diameter | 1–2 m |
Initial Value | Test 1 | Test 2 | Test 3 | Test 4 | |
---|---|---|---|---|---|
P1 tilt angle () | −5 | −17.94 | −13.98 | −1.64 | −6.09 |
P2 tilt angle () | 5 | 9.25 | 8.90 | 19.04 | 10.20 |
P3 tilt angle () | −5 | 9.25 | 9.23 | 19.04 | 29.20 |
P4 tilt angle () | 5 | −17.94 | −23.15 | −1.64 | −1.90 |
Failure-free cost function: | 33.06 | 29.22 | 29.12 | 30.29 | 30.28 |
Critical failure cost function: | 61.31 | 67.85 | 59.58 | 47.39 | 45.6667 |
Total force available in the vertical direction (%): | 99.6% | 96.92% | 96.62% | 97.24% | 96.27% |
Additional force to trim (%): | 0.40% | 3.18% | 3.50% | 2.84% | 3.87% |
Additional power to trim (%): | 0.6% | 4.8% | 5.3% | 4.3% | 5.9% |
Initial Unoptimized Config. (Figure 21 and Figure 22) | Non-Failure-Optimized Config. (Figure 23 and Figure 24; Figure 23; Figure 24) | Critical-Failure-Optimized Config. (Figure 23 and Figure 24) | |
---|---|---|---|
Continued Safe Flight after Failure (Y/N) | N | Y | Y |
Max. Attitude Transient after Failure (Degrees) | 20 | 15 | 12 |
Number of Saturated Rotors (Non-Failed) @t = 30 s | 4 (L02, R02, L04, R04) | 2 (L04, R04) | 0 |
Difference between Max. and Min. Rotational Speed (Non-Failed) @t = 30 s (Rad/s) | 288 (btw. L04 & R04) | 288 (btw. L04 & R04) | 158 (btw. L03 & R03) |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhang, J.; Söpper, M.; Holzapfel, F.; Zhang, S. Four-Dimensional Generalized AMS Optimization Considering Critical Engine Inoperative for an eVTOL. Aerospace 2024, 11, 990. https://doi.org/10.3390/aerospace11120990
Zhang J, Söpper M, Holzapfel F, Zhang S. Four-Dimensional Generalized AMS Optimization Considering Critical Engine Inoperative for an eVTOL. Aerospace. 2024; 11(12):990. https://doi.org/10.3390/aerospace11120990
Chicago/Turabian StyleZhang, Jiannan, Max Söpper, Florian Holzapfel, and Shuguang Zhang. 2024. "Four-Dimensional Generalized AMS Optimization Considering Critical Engine Inoperative for an eVTOL" Aerospace 11, no. 12: 990. https://doi.org/10.3390/aerospace11120990
APA StyleZhang, J., Söpper, M., Holzapfel, F., & Zhang, S. (2024). Four-Dimensional Generalized AMS Optimization Considering Critical Engine Inoperative for an eVTOL. Aerospace, 11(12), 990. https://doi.org/10.3390/aerospace11120990