# Improved Thrust Performance Optimization Method for UAVs Based on the Adaptive Margin Control Approach

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dynamical Modeling and Problem Description

#### 2.1. UAV Dynamics Modeling

#### 2.1.1. UAV Modeling Assumptions

- The mass of the UAV does not change during flight for a short period of time.
- The UAV is an ideal rigid body, and the effects of aircraft elasticity are ignored.
- The UAV is affected only by the acceleration of gravity, and the curvature of the Earth is neglected.
- Since the UAV is symmetric about the $x-y$ plane, ${I}_{xz}=0$ and ${I}_{yz}=0$.
- The change in the aircraft center of mass with fuel is neglected during the UAV.

#### 2.1.2. Dynamics Equations

_{V}is the speed tilt angle, and ψ

_{V}is the trajectory deflection angle.

#### 2.1.3. Kinematic Equations

#### 2.2. UAV Turbofan Engine Modeling

- Ignore the effect of the Reynolds number variation on the characteristics of the engine components; ignore the effect of atmospheric humidity on the parameters of the thermodynamic properties of the gas; the effect of rotor inertia is considered.
- The flow of air in the engine is treated as quasi one-dimensional flow, i.e., the airflow parameters are considered to be the same in the same cross-section of the engine.

#### 2.2.1. Inlet

#### 2.2.2. Fan

#### 2.2.3. Compressor

#### 2.2.4. Burner

#### 2.2.5. High-Pressure Turbine (HPT) and Low-Pressure Turbine (LPT)

#### 2.2.6. Mixer

#### 2.2.7. Nozzle

#### 2.3. Problem Description

## 3. Major Studies

#### 3.1. Thrust Optimization Based on the Adaptive Margin Model

#### 3.1.1. Angle of Attack Prediction for UAV

#### 3.1.2. Engine Model under the Influence of Inlet Distortion

#### 3.2. Adaptive Disturbance Rejection Control

#### 3.2.1. Design of Slow Loop Control Instruction

#### 3.2.2. Design of Adaptive Disturbance Rejection Control

## 4. Simulation Results

#### 4.1. Simulation Results of Thrust Optimization Based on the Adaptive Margin Model

- Under the same acceleration control parameters, the thrust optimization strategy proposed in this paper can significantly improve the acceleration capability of UAV and shorten the acceleration time.
- With improved thrust performance, the UAV requires a shorter full throttle time.
- At the same flat flying speed, the throttle command of the engine after thrust optimization is smaller than the original throttle command.
- At maximum throttle, the engine’s maximum thrust output can be increased by at least 8%.

#### 4.2. Simulation Results of Adaptive Disturbance Rejection Control

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Bello, A.B.; Navarro, F.; Raposo, J.; Miranda, M.; Zazo, A.; Álvarez, M. Fixed-Wing UAV Flight Operation under Harsh Weather Conditions: A Case Study in Livingston Island Glaciers, Antarctica. Drones
**2022**, 6, 384. [Google Scholar] [CrossRef] - Cao, S.; Yu, H. An Adaptive Control Framework for the Autonomous Aerobatic Maneuvers of Fixed-Wing Unmanned Aerial Vehicle. Drones
**2022**, 6, 316. [Google Scholar] [CrossRef] - Liu, Z.; Han, W.; Wu, Y.; Su, X.; Guo, F. Automated Sortie Scheduling Optimization for Fixed-Wing Unmanned Carrier Aircraft and Unmanned Carrier Helicopter Mixed Fleet Based on Offshore Platform. Drones
**2022**, 6, 375. [Google Scholar] [CrossRef] - Ming, Z. Research on Uav Application Development and Airworthiness Standard Management in China. Acad. J. Eng. Technol. Sci.
**2020**, 4, 37–46. [Google Scholar] - Cui, Y.P.; Xing, Q.H. The challenge and inspiration of UAVs to field air defense from the Russia-Ukraine War. Aerosp. Electron. Warf.
**2022**, 38, 1–3. [Google Scholar] - Li, R.J.; Gong, S. Development Direction Analysis of Future UCAV Power Plant. Aeronaut. Sci. Technol.
**2015**, 26, 1–5. [Google Scholar] - Hu, X.Y. UAV Propulsion System Technology Research. Gas Turbine Exp. Res.
**2008**, 1, 58–61. [Google Scholar] - Hu, X.Y. Development of High Altitude Long Endurance UAV Propulsion Technology. Gas Turbine Exp. Res.
**2006**, 4, 56–60. [Google Scholar] - Chen, D.; Tian, H.J.; Li, M.X.; Lei, Q.Q. Analysis to the Development of Power Systems for MALE UAVs. Aerosp. Power
**2022**, 5, 16–19. [Google Scholar] - Cheng, B.L.; Tang, H.; Xu, X.; Li, X.P. Performance Study on Turbofan Engine with Turbine Inter Burner. Aeroengine
**2010**, 36, 18–22. [Google Scholar] - Dong, H.B.; Shang, G.J.; Guo, Y.Q. Effect and verification of mass injecting pre-compressor cooling on control plan of turbonfan engine. J. Aerosp. Power
**2022**, 37, 404–408. [Google Scholar] - Sun, H.G.; Li, J.; Li, H.C.; Ye, B. The Analysis on Surge Margin’S Influence on Aeroengine Thrust Control System. Comput. Simul.
**2017**, 34, 84–89. [Google Scholar] - Longley, J.P. A review of non-steady flow models for compressor stability. J. Turbomach.
**1994**, 116, 202–215. [Google Scholar] [CrossRef] - Longley, J.P.; Shin, H.W.; Plumley, R.E. Effects of rotating inlet distortion on multistage compressor stability. ASME J. Turbomach.
**1996**, 118, 181–188. [Google Scholar] [CrossRef] - Wang, J.K.; Zhang, H.B.; Chen, K.; Sun, F.Y.; Zhou, X. High stability control of engine based on surge margin estimation model. J. Aerosp. Power
**2013**, 28, 2145–2154. [Google Scholar] - Liu, D.X. Aviation Gas turbine Engine Stability Design and Evaluation Technology, 6th ed.; Aviation Industry Press: Beijing, China, 2004; pp. 45–182. [Google Scholar]
- Bodó, Z.; Lantos, B. Modeling and control of fixed wing UAVs. In Proceedings of the IEEE 13th International Symposium on Applied Computational Intelligence and Informatics (SACI), Timisoara, Romania, 29–31 May 2019; pp. 332–337. [Google Scholar]
- Kim, C. Development of unified high-fidelity flight dynamic modeling technique for unmanned compound aircraft. Int. J. Aerosp. Eng.
**2021**, 2021, 5513337. [Google Scholar] - Zhou, W.X. Research on Object-Oriented Modeling and Simulation for Aeroengine and Control System; DR, Nanjing University of Aeronautics and Astronautics the Graduate School: Nanjing, China, 2006. [Google Scholar]
- Iliff, K.W. Flight-Determined Subsonic Longitudinal Stability and Control Derivatives of the F-18 High Angle of Attack Research Vehicle (HARV) with Thrust Vectoring; NASA, Dryden Flight Research Center: Edwards, CA, USA, 1997; pp. 17–19.
- Lee, K.; Lee, B.; Kang, S.; Yang, S.; Lee, D. Inlet Distortion Test with Gas Turbine Engine in the Altitude Engine Test Facility. In Proceedings of the 27th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Chicago, IL, USA, 30 June 2010; p. 4337. [Google Scholar]

**Figure 6.**The surface mean total pressure recovery coefficient ${\sigma}_{AV}$ of an inlet at different angles of attack during subsonic operation.

**Figure 9.**The result graph of engine thrust lifting: (

**a**) Speed result of the UAV acceleration process, (

**b**) Result of the UAV engine throttle command.

**Figure 12.**Simulation results of UAV adaptive disturbance rejection control in longitudinal flight: (

**a**) Result of the angle of attack response graph; (

**b**) Result of the pitch angular velocity response graph; (

**c**) Result of the pitch angular response graph; (

**d**) Result graph of the elevator deflection command.

**Figure 13.**Flight simulation results of UAV adaptive interference suppression control roll direction: (

**a**) The resulting graph of the tilt-angle response; (

**b**) Result diagram of aileron deflection command.

Equations of Motion Number ‘i’ | Coefficient of Motion Serial Number ‘j’ | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

1 | ${a}_{11}=\frac{{P}^{V}-{X}^{V}}{m}$ $\left({\mathrm{s}}^{-1}\right)$ | ${a}_{12}=0$ | ${a}_{13}=-g\mathrm{cos}\theta $ $\left(\mathrm{m}\xb7{\mathrm{s}}^{-2}\right)$ | ${a}_{14}=-\frac{{X}^{\alpha}+{P}^{\alpha}}{m}$ $\left(\mathrm{m}\xb7{\mathrm{s}}^{-2}\right)$ | - | ${a}_{16}=\frac{1}{m}$ $\left({\mathrm{Kg}}^{-1}\right)$ |

2 | ${a}_{21}=\frac{{M}_{z}^{V}}{{I}_{zz}}$ $\left({\mathrm{m}}^{-1}\xb7{\mathrm{s}}^{-1}\right)$ | ${a}_{22}=\frac{{M}_{z}^{{\omega}_{z}}}{{I}_{zz}}$ $\left({\mathrm{s}}^{-1}\right)$ | ${a}_{23}=0$ | ${a}_{24}=\frac{{M}_{z}^{\alpha}}{{I}_{zz}}\left({\mathrm{s}}^{-2}\right)$ ${a}_{24}^{\prime}=\frac{{M}_{z}^{\dot{\alpha}}}{{I}_{zz}}\left({\mathrm{s}}^{-1}\right)$ | ${a}_{25}=\frac{{M}_{z}^{{\delta}_{z}}}{{I}_{zz}}\left({\mathrm{s}}^{-2}\right)$ ${a}_{25}^{\prime}=\frac{{M}_{z}^{\dot{{\delta}_{z}}}}{{I}_{zz}}\left({\mathrm{s}}^{-1}\right)$ | ${a}_{26}=\frac{1}{{I}_{zz}}$ $\left({\mathrm{Kg}}^{-1}\xb7{\mathrm{m}}^{-2}\right)$ |

3 | ${a}_{31}=\frac{{P}^{V}\alpha +{Y}^{V}}{mV}$ $\left({\mathrm{m}}^{-1}\right)$ | ${a}_{32}=0$ | ${a}_{33}=\frac{g\mathrm{sin}\theta}{V}$ $\left({\mathrm{s}}^{-1}\right)$ | ${a}_{34}=\frac{P+{Y}^{\alpha}}{mV}$ $\left({\mathrm{s}}^{-1}\right)$ | ${a}_{35}=\frac{{Y}^{{\delta}_{z}}}{mV}$ $\left({\mathrm{s}}^{-1}\right)$ | ${a}_{36}=\frac{1}{mV}$ $\left(\mathrm{s}\xb7{\mathrm{Kg}}^{-1}\xb7{\mathrm{m}}^{-1}\right)$ |

Parameter | Symbol | Value |
---|---|---|

aircraft mass ($\mathrm{kg}$) | $m$ | 9295.44 |

wingspan ($\mathrm{m}$) | $b$ | 9.144 |

wing area (${\mathrm{m}}^{2}$) | $S$ | 27.87 |

mean aerodynamic chord ($\mathrm{m}$) | $\overline{c}$ | 3.45 |

roll moment of inertia ($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | ${I}_{xx}$ | 12,874.8 |

yaw moment of inertia ($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | ${I}_{yy}$ | 85,552.1 |

pitch moment of inertia ($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | ${I}_{zz}$ | 75,673.6 |

product moment of inertia ($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | ${I}_{xy}$ | 1331.4 |

product moment of inertia ($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | ${I}_{xz}$ | 0 |

product moment of inertia ($\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | ${I}_{yz}$ | 0 |

c.g. location ($\mathrm{m}$) | ${x}_{cg}$ | 0.3$\overline{c}$ |

reference c.g. location ($\mathrm{m}$) | ${x}_{cgr}$ | 0.35$\overline{c}$ |

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. |

© 2023 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

**MDPI and ACS Style**

Wang, Y.; Liu, H.; Liu, K.
Improved Thrust Performance Optimization Method for UAVs Based on the Adaptive Margin Control Approach. *Mathematics* **2023**, *11*, 1176.
https://doi.org/10.3390/math11051176

**AMA Style**

Wang Y, Liu H, Liu K.
Improved Thrust Performance Optimization Method for UAVs Based on the Adaptive Margin Control Approach. *Mathematics*. 2023; 11(5):1176.
https://doi.org/10.3390/math11051176

**Chicago/Turabian Style**

Wang, Yeguang, Honglin Liu, and Kai Liu.
2023. "Improved Thrust Performance Optimization Method for UAVs Based on the Adaptive Margin Control Approach" *Mathematics* 11, no. 5: 1176.
https://doi.org/10.3390/math11051176