# Simulation and Control Design of a Midrange WPT Charging System for In-Flight Drones

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

- The development of the modeling methodology for wireless dynamic charging systems by integrating the receiver trajectory and velocity in the model.
- Introducing the concept of the positioning mutual coupling function for the receiver trajectory; thus, it is possible to simulate a genuine continuous trajectory for UAVs and link it to the systems’ total input power consumption.
- As a consequence, the control design phase based on the developed comprehensive model is enhanced significantly.
- The development of a multiparameter discrete ESC algorithm for a 3D omnidirectional WPT system to perform real-time magnetic tracking for the drone’s hovering trajectory to maximize the power transfer.

## 3. System Modeling

#### 3.1. The Derivation of the Time-Variant Mutual Coupling Functions for a Hovering Drone Trajectory

_{x}, M

_{y}and M

_{z}for the coils X, Y and Z, respectively, resulting in three mutual coupling functions: Fx, Fy and Fz.

_{z}unlike the remaining two, M

_{x}and M

_{y}.

_{x}represented in black stars contains the Ansys simulation results, as mentioned earlier, whereas the red line is the calculated mutual coupling function for the coil X. We can notice how the mutual coupling values of M

_{x}are growing exponentially along the whole time period, while the oscillation occurs between 1.5 and 2 s. Thus, we can assume the existence of a function Fx which consists of an exponential and sinusoidal combination that can represent a good fit for the dataset M

_{x}. Similarly, for Figure 2b, the mutual coupling values of M

_{y}for the coil Y represented in the green line have the same pattern as M

_{x}with a slight phase shift in the oscillation, while the blue line in Figure 2c represents the M

_{z}dataset for the coil Z.

_{x}, a

_{x}, B

_{x}, b

_{x}………b

_{z}of the three mutual coupling functions in (2) are optimized using the nonlinear least squares method to enhance the fit goodness. The red, green and blue curves in Figure 2 represent the calculated mutual coupling functions in Equation (2) for the coils X, Y and Z, respectively, while the black dotted curves represent the dataset of the mutual coupling values simulated by ANSYS software: M

_{x}, M

_{y}, and M

_{z}.

#### 3.2. The System’s Input Power Formula

_{x}, L

_{y}, and L

_{z}, respectively, while the receiving coil is represented by the drone drawing, as shown in Figure 1, and its self-inductance value is L

_{λ}.

_{x}, C

_{y}, and C

_{z}in series with the coils’ resistors R

_{x}, R

_{y}and R

_{z}, while the receiver’s capacitor and self-resistor are C

_{λ}and R

_{λ}. Figure 3 depicts the electrical circuit for the 3DWPT system.

_{x}, i

_{y}, i

_{z}and i

_{λ}, respectively. Meanwhile, M

_{x}, M

_{y}, and M

_{z}are the mutual inductance values between the receiver and the transmitting coils X, Y and Z, respectively. All three transmitting coils are connected to a common DC source through a full-bridge MOSFET inverter, which is used in the current amplitude’s modeling.

_{x}, B

_{y}and B

_{z}produced by the current i

_{x}, i

_{y}, i

_{z}flowing on the coils X, Y, and Z, respectively, while θ and β are the magnetic angles which direct the magnetic field resultant B in the spherical coordinates. On the other hand, Figure 4b represents the drone’s position spherical coordinates. By taking the original of the plane as the center of the three orthogonal coils, α and ϕ are the azimuthal angle and the elevation angle of the drone’s position, while d is the distance between the plane origin and the drone. It is clear from Figure 4 that if we render the values of the magnetic angles equal to the position angles, it is possible to direct the magnetic field resultant to the exact location of the drone, hence maximizing the wireless power transfer efficiency.

## 4. The Extremum-Seeking Control Implementation for the 3DWPT System

## 5. External Mode Simulation Results

#### 5.1. The ESC Step Response for a Static Position

#### 5.2. The ESC Power Maximization for a Drone-Hovering Movement

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, H.; Gao, S.-P.; Ngo, T.; Wu, W.; Guo, Y.-X. Wireless Power Transfer Antenna Alignment Using Intermodulation for Two-Tone Powered Implantable Medical Devices. IEEE Trans. Microw. Theory Tech.
**2019**, 67, 1708–1716. [Google Scholar] [CrossRef] - Khalil, H.; Rahman, S.U.; Ullah, I.; Khan, I.; Alghadhban, A.J.; Al-Adhaileh, M.H.; Ali, G.; ElAffendi, M. A UAV-Swarm-Communication Model Using a Machine-Learning Approach for Search-and-Rescue Applications. Drones
**2022**, 6, 372. [Google Scholar] [CrossRef] - Anyapo, C.; Intani, P. Wireless Power Transfer for Autonomous Underwater Vehicle. In Proceedings of the 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), Seoul, Republic of Korea, 15–19 November 2020; pp. 246–249. [Google Scholar]
- Yu, L.; Wu, L.; Zhu, Y.; Cao, X.; Zhang, G.; Xiang, S. Wireless Charging Concave Coil Design for UAVs. Electronics
**2022**, 11, 1962. [Google Scholar] [CrossRef] - Hu, Y.H.; Yuan, X.; Zhang, G.; Schmeink, A. Sustainable wireless sensor networks with UAV-enabled wireless power transfer. IEEE Trans. Veh. Technol.
**2021**, 70, 8050–8064. [Google Scholar] [CrossRef] - Chai, W.; Zhang, H.; Wu, S.; Cai, C. Design of two orthogonal transmitters with double L-type ferrite for the Wireless Charging System in Unmanned Aerial Vehicles. IEEE Trans. Transp. Electrif.
**2022**, 9, 1985–1992. [Google Scholar] [CrossRef] - Bie, Z.; Zhang, J.; Song, K.; Zhu, C. A free-rotation asymmetric magnetic coupling structure of UAV wirelesscharging platform with conformal pickup. IEEE Trans. Ind. Electron.
**2022**, 69, 10154–10161. [Google Scholar] [CrossRef] - Arteaga, J.M.; Aldhaher, S.; Kkelis, G.; Kwan, C.; Yates, D.C.; Mitcheson, P.D. Dynamic capabilities of multi-MHz inductive power transfer systems demonstrated with batteryless drones. IEEE Trans. Power Electron.
**2019**, 34, 5093–5104. [Google Scholar] [CrossRef] - Aldhaher, S.; Mitcheson, P.D.; Arteaga, J.M.; Kkelis, G.; Yates, D.C. Light-weight wireless power transfer for mid-air charging of drones. In Proceedings of the 2017 11th European Conference on Antennas and Propagation (EUCAP), Paris, France, 19–24 March 2017; pp. 336–340. [Google Scholar]
- Shi, K.; Tang, C.; Wang, Z.; Li, X.; Zhou, Y.; Fei, Y. A magnetic integrated method suppressing power fluctuation for EV dynamic wireless charging system. IEEE Trans. Power Electron.
**2022**, 37, 7493–7503. [Google Scholar] [CrossRef] - Qi, C.; Yang, F.; Duan, H.; Zhang, J. An Omnidirectional WPT System Based on Three-Phase Frustum-shaped Coils. In Proceedings of the IECON 2022–48th Annual Conference of the IEEE Industrial Electronics Society, Brussels, Belgium, 17–20 October 2022; IEEE: Toulouse, France; pp. 1–6. [Google Scholar]
- Zhou, J.; Zhang, B.; Xiao, W.; Qiu, D.; Chen, Y. Nonlinear paritytime-symmetric model for constant efficiency wireless power transfer: Application to a drone-in-flight wireless charging platform. IEEE Trans. Ind. Electron.
**2019**, 66, 4097–4107. [Google Scholar] [CrossRef] - Wang, J.; Chen, R.; Cai, C.; Zhang, J.; Wang, C. An Onboard Magnetic Integration-Based WPT System for UAV Misalignment-Tolerant Charging With Constant Current Output. IEEE Trans. Transp. Electrif.
**2023**, 9, 1973–1984. [Google Scholar] [CrossRef] - Wu, S.; Cai, C.; Liu, X.; Chai, W.; Yang, S. Compact and Free-Positioning Omnidirectional Wireless Power Transfer System for Unmanned Aerial Vehicle Charging Applications. IEEE Trans. Power Electron.
**2022**, 37, 8790–8794. [Google Scholar] [CrossRef] - Saviolo, A.; Mao, J.; TMB, R.B.; Radhakrishnan, V.; Loianno, G. AutoCharge: Autonomous Charging for Perpetual Quadrotor Missions. In Proceedings of the 2023 IEEE International Conference on Robotics and Automation (ICRA), London, UK, 29 May–2 June 2023; pp. 5400–5406. Available online: https://ieeexplore.ieee.org/servlet/opac?punumber=10160211 (accessed on 20 June 2023).
- Wang, X.; Yu, C.; Wu, Y.; Wang, J. Structure Design of Quadrilateral Overlapped Wireless Power Transmission Coupling Coil. Sensors
**2022**, 22, 5955. [Google Scholar] [CrossRef] [PubMed] - Henriques, E.D.M.; Stegen, S. Concave Ferrite Core for Wireless Power Transfer (WPT). Energies
**2023**, 16, 4553. [Google Scholar] [CrossRef] - Kumar, N.; Puthal, D.; Theocharides, T.; Mohanty, S.P. Unmanned aerial vehicles in consumer applications: New applications in current and future smart environments. IEEE Consum. Electron. Mag.
**2019**, 8, 66–67. [Google Scholar] [CrossRef] - Zhang, H.; Chen, Y.; Jo, C.-H.; Park, S.-J.; Kim, D.-H. DC-link and switched capacitor control for varying coupling conditions in inductive power transfer system for unmanned aerial vehicles. IEEE Trans. Power Electron.
**2021**, 36, 5108–5120. [Google Scholar] [CrossRef] - Chittoor, P.K.; Chokkalingam, B.; Mihet-Popa, L. A review on UAV wireless charging: Fundamentals, applications, charging techniques and standards. IEEE Access
**2021**, 9, 69235–69266. [Google Scholar] [CrossRef] - Feng, T.; Sun, Y.; Zuo, Z.; Wang, Z.; Dai, X. Magnetic field analysis and excitation currents optimization for an omnidirectional WPT system based on three-phase tubular coils. IEEE Trans. Ind. Appl.
**2021**, 58, 1268–1278. [Google Scholar] [CrossRef] - Yu, X.; Feng, J.; Li, Q. A Planar Omnidirectional Wireless Power Transfer Platform for Portable Devices. In Proceedings of the 2023 IEEE Applied Power Electronics Conference and Exposition (APEC), Orlando, FL, USA, 19–23 March 2023; pp. 1654–1661. [Google Scholar] [CrossRef]
- Tian, X.; Chau, K.T.; Liu, W.; Pang, H.; Lee, C.H.T. Maximum Power Tracking for Magnetic Field Editing-Based Omnidirectional Wireless Power Transfer. IEEE Trans. Power Electron.
**2022**, 37, 12901–12912. [Google Scholar] [CrossRef] - Feng, T.; Zuo, Z.; Sun, Y.; Dai, X.; Wu, X.; Zhu, L. A Reticulated Planar Transmitter Using a Three-Dimensional Rotating Magnetic Field for Free-Positioning Omnidirectional Wireless Power Transfer. IEEE Trans. Power Electron.
**2022**, 37, 9999–10015. [Google Scholar] [CrossRef] - Dang, X.; Jayathurathnage, P.; Liu, F.; Al Mahmud, S.A.; Simovski, C.R.; Tretyakov, S.A. High-Efficiency Omnidirectional Wireless Power Transfer System. IEEE J. Emerg. Sel. Top. Ind. Electron.
**2022**, 3, 403–410. [Google Scholar] [CrossRef] - Gu, Y.; Wang, J.; Liang, Z.; Zhang, Z. Mutual-Inductance-Dynamic-Predicted Constant Current Control of LCC-P Compensation Network for Drone Wireless In-Flight Charging. IEEE Trans. Ind. Electron.
**2022**, 69, 12710–12719. [Google Scholar] [CrossRef] - Yilmaz, S.; Furat, M. A real-time cost optimization of two-section oven system with discrete gradient extremum seeking control: An experimental study in iron and steel industry. J. Process Control
**2023**, 122, 84–99. [Google Scholar] [CrossRef] - Ng, W.M.; Zhang, C.; Lin, D.; Hui, S.Y.R. Two- and Three-Dimensional Omnidirectional Wireless Power Transfer. IEEE Trans. Power Electron.
**2014**, 29, 4470–4474. [Google Scholar] [CrossRef] [Green Version] - Zhang, C.; Lin, D.; Hui, S.Y. Basic control principles of omnidirectional wireless power transfer. IEEE Trans. Power Electron.
**2015**, 31, 5215–5227. [Google Scholar] - Ariyur, K.B.; Krstic, M. Real-Time Optimization by Extremum-Seeking Control; John Wiley & Sons: New York, NY, USA, 2003. [Google Scholar]

**Figure 2.**The mutual coupling curve fitting process of the 3D WPT system: (

**a**) The predicted mutual coupling function Fx versus M

_{x}; (

**b**) The predicted mutual coupling function Fy versus M

_{y}; (

**c**) The predicted mutual coupling function Fz versus M

_{z}.

**Figure 4.**The mutual coupling curve fitting process of the 3D WPT system: (

**a**) The magnetic angles for the 3DWPT system; (

**b**) The drone’s position angles.

**Figure 10.**The ESC tracking process when the drone steps in the trajectory Γ: (

**a**) the closed-loop step response for the magnetic azimuthal angle α°; (

**b**) the closed-loop step response for the magnetic elevation angle ϕ°.

**Figure 13.**Magnetic tracking for the drone-hovering trajectory Γ: (

**a**) Tracking process for the magnetic azimuthal angle; (

**b**) Tracking process for the magnetic elevation angle.

The Mutual Coupling Functions | The Sum of Squared Errors (SSE) | R-Squared | Adjusted R-Squared | Root Mean Squared Error (RMSE) |
---|---|---|---|---|

${F}_{x}(t)$ | 2.755 × 10^{−12} | 0.9888 | 0.9888 | 1.174 × 10^{−7} |

${F}_{y}(t)$ | 5.639 × 10^{−13} | 0.9978 | 0.9978 | 5.31 × 10^{−8} |

${F}_{z}(t)$ | 2.522 × 10^{−13} | 0.9991 | 0.9991 | 3.578 × 10^{−8} |

Parameters | Ref. [20] | Ref. [21] | This Work |
---|---|---|---|

System | 3D-Omnidirectional WPT | Planar WPT | 3D-Omnidirectional WPT |

Coil structure | Six orthogonal coils | One planar coil | Three orthogonal coils |

Control method | phase-lock-loop | PI Controller | ESC |

Receiver dynamics | Not provided | Not provided | Continuous 3D trajectory |

Tracking response time | Not provided | 320 ms | 2 ms |

The receiver velocity | Not provided | Not provided | 8 m/s |

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**

Allama, O.; Habaebi, M.H.; Khan, S.; Islam, M.R.; Alghaihab, A.
Simulation and Control Design of a Midrange WPT Charging System for In-Flight Drones. *Energies* **2023**, *16*, 5746.
https://doi.org/10.3390/en16155746

**AMA Style**

Allama O, Habaebi MH, Khan S, Islam MR, Alghaihab A.
Simulation and Control Design of a Midrange WPT Charging System for In-Flight Drones. *Energies*. 2023; 16(15):5746.
https://doi.org/10.3390/en16155746

**Chicago/Turabian Style**

Allama, Oussama, Mohamed Hadi Habaebi, Sheroz Khan, Md. Rafiqul Islam, and Abdullah Alghaihab.
2023. "Simulation and Control Design of a Midrange WPT Charging System for In-Flight Drones" *Energies* 16, no. 15: 5746.
https://doi.org/10.3390/en16155746