# A Thrust Cooperative Control Strategy of Multiple Propulsion Motors for Distributed Electric Propulsion Aircraft

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Thrust Cooperative Control Strategy

#### 2.1. Synchronous Cooperative Control Strategy

#### 2.1.1. Relative Coupling Control

_{ref}represents the given speed of all motors, and its value is provided by the aircraft control system. In this paper, it is assumed that its value is known and remains unchanged. T

_{Li}represents the load torque of each motor, n

_{i}represents the actual speed of each motor, and y

_{i}represents the compensated speed of each motor output by the speed compensator. It can be seen from Figure 2 that the speed compensator module is the key part of the relative coupling control. Taking speed compensator 1 as an example, the structure of this module is shown in Figure 3.

_{i}represents the speed proportional factor of motor i. When each motor works at the same speed, the value of λ is 1. k

_{ij}is the feedback gain coefficient to compensate the difference of moment of inertia between the motor i and the motor j. The value can be expressed as:

_{ij}is 1.

#### 2.1.2. Improved Relative Coupling Control

_{v}and k

_{a}represent the velocity compensation coefficient and acceleration compensation coefficient respectively, and n

_{erm}represents the speed of the motor with the largest error from the given speed. However, excessive compensation will affect the stability of the system, so it is necessary to reasonably select the values of k

_{v}and k

_{a}.

#### 2.2. Distributed Cooperative Control Strategy

_{i}[20], so as to calculate the steering angular velocity by Equation (8):

^{T}, then the compensation speed of motor i output by the speed distributor can be obtained by Equation (10):

_{1}, L

_{2}, L

_{3}, and L

_{4}of the coefficient matrix shall be selected according to the position of the fuselage where each propulsion motor is located.

## 3. Results

#### 3.1. Simulation Verification

_{ref}. The load simulation motor is coaxially connected with the propulsion motor to simulate the load characteristics of the propeller. The electric energy generated by the load simulation motors is transmitted to a 540 V DC bus. Key parameters are shown in Table 2.

#### 3.1.1. Simulation of Synchronous Cooperative Control

#### 3.1.2. Simulation of Distributed Cooperative Control

#### 3.2. Experimental Verification

#### 3.2.1. Experiment of Synchronous Cooperative Control

#### 3.2.2. Experiment of Distributed Cooperative Control

## 4. Conclusions

- The proposed SCCS in this paper can not only be applied to the system with more than two motors, but also has stronger synchronization performance than the relative coupling control. In this way, it can ensure that the airplane will not yaw due to the inconsistency of left and right thrust when flying in a straight line.
- The proposed DCCS can make the airplane realize yaw control without relying on ailerons or vectoring nozzles, but by adjusting the speeds of motors on both sides. Thus, the mechanical structure of the airplane is simplified.
- The combination of the two control strategies can realize the straight-line flight and yaw control of the airplane.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Variables | Definitions |
---|---|

${n}_{ref}$ | given speed of all motors |

${n}_{i}$ | actual speed of motor i |

${n}_{i}^{*}$ | given speed after compensation of motor i |

Δn | output value of yaw angle controller |

Δ ${n}_{i}$ | compensation speed of motor i output by the speed distributor |

n_{erm} | maximum speed synchronization error |

${y}_{i}$ | speed compensator output of motor i |

${e}_{id}$ | improved speed compensator output of motor i |

T_{Li} | load torque of motor i |

${a}_{i}$ | acceleration of motor i |

λ_{i} | speed proportional factor of motor i |

k_{ij} | feedback gain coefficient |

${J}_{i}$ | moment of inertia of motor i |

k_{v} | velocity compensation coefficient |

k_{a} | acceleration compensation coefficient |

$\omega $ | steering angular velocity of the aircraft |

$B$ | steering moment of inertia of the aircraft |

M | yaw moment of the aircraft |

$\theta $* | given yaw angle |

$\theta $ | actual yaw angle |

F_{i} | thrust output of propeller i |

Parameters | Values |
---|---|

bus voltage | 270 V |

rated speed of motors | 2000 rpm |

rated power of motors | 15 kW |

flux linkage of permanent magnet | 0.1225 Wb |

quadrature axis inductance | 0.8 mH |

direct axis inductance | 0.8 mH |

moment of inertia of propulsion motors | 0.008 kg∙m^{2} |

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**MDPI and ACS Style**

Weng, L.; Zhang, X.; Yao, T.; Bu, F.; Li, H.
A Thrust Cooperative Control Strategy of Multiple Propulsion Motors for Distributed Electric Propulsion Aircraft. *World Electr. Veh. J.* **2021**, *12*, 199.
https://doi.org/10.3390/wevj12040199

**AMA Style**

Weng L, Zhang X, Yao T, Bu F, Li H.
A Thrust Cooperative Control Strategy of Multiple Propulsion Motors for Distributed Electric Propulsion Aircraft. *World Electric Vehicle Journal*. 2021; 12(4):199.
https://doi.org/10.3390/wevj12040199

**Chicago/Turabian Style**

Weng, Luhui, Xuan Zhang, Taike Yao, Feifei Bu, and Hang Li.
2021. "A Thrust Cooperative Control Strategy of Multiple Propulsion Motors for Distributed Electric Propulsion Aircraft" *World Electric Vehicle Journal* 12, no. 4: 199.
https://doi.org/10.3390/wevj12040199