﻿ 基于混合遗传算法的直升机前推/后拉配平<sup>*</sup>
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1. 沈阳航空航天大学 航空制造工艺数字化国防重点学科实验室, 沈阳 110136;
2. 北京航空航天大学 机械工程及自动化学院, 北京 100083

Push-forward/pull-backward trim for helicopter based on hybrid genetic algorithm
WANG Wei1, LIU Chun1, LI Dongsheng2
1. Key Laboratory of Fundamental Science for National Defense of Aeronautical Digital Manufacturing Process, Shenyang Aerospace University, Shenyang 110136, China;
2. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-10-27; Accepted: 2017-02-06; Published online: 2017-03-24 10:25
Foundation item: Key Laboratory of National Defense Open Foundation of Shenyang Aerospace University (SHSYS2015004)
Corresponding author. WANG Wei, E-mail: wangwei7832@163.com
Abstract: To solve the problems that helicopter trim model has multivariate nonlinear equations, it is difficult to determine its initial value and the global optimal solution is non-unique, an efficient hybrid iteration algorithm is presented in this paper, which combines the genetic algorithm and the quasi-Newton method. The dynamic equations of the different modules of the helicopter are introduced. In modeling the rotor, considering characteristics of the motion and control of the rotor in the actual flight environment, an aerodynamic model of rotor based on dynamic inflow and the blade element theory with the rotor trim is established. The trim control vector and the constraint equations for push-forward/pull-backward are deduced in detail based on helicopter flight dynamic model. Since the objective function is constructed, trim problems are transformed into optimal computation. UH-60A helicopter in the push-forward/pull-backward flight is trimmed, and the trim results are compared with flight test data. It is shown that the pull-backward results agree well with flight data, and there is the discrepancy between the push-forward results and flight data. The primary contribution to the discrepancy of the trim of collective and pedal comes from inaccurate prediction of the unsteady aerodynamic characteristics of the rotor. It is a universal method that can be applied to helicopter trim simulation of different stable flight conditions.
Key words: helicopter     flight simulation     trim     hybrid genetic algorithm     push-forward/pull-backward

1 数学模型 1.1 坐标系

 图 1 前推/后拉的配平状态 Fig. 1 Trim attitude of push-forward/pull-backward
1.2 旋翼模型

 (1)

 (2)

 (3)

 (4)

 (5)

1.3 尾桨模型

 (6)

 (7)
1.4 机身、平尾及垂尾模型

1.5 起落架模型

 (8)

1.6 全机重力模型

 (9)

1.7 全机动力学模型

 (10)
 (11)

 (12)

 (13)

 (14)

2 配平算法 2.1 配平过程

 (15)

 (16)

 (17)

 (18)

 (19)

 图 2 配平过程 Fig. 2 Trim process
2.2 最优化算法

 (20)

g(X)=0时，{X}为式(14) 的精确解。

 (21)

 (22)

k越小，新个体x1*就越接近旧个体x1，适应度低的个体既是最优个体，适应度高的个体遗传到下一代继续进行迭代计算。变异操作采用均匀变异(uniform mutation)来完成个体基因值的变异。

 图 3 混合遗传算法流程图 Fig. 3 Flowchart of hybrid genetic algorithm

3 实例验证

 (23)

δ=[0°, 0°, 10.4°, 2.1°, 0°, 20.5°]

δ′=[0.2°, －0.5°, 8.5°, 1.9°, －0.64°, 22.06°]

 图 4 目标函数迭代曲线 Fig. 4 Iterative curves of objective function

 图 5 加速度和角加速度配平结果(机体坐标系) Fig. 5 Trim results of acceleration and angular acceleration in body coordinate system

 图 6 旋翼功率配平结果 Fig. 6 Trim results of rotor power
 图 7 Euler配平结果(地球惯性坐标系) Fig. 7 Trim results of Euler angles in earth inertial coordinate system

 图 8 总距杆、横向周期变距杆、纵向周期变距杆及脚蹬配平结果 Fig. 8 Trim results of collective stick, lateral cycle stick, longitudinal cycle stick and pedal
4 结论

1) 建立的混合遗传算法能够快速、准确捕捉到直升机全机的配平最优解，满足直升机稳定前推/后拉飞行的约束条件。

2) 在前推阶段，突出的旋翼非定常特性是引起总距和脚蹬配平计算误差的主要原因；在后拉阶段，配平结果与飞行数据吻合较好。

3) 本文的配平算法通用性强，只要改变边界条件、约束方程和配平控制量，能够适用于不同飞行条件下的直升机配平仿真工作。

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#### 文章信息

WANG Wei, LIU Chun, LI Dongsheng

Push-forward/pull-backward trim for helicopter based on hybrid genetic algorithm

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(10): 1994-2002
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0834