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Heavy helicopter-slung-load coupling system flying qualities in closed-loop state
ZHU Xiaoyu , CAO Yihua , CAO Long
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-07-01; Accepted: 2015-10-30; Published online: 2016-01-18 16:42
Corresponding author. CAO Yihua, Tel: 010-82339537 E-mail: yihuacaobu@126.com
Abstract: Flying qualities of a heavy helicopter augmented with an automatic flight control system (AFCS) and flying with externally slung loads are investigated using the mathematical model of the CH-53A/D helicopter. A nonlinear dynamical model of helicopter-slung-load in closed-loop state was built based on single mass-point hypothesis and a control system model. Under this hypothesis, extra degrees of freedom and constraints were brought in by the consideration of the slung-load, which made the set of equations of motion increased to a 13-order one. The coupling system in closed-loop state was linearized under small-perturbed conditions. After this, the slung-load flight control response characteristics in both time and frequency domain were analyzed. The effect of slung-load mass, slung-load rope length and helicopter velocity on coupling system's flight quality was analyzed according to the handling qualities requirements for military rotorcraft indicated by ADS-33E. The final results show that the slung-load mass, slung-load rope length and helicopter velocity have varying degrees of impact on the time domain features and handling qualities of the coupling system.
Key words: helicopter     slung-load     closed-loop     flying qualities     control system

1 直升机-吊挂耦合系统闭环模型 1.1 直升机-吊挂耦合系统模型及小扰动线化

1.1.1 线性全量方程

 图 1 直升机体轴系与吊挂姿态角定义 Fig. 1 Definition of helicopter body reference frame and attitude angles of slung-load

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1.1.2 小扰动线化

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1.2 带控制系统的直升机-吊挂耦合系统模型

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MδuMξuMxLuMuu分别为控制变量[θom B1 A1 θot]TδξxLu相对应的系数矩阵。具体的矩阵形式为

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 吊挂绳长/m 吊挂物质量/t 俯仰通道 滚转通道 ωBW, θ/(rad·s-1) τp, θ/s ωBW, φ/(rad·s-1) τp, φ/s 60 4 0.402 3.8296 0.420 1.0749 40 4 0.574 5.4538 0.611 0.8943 无吊挂 0.442 0.1844 0.663 0.5389 注：ωBW, θ—俯仰通道带宽；τp, θ—俯仰通道相位延迟；ωBW，φ—滚转通道带宽；τp, φ—滚转通道相位延迟。

 图 2 俯仰通道伯德图 Fig. 2 Bode diagram of pitch channel
 图 3 滚转通道伯德图 Fig. 3 Bode diagram of roll channel

1)幅频特性的峰值Mr随绳长增加而增大，这意味着系统的平稳性随绳长增加而变差，阶跃响应的超调量也变大。而幅频响应峰值频率ωr随绳长增加而变小，这是由于绳长增加后，吊挂摆动的固有频率减小而造成的。2个算例中CH-53A/D的带宽均较小，意味着驾驶员可用的、距不稳定边界尚有适当余量的最大操纵频率较小。并且随着吊挂绳长的增加，俯仰通道和滚转通道的带宽均是减小的。这说明，吊挂的绳长越长，系统对阶跃输入的响应越慢，所需的调节时间越长。

2)对于相位滞后指标，表示驾驶员操纵频率接近相角穿越频率ωg时，直升机走向不稳定的快慢程度。2个算例的俯仰通道和滚转通道的指标数值均不小，说明相频曲线下降较快，直升机走向不稳定的趋势也较快，但与绳长的关系表现的并不明显。但滚转通道的相位滞后指标明显优于俯仰通道，说明直升机在滚转通道的飞行品质优于俯仰通道。无吊挂时，滚转通道带宽品质劣于俯仰通道，说明吊挂对俯仰通道的影响更严重。

2.2 轴间耦合特性分析

2.2.1 总距-偏航特性

 图 4 总距-偏航耦合品质指标算例 Fig. 4 Example of yaw due to collective coupling

2.2.2 滚转-俯仰耦合特性

 图 5 滚转-俯仰耦合品质指标算例 Fig. 5 Example of pitch due to roll coupling
2.3 垂直轴操纵功效

2.3.1 垂直轴操纵功效随吊挂质量变化

 图 6 垂直轴操纵功效随吊挂质量变化算例 Fig. 6 Example of vertical control power changing with slung-load mass

2.3.2 垂直轴操纵功效随前飞速度变化

 图 7 垂直轴操纵功效随前飞速度变化算例 Fig. 7 Example of vertical control power changing with velocity
3 结论

1)耦合系统的带宽随绳长增加而减小，平稳性随绳长增加而变差；阶跃响应的超调量也变大；幅频响应峰值频率ωr随绳长增加而变小；相位滞后指标随绳长变化不明显。综合来看绳长越短，耦合系统的时域特性越好，同时吊挂的引入对俯仰通道的相位滞后指标影响更严重。

2)对于轴间耦合特性来说，总距的操纵输入对偏航的角速度有一定影响；而相同的前飞速度和吊挂质量下，绳长对滚转-俯仰耦合品质的影响不大。

3)对于垂直轴操纵功效，随着吊挂质量增加，系统的垂直轴操纵功效品质等级变差；随着前飞速度增加，该项指标呈现先变差后变好的趋势；但同样的前飞速度和吊挂质量下，该项指标受绳长的影响并不明显。

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#### 文章信息

ZHU Xiaoyu, CAO Yihua, CAO Long

Heavy helicopter-slung-load coupling system flying qualities in closed-loop state

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(7): 1550-1556
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0442