Identification of flight dynamics models of a small-scale unmanned helicopter in hover condition
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摘要:
为了更好地研究小型无人直升机悬停状态动力学特性，对一个8.1 kg三轴陀螺仪增稳的电动直升机，从线性系统辨识方面及非线性建模方面，进行了动力学模型深入研究。在线性系统辨识过程中，应用频域辨识方法，在飞行中同时采集陀螺仪之前及之后的操纵数据进行双系统辨识。在非线性建模过程中，机体、旋翼及尾桨动力学被分别建模。尾桨动力学应用3阶段辨识法单独提取基底、陀螺仪及整体增稳模型。结合2种分析过程，应用非线性-线性模型结合修正方法，提高相互的仿真精度。结果表明：13阶高阶模型在线性辨识过程中相对比11阶模型表现更优；双系统线性模型的基底模型数据具有高质量高频特性，最高频率限制可达30 rad/s；除挥舞方程参数和尾桨参数以外，非线性数学模型（NMM）进行了7个非线性变量的修正，有效地拟合了悬停实验数据。
Abstract:In order to better study the hover dynamics characteristics of small-scale unmanned helicopter, the in-depth dynamics model analysis of linear system identification and nonlinear modeling was conducted in this paper on an 8.1 kg electric helicopter with 3-axis gyro augmentation. In the linear system identification procedure, frequency-domain identification method was adopted. Double systems were obtained by using command signals from both before and after the gyro part. In the nonlinear modeling procedure, body dynamics, rotor dynamics, and tail rotor dynamics were modeled separately. The tail rotor dynamics utilized 3-stage identification method to extract the base model, the gyro model, and the overall model. A nonlinear-linear combined modification method was decided for improving the models' performance. The results show that the 13-state high-order model has higher simulation accuracy compared with the 11-state model. The flight data of the helicopter's base model for dual system linear model has high quality in high-frequency domain, and the maximum frequency is 30 rad/s. Apart from the flapping equation parameters and tail rotor parameters, the combined modification method got 7 parameters of the nonlinear mathematical model (NMM) corrected, which fits the experimental hover data effectively.
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图 4 Model A 13阶高阶模型频域辨识结果与悬停实验数据对比
Figure 4. Comparison of frequency-domain identification results of 13-state high-order model with experimental hover data for Model A
图 5 Model B 13阶高阶模型频域辨识结果与悬停实验数据对比
Figure 5. Comparison of frequency-domain identification results of 13-state high-order model with experimental hover data for Model B
图 6 Model A 13阶高阶模型时域仿真结果与悬停实验数据对比
Figure 6. Comparison of time-domain simulation results of 13-state high-order model with experimental hover data for Model A
图 7 Model B 13阶高阶模型时域仿真结果与悬停实验数据对比
Figure 7. Comparison of time-domain simulation results of 13-state high-order model with experimental hover data for Model B
表 1 JR700与3种小型无人直升机结构参数对比
Table 1. JR700 structural parameters compared with three kinds of small-scale unmanned helicopters
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表 2 JR700悬停纵横向耦合模型辨识结果
Table 2. Identified results of coupled roll-pitch model for JR700 in hover condition
参数 Model A Model B 数值 CR(Cramer-Rao)/% 敏感度/% 数值 CR(Cramer-Rao)/% 敏感度/% τf 0.078 41 10.01 0.895 9 0.055 95 8.32 1.066 Ma 195.10 11.54 2.248 440.4 6.59 2.656 Lb 224.12 20.05 2.010 740.2 5.765 2.521 Ba 0.275 6 10.44 2.241 0.252 2 17.47 8.066 Ab 0.275 6 0.252 2 Aδlat 0.034 64 11.88 2.444 0.083 12 9.017 2.165 Aδlon 0.386 3 8.710 1.693 0.446 2 8.122 1.962 Bδlat 0.407 4 9.563 1.538 0.508 9 7.983 1.859 Bδlon -0.042 43 14.75 3.415 -0.093 63 9.941 2.373 价值函数 107.092 29.686 5
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表 3 13阶IDM悬停辨识参数
Table 3. Identified parameters in 13-state IDM in hover condition
参数 Model A Model B 数值 CR/% 敏感度/% 数值 CR/% 敏感度/% τf 0.071 30 7.425 0.681 8 0.055 60 8.204 0.856 0 Xu -0.060 20c -0.060 20c Xa -9.8a -9.8a Yv -0.142 0c -0.142 0c Yb 9.8a 9.8a Zw -1.714 12.09 5.473 -1.714 12.67 5.795 Mu 0.037 10a 0.045 80a Mv -0.001 62a -0.004 42a Ma 191.3 6.422 1.714 448.4 7.465 3.006 Lu -0.002 21a -0.002 81a Lv -0.102 2a -0.158 0a Lb 237.2 6.753 1.735 740.9 5.905 2.530 Nr 0.409 3 19.85 5.892 -1.084 28.2 13.47 Kxr -403.70 21.23 1.779 Kxx -20.47 15.36 1.965 Ba -0.426 6 4.567 1.425 0.208 6 20.03 9.650 Ab -0.426 6 0.208 6 Aδlat 0.025 47 7.875 2.553 -0.032 70 24.62 5.610 Aδlon -0.343 2 6.999 1.430 -0.456 8 7.78 1.78 Bδlat 0.391 3 7.242 1.094 0.504 6 8.011 1.655 Bδlon -0.021 31 23.06 7.520 -0.053 30 18.46 4.161 Zδcol -45.87 4.251 1.925 -45.87 4.253 1.944 Nδcol -10.58 19.93 9.765 0b Nδped 176.01 11.47 1.874 75.28 2.844 3.778 价值函数 49.098 9 39.907 8 注：上标a表示理论值；b表示由模型结构考虑移除的参数；c表示单独辨识参数并在模型中固定不变。
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表 4 NMM主要修正参数
Table 4. Main modified parameters in NMM
参数 数值 a0 5.75 Kcol 0.293 2 Kβ 160.57 Ixx 0.396 Iyy 0.653 ΔXu -0.041 ΔYv -0.048 5
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表 5 JR700悬停模型与3种小型无人直升机主要参数对比
Table 5. JR700 key parameters compared with three kinds of small-scale unmanned helicopter in hover model
参数 JR700 13阶 Raptor 50 X-cell HeLion Model A Model B τf 0.071 30 0.055 60 0.043 0.052 τs+τf 0.127 0.272 0.299 Lb 237.2 740.9 735.5 320 583.5 Ma 191.3 448.4 228 204 265.3 Aδlat 0.025 47 -0.032 70 0.008 9a 0 0 Aδlon -0.343 2 -0.456 8 -0.242 2a -0.53a -0.42a Bδlat 0.391 3 0.504 6 0.031 5a 0.42a 0.4a Bδlon -0.021 31 -0.053 30 -0.011 2a 0 0 注：上标a表示原始数值[3, 7-8]按本文单位标准换算。
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表 6 JR700悬停模型主要特征值与模态
Table 6. Main eigenvalues and modes of JR700 hover model
模态 13阶Model A 13阶Model B 俯仰耦合模态 [0.673 7, 14.666 0] [0.426 1, 21.621 4] 滚转耦合模态 [0.285 9, 14.593 5] [0.328 8, 26.942 2] 航向模态 [0.504 5, 19.883 2] (-1.084 0) 垂向模态 (-1.713 6) (-1.713 6) 纵向速度模态 [0.257 8, 0.139 7] [0.357 6, 0.192 2] 横向速度模态 [0.240 8, 0.256 6] [0.239 0, 0.131 9]
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