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1. 南京航空航天大学直升机旋翼动力学国家级重点实验室, 南京 210016;
2. 清华大学航天航空学院, 北京 100084

LADRC-based attitude decoupling control for helicopter and parameters tuning
WU Chao1, WANG Haowen2, JIANG Chen2, ZHANG Yuwen2, NI Xianping1
1. National Key Laboratory of Science and Technology on Rotorcraft Aeromechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
Abstract: To meet the ADS-33E-PRF flight quality and effectively overcome the influence of external disturbance, an attitude control strategy based on a linear active disturbance rejection control (LADRC) is proposed for helicopter. Flight dynamics model of UH-60A and the wind model were established. UH-60A was trimmed for verifying accuracy of dynamic model and trim algorithm. Helicopter attitude decoupling control loop based on the single input/single output second-order LADRC controller was set up with stabilization feedback loop. The controller parameter tuning problem was transformed into constrained optimization problem in time and frequency domain according to quality requirement of ADS-33E-PRF. Combining H-infinity synthesis algorithm and steepest descent algorithm, the optimization of parameters was calculated. Quality assessment of attitude control was made and the control loop was applied to the attitude hold control simulation in atmospheric disturbance. The results of simulation and quality evaluation show that the attitude control system based on LADRC has good decoupling performance and capability of anti-disturbance.
Key words: helicopter     attitude decoupling     parameters tuning     linear active disturbance rejection     flight quality

1 飞行动力学模型

1.1 各部件动力学模型 1.1.1 旋翼动力学模型

1.1.2 尾桨动力学模型

1.1.3 平尾、垂尾和机身动力学模型

1.2 全机飞行动力学模型

1.3 风 模 型

2 配平和线性化

 图 1 配平结果曲线 Fig. 1 Curves of trim results

 飞行参数 数值 V/(m·s-1) [10 -0.017 0.451]T W/(rad·s-1) [0 0 0]T α/rad [-0.038 0.045 0]T a/rad [0.056 0.006 -0.016]T U/% [5.50 -0.232 -0.183 -1.48]T

3 姿态解耦控制器的设计

X1=α,X2=W,Xr为其余状态向量,Xa=[δ1s δ1c δ0TR]T,则式(6)和式(7)可表示为

 图 3 带反馈内回路的姿态控制器 Fig. 3 Attitude controller with inner feedback loop

3.3 参数整定

f$\phi$fθfψ为3个通道阶跃响应的误差平方和；N为采样点数.为满足ADS-33E-PRF[24]规定的飞行品质需求,本文将飞行品质要求引入作为约束函数.由于本文的基准状态为小速度前飞,因此对悬停和小速度所规定的飞行品质指标进行了剪裁,选取以下5个约束:

1) 稳定性约束st.1.

2) 3个通道带宽约束st.2.

 图 4 带宽一级飞行品质边界线 Fig. 4 Border lines for bandwidth flight quality 1

3) 俯仰和滚转耦合约束st.3.

4) 快捷性约束st.4.

 图 5 快捷性一级飞行品质边界线 Fig. 5 Border lines for quickness flight quality 1

5) 抗干扰约束st.5.

1) 调入上述计算的参数初值,给定终止误差ε=1×10-5,k=0.

2) 计算梯度$\nabla {f_n}\left( {{x^k}} \right)$,若$\nabla {f_n}\left( {{x^k}} \right) \le \varepsilon$,迭代结束,输出xk,否则进入步骤3).

3) 对${f_n} = \left( {{x^k} + {t_k}{p^k}} \right) = \min {f_n}\left( {{x^k} + t{p^k}} \right)$进行一维寻优,求解tk,其中${p^k} = - \nabla {f_n}\left( {{x^k}} \right),t > 0$.

4) 计算${x^{k + 1}} = {x^k} + {t_k}{p^k}$,令k=k+1,返回步骤2).

3.4 计算结果与品质评估

 控制器 k1 ωo k2 bi,0
 $\phi$LADRC 74.24 6.8 3.01 0.54 θLADRC 29.27 7.33 4.23 1.28 ψLADRC 40.83 6.47 3.57 0.52

1) 特征值位置.

 图 6 闭环系统特征值 Fig. 6 Eigenvalues of closed-loop system

2) 带宽和延迟.

 图 7 滚转通道频响 Fig. 7 Frequency response of roll channel

 图 8 俯仰通道频响 Fig. 8 Frequency response of pitch channel

 图 9 偏航通道频响 Fig. 9 Frequency response of yaw channel

3) 俯仰和滚转耦合.

 图 10 滚转通道阶跃输入下的耦合 Fig. 10 Coupling effects with a step input of roll channel

 图 11 俯仰通道阶跃输入下的耦合 Fig. 11 Coupling effects with a step input of pitch channel

4) 快捷性.

 图 12 滚转通道尖峰输入响应 Fig. 12 Spike input response of roll channel

 图 13 俯仰通道尖峰输入响应 Fig. 13 Spike input response of pitch channel

 图 14 偏航通道尖峰输入响应 Fig. 14 Spike input response of yaw channel

5) 抗干扰性.

 图 15 非线性动力学的姿态控制器 Fig. 15 Attitude controller for nonlinear dynamics

 图 16 地面坐标系下的风扰动 Fig. 16 Wind disturbance in ground coordinate system

 图 17 风扰下的姿态保持 Fig. 17 Attitude hold with wind disturbance

 图 18 姿态控制器飞行品质评估结果汇总 Fig. 18 Summary of flight quality evaluation results for attitude controller

4 结 论

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#### 文章信息

WU Chao, WANG Haowen, JIANG Chen, ZHANG Yuwen, NI Xianping

LADRC-based attitude decoupling control for helicopter and parameters tuning

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(11): 2085-2094.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0710