Research on seakeeping of unmanned hydrofoil based on LQR and ZOA
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摘要: 文中选取横摇、纵摇和垂荡运动幅值为衡量耐波性的指标, 采用线性二次型调节器(LQR), 并用斑马优化算法(ZOA)优化LQR控制器参数, 完成了无人水面水翼航行器耐波性研究。首先, 以无人水翼航行器为研究对象, 以差动襟翼转动角度和电机推力作为控制变量, 建立其运动学与动力学模型, 并将数学模型进行线性化处理; 然后将不规则海浪的质点垂加速度与波倾角作为干扰, 采用Simulink进行LQR控制器仿真; 以降低无人水翼航行器航行过程中的运动幅值为目标, 在不同采样频率及种群数量下, 分别使用ZOA和粒子群算法对LQR控制器的参数进行寻优并作对比; 最后在不同遭遇角的随机海浪干扰下对耐波性指标进行仿真分析, 验证LQR和ZOA方法有效性与可行性, 并给出水翼航行器的合理航向角, 为无人水翼航行器的姿态控制及耐波性研究提供理论参考。Abstract: In this paper, the motion amplitudes of roll, pitch and heave were selected as the indexes to measure seakeeping. LQR controller was adopted, and the parameters of LQR controller were optimized by ZOA. Firstly, the kinematics and dynamics models of unmanned hydrofoil were established with the differential flap rotation angle and motor thrust as the control variables, and the mathematical models were linearized. Then, the particle vertical acceleration and wave angle of irregular waves were taken as interference, and LQR controller simulation was carried out by Simulink. The objective was to reduce the motion amplitude of unmanned hydrofoil during navigation, and the parameters of LQR controller are optimized and compared by ZOA and PSO optimization algorithms respectively under different sampling frequencies and population numbers. Finally, the seakeeping index is simulated under the random wave interference of different encounter angles to verify the effectiveness and feasibility of LQR and ZOA methods, and to give the reasonable heading Angle of the outwater wing vehicle, which provides a theoretical reference for the attitude control and seakeeping research of the unmanned hydrofoil vehicle.
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图 5 水翼航行器运动建模仿真框图
Figure 5. Motion modeling and simulation block diagram of hydrofoil vehicle
图 7 在遭遇角为0°、30°、45°、60°、90°时两种算法优化对比
Figure 7. Optimization comparison between the two algorithms when the encounter angle is 0°, 30°, 45°, 60° and 90°
表 1 航行器结构参数
Table 1. Structure parameters of the vehicle
参数 数值 航行器质量m/kg 5.39×10 重力加速度g/m·s−2 9.80 航行器绕ObXb的转动惯量Ixx/kg·m2 8.71 前翼翼展l1/m 7.54×10−1 前翼翼弦b1/m 1.47×10−1 后翼翼展l2/m 4.75×10−1 后翼翼弦b2/m 9.00×10−2 前翼升力点到重心的横向距离lx1/m 2.57×10−1 后翼升力点到重心的横向距离lx2/m 8.57×10−1 横摇阻尼系数Nφ 5.48×10−2 表层海水密度ρ/kg·m-3 1.02×103 横稳心高h/m 1.11 
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表 2 目标函数最优值
Table 2. Optimal value of objective function
遭遇角 0° 30° 45° 60° 90° 最优值 0.266 0.264 0.263 0.257 0.271
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