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摘要:
针对在线轨迹实时规划算法，提出了一种基于虚拟域预测控制的轨迹跟踪方法。该方法采用多项式近似系统模型，引入虚拟路径及反动力解算方法，将时域转化为虚拟域，较在时域上近似模型的控制方法解耦效果好，实时性强。通过反动力学解算、非线性规划的输入设置可直接得到连续的控制量，相对于传统非线性预测控制的软约束的方法，从根本上保证了控制量的连续性。以拦截弹道导弹为背景，在初始状态量添加小扰动及末端条件改变的条件下，进行仿真验证。结果表明：与非线性反馈跟踪方法相比，曲线平滑，在遭遇点脱靶量、末端路径倾角及偏角误差较小，实时性同样可满足控制需求。
Abstract:A trajectory tracking method based on predictive control in the virtual domain is proposed for the algorithm of online real-time trajectory planning. The method uses polynomial approximate system model and introduces virtual path and inverse dynamics to convert time domain into virtual domain. Its advantage is that the decoupling effect is good and it takes less compute time than the control method of approximate model in the time domain. Through inverse dynamics, the import configuration of nonlinear programming ensures the continuous controls, which cannot be guaranteed by the nonlinear predictive control of traditional soft constraint method. In the background of intercepting ballistic missiles, simulation verification is carried out under the condition of initial minor disturbances and terminal condition change. The simulation results demonstrate that, compared with nonlinear feedback tracking method, the curve is smooth, the miss distance, pitch angle error and yaw angle error are small, and instantaneity can meet the control requirements.
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Key words:
- missile /
- control theory /
- nominal guidance law /
- trajectory tracking /
- predictive control /
- interception
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图 5 拦截弹路径倾角、路径偏角、速度、侧向过载及法向过载变化
Figure 5. Trajectory angle, yaw angle, velocity, side load and normal load variation of interceptor
图 6 遭遇点位置改变时的拦截弹轨迹
Figure 6. Trajectories of interceptor when point of encounter is changed
图 7 遭遇点位置改变时的拦截弹路径倾角、路径偏角、速度、侧向过载及法向过载变化
Figure 7. Trajectory angle, yaw angle, velocity, side load and normal load variation of interceptor when point of encounter position is changed
表 1 拦截弹初始条件
Table 1. Initial conditions for interceptor
参数 数值 位置(x, y, z)/km (100, 100, 8.460) V/(m·s-1) 566 γ/(°) 0 ψ/(°) -133 
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表 2 拦截弹末端条件
Table 2. Final conditions for interceptor
参数 数值 (x, y, z)/km (20.533, 0, 29.216) γ/(°) 0 ψ/(°) -107.647
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表 3 初始小扰动及终端输出误差
Table 3. Different initial minor disturbances and corresponding output errors at end of interception
方案 (x, y, z)/km V/(m·s-1) γ/(°) ψ/(°) 脱靶量/m Eγ/(°) Eψ/(°) CPU计算时间/s 1 (105, 105, 8.883)(+5%) 566 0 -133 0.231 0.119 0.163 0.011 5 2 (100, 100, 8.460) 594.3(+5%) 0 -133 0.437 0.147 0.203 0.014 5 3 (100, 100, 8.460) 566 2 -133 0.195 0.298 0.097 0.013 7 4 (100, 100, 8.460) 566 0 -130.3(+2%) 0.275 0.147 0.359 0.013 9 5 (105, 105, 8.883)(+5%) 594.3(+5%) 2 -130.3(+2%) 0.493 0.510 0.529 0.015 2 FL[20] (105, 105, 8.883)(+5%) 594.3(+5%) 2 -130.3(+2%) 1.543 1.589 1.641 0.009 2
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表 4 遭遇点位置改变及终端输出误差
Table 4. Changes of point encounter position and corresponding output errors at end of interception
方案 时间/s 拦截弹位置/km 目标位置/km 脱靶量/m Eγ/(°) Eψ/(°) 1 3 (104.383, 104.337, 8.481) (20, 0, 29) 0.193 0.119 0.163 2 20.1 (76.923, 77.943, 11.649) (14.6, 0, 20) 0.165 0.127 0.161 3 30.8 (45.648, 50.222, 18.144) (11, 0, 15) 0.183 0.115 0.174
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