Prescribed-time Tracking Control of Hypersonic Vehicles by Time-varying High-gain Feedback
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摘要: 研究了高超声速飞行器控制通道存在未知环境干扰时的指定时间跟踪控制问题. 基于高超声速飞行器的输入输出线性化模型, 借助参量 Lyapunov方程的一些性质, 设计一种光滑、有界的时变高增益控制律. 相比于现有的高超声速飞行器有限/固定时间控制方法, 该算法不会出现抖振现象, 同时收敛时间不依赖于初始状态且可以事先设定. 当高超声速飞行器存在未知的有界环境匹配干扰时, 该控制器能使高度和速度在指定时间跟踪上参考信号. 仿真结果验证了方法的有效性.Abstract: The prescribed-time tracking control problem of hypersonic vehicles in the presence of unknown environmental disturbances in the control channel is studied. Based on the input-output linearization model of hypersonic vehicles and some properties of a parametric Lyapunov equation, a smooth and bounded time-varying high-gain controller is proposed. Compared with the existing finite/fixed time control methods for hypersonic vehicles, the chattering phenomenon does not appear in the algorithm, and the convergence time does not depend on the initial state and can be set in advance. When the hypersonic vehicle has unknown bounded environmental matched disturbance, the proposed controller can ensure that the altitude and velocity track the reference signals in the prescribed time. Finally, simulation results verify the effectiveness of the proposed method.
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图 1 速度、飞行航迹角、高度和攻角变化曲线
Fig. 1 The curves of changes in velocity, flight path angle, altitude and angle of attack
图 2 俯仰角速率、发动机节流阀开度及其导数变化曲线
Fig. 2 The curves of changes in pitch rate, engine throttle setting and their time-derivative
图 4 速度误差及其导数变化曲线
Fig. 4 The curves of changes in velocity errors and their time-derivatives
图 5 高度误差及其导数变化曲线
Fig. 5 The curves of changes in altitude errors and their time-derivatives
表 1 高超声速飞行器参数以及飞行环境参数
Table 1 The parameters of the hypersonic vehicle and the flight environment
模型参数 符号 值 质量 $m$ 136817.841 kg 地球半径 $R_{{\rm{e}}}$ 6371386.8 m 参考面积 $S$ 334.729653 m2 平均气动弦长 $\bar{c}$ 80 升降副翼弦长 $c_{{\rm{e}}}$ 0.029 2 绕$ y $轴的转动惯量 $ I_{yy} $ 9.4907 × 106 kg$\cdot\; {\rm{m} }^2$ 空气密度 $\rho$ 0.0125 kg/m3 重力常数 $\mu $ 3.9360 × 1014 m3/s2 
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