﻿ 基于轨迹线性化控制的再入轨迹跟踪制导
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Trajectory linearization control based tracking guidance design for entry flight
SHEN Zuojun, ZHU Guodong
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract: A novel use of trajectory linearization control (TLC) method was introduced in the guidance law design for hypersonic vehicle entry flight. By exploiting the inherent characteristics of time scale separation of entry vehicle dynamics, altitude and velocity could be controlled separately via outer and inner loop design. In the outer loop, path angle was used as pseudo-control for controlling the altitude. In the inner loop, the flight path angle command and velocity were tracked using bank angle and angle of attack as controls. A linear time-varying controller was designed for the feedback loop to stabilize the error dynamics. Feedback gains were computed online and are the symbolical functions of reference trajectory, therefore no explicit gain scheduling or mode-switching were needed. Extensive dispersion simulations show that this guidance algorithm can achieve precise trajectory tracking and is trajectory-independent. The simulations also show that an integrated entry guidance approach which combines the use of TLC-based tracking guidance law design and on-board reference trajectory planning can significantly enhance the autonomy and adaptability of entry flight.
Key words: trajectory linearization control (TLC)     entry flight     trajectory tracking guidance     time scale separation     nonlinear control

1 制导问题描述 1.1 再入动力学方程

1.2 再入轨迹约束条件

1.3 飞行器模型

1.4 参考轨迹分析

 图 1 再入轨迹的构成 Fig. 1 Composition of entry trajectory

2 轨迹跟踪制导律设计 2.1 TLC理论

TLC(其概念如图 2所示)结构由两部分组成:通过非线性模型伪逆求得给定标称输出η-(t)对应的标称控制量$\bar \mu$(t),以粗略对消系统的非线性,并将一般的轨迹跟踪问题转化为在误差坐标系的状态调节问题，上方带“-”的变量为变量的标称值;将非线性时变误差动力学方程组线性化,通过李雅普诺夫坐标变换将一般的线性时变方程组转化为线性时变系统标准型,并通过配置Parallel Differential Spectrum(PD谱)对误差动态进行镇定.反馈控制项$\tilde \mu$(t)由时变镇定控制器产生,并可写为状态误差量的线性反馈形式$\tilde \mu$(t)=K(t)$\tilde \xi$(t).上方带“~”的变量为变量的状态误差量.非线性模型中的ξ(t)、μ(t)、η(t)和θ(t)分别为状态、输入、输出和时变参数向量.f(·)和g(·)为非线性向量函数.关于非线性伪逆和PD谱配置的理论见文献[12].

 图 2 TLC概念图 Fig. 2 Conceptual configuration of TLC

TLC对跟踪误差信号可以保证指数稳定性,闭环系统对正则扰动及奇异摄动都有很好的适应性.

2.2 环路划分和独立变量的选取

TLC的控制策略是基于奇异摄动理论中的时间尺度分离思想,将全量、刚体的飞行器动力学模型分为2个回路,即制导回路(其TLC结构如图 3所示,带角标C的变量为环路的控制输出)和姿态回路;4个环路,对应高度(极慢动态)、速度(慢动态)、姿态角(较慢动态)和姿态角速率(快动态)环路,分别进行设计.本文分析仅涉及包含高度、速度环路的制导回路设计.

 图 3 制导回路TLC结构图 Fig. 3 Configuration of TLC in guidance loop

2.3 高度环路设计

2.4 速度环路设计

3 控制器参数设置与调整

 高度环路 速度环路 ξ11=1.4ωn11=6.5-5.0×$\bar V$ ξ21=1.4ωn21=32.0-25.0×$\bar V$ξ22=1.4ωn22=10.0

4 仿真验证

LQR权重矩阵按文献[7]中的偏差量原则选取,其中Q=diag[4×109,2.5×106,3.28×105],R=diag[3.28×103,25].滚动时域控制用迎角和倾侧角镇定高度和速度偏差,权重矩阵取为Q′=diag[1,1],R′=diag[100,0.1].初始再入时步长取h=0.006,线性过渡到再入末端时的h=0.0045,步数N=7.侧向制导律使用航向角误差漏斗逻辑[2].为更好地对比不同控制方法高度和速度跟踪精度,仿真截止条件取为2300m/s的Pre-TAEM速度对应的sTravel(这里统一取为距离TAEM300km),并要求飞行器大致指向目标.

 拉偏项目 拉偏范围 水平风拉偏/(°) [0,360]10%概率风 密度拉偏/% [-10,10] 阻力拉偏/% [-15,15] 升力拉偏/% [-10,10] 再入高度拉偏/km [-1,1] 再入经度拉偏/km 对应[-3,3] 再入纬度拉偏/km [-3,3] 再入速度拉偏/(m·s-1) [-100,100] 再入轨迹倾角拉偏/(°) [-0.5,0.5] 再入航向角拉偏/(°) [-1.0,1.0]

 图 4 速度-高度剖面打靶结果 Fig. 4 Shooting results in velocity-altitude profile

 图 5 速度-高度剖面跟踪 Fig. 5 Trajectory tracking in velocity-altitude profile

 图 6 航程速度剖面的速度跟踪 Fig. 6 Velocity tracking in range-velocity profile

 图 7 迎角控制历程 Fig. 7 Angle of attack command history

 图 8 倾侧角控制历程 Fig. 8 Bank angle command history

5 结 论

1) TLC方法在初始状态拉偏和扰动情况下也能实现很高的跟踪精度,体现了方法的有效性和鲁棒性.

2) 与LQR方法的仿真结果相比,TLC需要调整的参数更少,参数的选取更直观,对不同参考轨迹有很好的适应性,是一种完全在线的非线性控制方法.与近似滚动时域控制相比,TLC在控制精度略优于前者的情况下计算量显著减小.

3) 在再入轨迹跟踪制导律中使用TLC控制,可以做到制导环和姿态环控制结构的统一和设计时的一体化;高度、速度、姿态角和姿态角速度的四环路TLC控制策略将更便于制导和控制参数的匹配和实时调整.

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#### 文章信息

SHEN Zuojun, ZHU Guodong

Trajectory linearization control based tracking guidance design for entry flight

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(11): 1975-1982.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0424