Finite-time Control for Morphing Aerospace Vehicle Based on Time-varying Barrier Lyapunov Function
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摘要: 针对复杂扰动下可执行多种任务的复合式变体无人机, 提出了一种基于浸入与不变理论和隐含系统状态受限条件的复合时变障碍Lyapunov函数的控制方案. 设计了一种基于浸入与不变理论的扰动观测器, 构建了一种基于监督因子的有限时间动态尺度调节器. 在此基础上, 设计了一种基于复合时变障碍Lyapunov函数和动态滑模面的控制器, 保证系统状态始终在约束条件之内. 通过衍生定理证明轨迹跟踪误差是有限时间稳定的. 最终仿真结果验证了所提方案的有效性.
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关键词:
- 变体无人机 /
- 浸入与不变 /
- 动态尺度因子 /
- 监督因子 /
- 障碍Lyapunov函数
Abstract: A control scheme based on immersion and invariance (I&I) theory and a composite time-varying barrier Lyapunov function (CTV-BLF) with implied system state constraint conditions is proposed for the morphing aerospace vehicle which can perform multiple tasks under complex disturbances. A disturbance observer based on I&I theory is designed, in which a finite-time dynamic scaling regulator based on supervision factor is constructed. On this basis, a controller based on CTV-BLF and dynamic sliding surface is designed to guarantee that the constraints are always not violated. The derivative theorem proves that the trajectory tracking error is stable in finite time. Final simulation results verify the effectiveness of the proposed scheme. -
图 2 变体无人机机体受力及坐标示意图
Fig. 2 Schematic diagram of body force and coordinates of the morphing aerospace vehicle
图 6 算例1中两种基于I&I理论扰动观测器的扰动观测误差
Fig. 6 Disturbances observation errors of two observers based on I&I theory in Case 1
图 9 算例 2中三种方法轨迹跟踪误差及箱线图分析
Fig. 9 Trajectory tracking errors and boxplot analysis of the three methods in Case 2
图 10 算例 2中三种方法姿态跟踪误差及箱线图分析
Fig. 10 Attitude tracking errors and boxplot analysis of the three methods in Case 2
图 12 算例2中三种方法的控制输入信号响应
Fig. 12 Control input signal responses of the three methods in Case 2
图 13 算例2中三种方法的虚拟控制输入信号响应
Fig. 13 Virtual control input signal responses of the three methods in Case 2
图 11 算例2中三种方法对外部扰动的估计效果
Fig. 11 Estimation effects on external disturbances of the three methods in Case 2
图 15 算例2测试周期中本文方法机翼与机身夹角
${\theta _f}$ 与机体速度变化的对应过程Fig. 15 The corresponding process of the angle
${\theta _f}$ between wing and fuselage, and the change of airframe velocity of the proposed method in Case 2
图 14 算例2测试周期中机翼与机身夹角
${\theta _f}$ 自适应响应过程Fig. 14 The adaptive response of the angle
${\theta _f}$ between wing and fuselage during the test period in Case 2
图 16
${\alpha _i} = 2$ 时6个控制通道FT-DSF自适应过程Fig. 16 FT-DSF adaptive process of six control channels when
${\alpha _i} = 2$ 
图 17 监督因子
${\alpha _1}$ 的变化对FT-DSF${r_1}$ 及动态尺度误差${z_1}$ 的响应过程(以$x$ 子系统为例)((a) 随着${\alpha _1}$ 不同取值${r_1}$ 的自适应收敛响应; (b)${\alpha _1}$ 不同取值对应${r_1}$ 的最终收敛值的变化趋势; (c) 随着${\alpha _1}$ 不同取值${z_1}$ 的自适应收敛响应)Fig. 17 The responses of FT-DSF
${r_1}$ and dynamic scaling error${z_1}$ in response to the supervision factor${\alpha _1}$ (take the$x$ subsystem as an example) ((a) Adaptive convergent response of${r_1}$ with different values of${\alpha _1}$ ; (b) Different values of${\alpha _1}$ correspond to the change trend of the final convergence value of${r_1}$ ; (c) Adaptive convergent response of${z_1}$ with different values of${\alpha _1}$ ) -
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