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(Immersion and invariance, I&I)理论和隐含系统状态受限条件的复合时变障碍Lyapunov函数(Composite time-varying barrierLyapunov function, CTV-BLF)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因子(Finite-time dynamic scaling factor, FT-DSF)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 factor (FT-DSF) 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2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3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3种方法姿态角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3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3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3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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