Modeling and Fixed-time Prescribed Performance Control for Hypersonic Morphing Vehicle
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摘要: 以一种折叠式高超声速变外形飞行器(Hypersonic morphing vehicle, HMV)为研究对象, 综合考虑变形引起的气动特性、动力学特性的动态变化和模型不确定性、外部干扰的影响, 开展飞行器建模与固定时间预设性能控制方法研究. 首先, 建立高超声速变外形飞行器的运动模型和姿态控制模型; 然后, 采用固定时间干扰观测器实现对模型不确定性和外部干扰构成的复合总扰动的精确估计, 并设计一种新型固定时间预设性能函数以定量描述期望性能约束, 在此基础上, 基于预设性能控制架构并结合动态面控制技术设计预设性能姿态控制器, 利用Lyapunov稳定性理论证明闭环系统的固定时间稳定性; 最后, 通过数值仿真验证所提出方法的有效性和鲁棒性.
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关键词:
- 高超声速变外形飞行器 /
- 固定时间 /
- 预设性能 /
- 干扰观测器 /
- 动态面控制
Abstract: Taking a folding hypersonic morphing vehicle (HMV) as the research object, comprehensively considering dynamic changes caused by the deformation of aerodynamic characteristics and kinetics characteristics, as well as the influence of model uncertainties and external disturbances, the research on vehicle motion modeling and fixed-time prescribed performance control method is carried out. Firstly, the motion model and attitude control model of hypersonic morphing vehicle are established. Then, a fixed-time disturbance observer is established to accurately estimate the complex disturbance composed of model uncertainties and external disturbances, a novel fixed-time prescribed performance function is designed to quantitatively describe the expected performance constraints, the attitude controller is designed by integrating the dynamic surface control technique into the prescribed performance control framework, and the fixed-time stability of the closed-loop system is proved by Lyapunov stability theory. Finally, the numerical simulation is carried out to verify the effectiveness and robustness of the proposed method. -
图 1 高超声速变外形飞行器气动外形及变形过程示意图
Fig. 1 Aerodynamic shape and morphing process of hypersonic morphing vehicle
图 5 滚转力矩系数随折叠角变化曲线
Fig. 5 Curves of rolling moment coefficient varying with folding angle
图 6 偏航力矩系数随折叠角变化曲线
Fig. 6 Curves of yawing moment coefficient varying with folding angle
图 7 俯仰力矩系数随折叠角变化曲线
Fig. 7 Curves of pitching moment coefficient varying with folding angle
图 8 飞行器固定时间预设性能控制方案框图
Fig. 8 Flowchart of fixed-time prescribed performance control for HMV
图 14 仿真1气动力和附加力变化曲线 (0 ~ 3 s)
Fig. 14 Curves of aerodynamic force and additional force in Simulation 1 (0 ~ 3 s)
图 15 仿真1气动力和附加力变化曲线 (5 ~ 9 s)
Fig. 15 Curves of aerodynamic force and additional force in Simulation 1 (5 ~ 9 s)
图 16 仿真1气动力和附加力变化曲线 (11 ~ 16 s)
Fig. 16 Curves of aerodynamic force and additional force in Simulation 1 (11 ~ 16 s)
图 17 仿真1气动力矩和附加力矩变化曲线 (0 ~ 3 s)
Fig. 17 Curves of aerodynamic torque and additional torque in Simulation 1 (0 ~ 3 s)
图 18 仿真1气动力矩和附加力矩变化曲线 (5 ~ 9 s)
Fig. 18 Curves of aerodynamic torque and additional torque in Simulation 1 (5 ~ 9 s)
图 19 仿真1气动力矩和附加力矩变化曲线 (11 ~ 16 s)
Fig. 19 Curves of aerodynamic torque and additional torque in Simulation 1 (11 ~ 16 s)
图 23 仿真2总扰动及其观测误差曲线
Fig. 23 Curves of total disturbance and its observation error in Simulation 2
表 1 气动模型状态量范围
Table 1 State quantity range of aerodynamics model
状态量 符号 取值范围 马赫数 Ma $\left [ 2,18 \right ]$ 攻角 $\alpha $ $\left [ 0^{\circ},20^{\circ} \right ]$ 侧滑角 $\beta $ $\left [ -2^{\circ},2^{\circ} \right ] $ 滚转舵偏角 $\delta_x$ $ \left [ -20^{\circ},20^{\circ} \right ] $ 偏航舵偏角 $\delta_y$ $ \left [ -20^{\circ},20^{\circ} \right ] $ 俯仰舵偏角 $\delta_z$ $ \left [ -20^{\circ},20^{\circ} \right ] $ 折叠角 $\delta_f$ $\left [ -30^{\circ},155^{\circ} \right ]$ 
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表 2 高超声速变外形飞行器机体参数
Table 2 Body parameters of HMV
参量 符号 数值 单位 机身质量 $m_f$ 2950 kg 折叠翼质量 $m_1, m_2$ 55 kg $x$主轴转动惯量 $I_{xx}$ $\left [ 283,298 \right ] $ kg·m2 $y$主轴转动惯量 $I_{yy}$ $\left [ 2\;679,2\;722 \right ]$ kg·m2 $z$主轴转动惯量 $I_{zz}$ $\left [ 2\;528,2\;630 \right ]$ kg·m2 惯量积 $I_{xy}$ $\left [ 163,169 \right ] $ kg·m2 参考面积 $S_r$ 1.8 m2 参考气动弦长 $c_A$ 2.4 m 参考气动展长 $b_A$ 1.1 m
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表 3 仿真参数设置
Table 3 Setting of simulation parameters
参数类型 参数值 初始状态参数 $H=35$ km, $V=3\;200$ m/s $\lambda ={{120}^{\circ }}$, $\phi ={{20}^{\circ}}$, $\theta=-{{1}^{\circ}}$, ${{\psi}_{v}}={{10}^{\circ}}$ $\alpha={{8}^{\circ}}$, $\beta={{1}^{\circ}}$, $\sigma={{18}^{\circ}}$ ${{\omega}_{x}}={{\omega}_{y}}={{\omega}_{z}}=0$, ${{\delta}_{x}}={{\delta}_{y}}={{\delta}_{z}}=0$ 控制参数 ${{\boldsymbol{\rho }}_{0}}={{\left[ {{\rho }_{0,1}},{{\rho }_{0,2}},{{\rho }_{0,3}} \right]}^{\text{T}}}={{\left[ 5,3,5 \right]}^{\text{T}}}$ ${{\boldsymbol{\rho }}_{\infty }}={{\left[ {{\rho }_{\infty ,1}},{{\rho }_{\infty ,2}},{{\rho }_{\infty ,3}} \right]}^{\text{T}}}={{\left[ 0.2,0.1,0.3 \right]}^{\text{T}}}$ ${{m}_{1,i}}=3$, ${{m}_{2,i}}=5$, ${{n}_{1,i}}=5$, ${{n}_{2,i}}=7$ ${{\alpha }_{01,i}}=0.15$, ${{\alpha }_{02,i}}=0.2$, ${{\delta }_{1,i}}={{\delta }_{2,i}}=1$ ${{k}_{1,i}}={{k}_{2,i}}=2$, $\text{ }{{k}_{3,i}}={{k}_{4,i}}=4$ ${{\varepsilon }_{1,i}}=0.02$, ${{\gamma }_{1,i}}=0.6$, ${{\gamma }_{2,i}}=1.4$ ${{k}_{z1,i}}=4$, ${{k}_{z2,i}}=4$, ${{\varepsilon }_{0,i}}=0.2$ 仿真步长 d$t$= 0.01 s 外部干扰项 $\Delta {{d}_{1,1}}=500\left( -\cos ({\pi t}/{20})+\sin ({\pi t}/{40}) \right)\;\text{N}\cdot \text{m}$ $\Delta {{d}_{1,2}}=300\left( -\cos ({\pi t}/{30})+\sin ({\pi t}/{60}) \right)\;\text{N}\cdot \text{m}$ $\Delta {{d}_{1,3}}=1\;000\cos ({\pi t}/{30})\sin ({\pi t}/{20})\;\text{N}\cdot \text{m}$ 模型不确定项 $\Delta{{C}_{L}}=\Delta{{C}_{D}}=\Delta{{C}_{Y}}=\pm20\%$ $\Delta{{C}_{mx}}=\Delta{{C}_{my}}=\Delta{{C}_{mz}}=\pm20\%$ $\Delta{{I}_{xx}}=\Delta{{I}_{yy}}=\Delta{{I}_{zz}}=\Delta{{I}_{xy}}=\pm20\%$ $\Delta{{S}_{r}}=\Delta{{b}_{A}}=\Delta{{c}_{A}}=\pm5\%$
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