Vibration control of flexible spacecraft with output constraints and external disturbances
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摘要:
针对具有输出约束及外部干扰的柔性航天器系统，提出一种直接关节力矩输入的振动控制方法。利用哈密顿原理，系统动力学特性由偏微分方程（PDE）和常微分方程（ODE）耦合组成的分布参数模型来描述。设计了非线性干扰观测器补偿外界干扰，并基于正切型障碍李雅普诺夫函数解决了航天器姿态角度误差和振动误差的多输出约束问题。利用扩展的拉塞尔不变集原理和半群理论证明了系统的渐近稳定性。不仅实现了姿态角的位置控制，还抑制了柔性航天器的弹性振动。通过对比仿真验证了所提方法的有效性。
Abstract:A vibration control with direct joint torque input is presented for flexible spacecraft systems subject to external disturbances and output limits. Firstly, the dynamic characteristics of the system are described by a distributed parameter model which is composed of partial differential equation (PDE) and ordinary differential equation (ODE). Secondly, the tangential barrier Lyapunov function is used to ensure that the output constraints of vibration errors and attitude angle errors are met by a nonlinear disturbance observer that is intended to adjust for external disturbances. The asymptotic stability of the system is proved by extended LaSalle’s invariance principle and semigroup theory. It not only realizes the position control of attitude angle, but also restrains the elastic vibration of flexible spacecraft. Finally, the effectiveness of the proposed control method is verified by comparison simulations.
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图 3 无控制输入的弹性挠度$\omega (x,t)$
Figure 3. Elastic deflection $\omega (x,t)$ without control input
图 4 PD应变力及剪切力反馈控制方法的弹性挠度$\omega (x,t)$
Figure 4. Elastic deflection $\omega (x,t)$ with PD strain force and share force control
图 9 末端的弹性变形$\omega (l,t)$
Figure 9. Elastic deformation $\omega (l,t)$ of the end point
图 5 本文控制方法的弹性挠度$\omega (x,t)$
Figure 5. Elastic deflection $\omega (x,t)$ with the proposed control method
图 6 姿态角度$\theta $及角速度$\dot \theta $的跟踪曲线
Figure 6. Tracking curves of attitude angle $\theta $ and angular velocity $\dot \theta $
图 7 外部干扰${\tau _{\mathrm{d}}}$及其观测值${\hat \tau _{\mathrm{d}}}$
Figure 7. External disturbance ${\tau _{\mathrm{d}}}$ and its estimate ${\hat \tau _{\mathrm{d}}}$
表 1 航天器物理参数
Table 1. The physical parameters of spacecraft
悬臂梁长度l/m 悬臂梁尖端质量m/kg 单位长度均匀质量$ \rho $/(kg·m−1) 刚性轮轴半径r/m 弯曲刚度E/(N·m) 转动惯量$ {I_{\rm{h}}} $/(N·m2) 10 5 8 1 300 120 
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表 2 系统控制参数
Table 2. System control parameters
角度误差约束值$ {k_{{\rm{b}}1}} $ 控制参数$ \lambda $ 控制参数$ {k_{\mathrm{f}}} $ 控制参数$ {k_{\mathrm{s}}} $ 控制参数$ K $ 振动约束值$ {k_{{\rm{b}}2}} $ 控制参数$ {k_{\mathrm{p}}} $ 控制参数$ {k_{\mathrm{d}}} $ 控制参数$ {k_{\mathrm{v}}} $ 0.21 5 10 400 150 2.4 550 400 2
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