| 引用本文: | 张涵雯,王军民.具有外部干扰的不稳定剪切梁的输入–状态稳定[J].控制理论与应用,2023,40(8):1339~1348.[点击复制] |
| ZHANG Han-wen,WANG Jun-min.Input-to-state stabilization of a destabilized shear beam with external disturbances[J].Control Theory and Technology,2023,40(8):1339~1348.[点击复制] |
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| 具有外部干扰的不稳定剪切梁的输入–状态稳定 |
| Input-to-state stabilization of a destabilized shear beam with external disturbances |
| 摘要点击 2195 全文点击 336 投稿时间：2022-04-19 修订日期：2023-04-17 |
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| DOI编号 10.7641/CTA.2022.20291 |
| 2023,40(8):1339-1348 |
| 中文关键词 不稳定剪切梁方程 反馈控制 自抗扰控制方法 输入–状态稳定性 |
| 英文关键词 destabilized shear beam feedback control active disturbance rejection control input-to-state stabilization |
| 基金项目 国家自然科学基金项目(62073037, 12131008). |
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| 中文摘要 |
| 本文针对一端受到范德华力的不稳定剪切梁方程, 考虑其输入–状态稳定性问题. 通过可逆变换把方程等价地变成一个具有反馈循环的2 × 2的一阶运输方程与常微分方程的耦合系统. 通过自抗扰控制方法, 给出具有时变增益的扩张状态观测器来估计干扰. 应用Backstepping变换和干扰估计量, 设计系统的反馈控制来补偿系统本身的不稳定以及消除匹配干扰. 通过C0–半群方法证明闭环系统的适定性, 以及Lyapunov方法证明闭环系统的输入–状态稳定性. 数值仿真验证理论结果的正确性. |
| 英文摘要 |
| In this paper, the input-to-state stabilization of an unstable shear beam with van der Waals forces at one end is considered. Through an invertible transformation, the equation is transformed into a 2 × 2 system of first-order transport equations, which convects in opposite directions cascaded with an ordinary differential equation (ODE). Using the active disturbance rejection control (ADRC) method, an extended state observer with the time-varying gain is given to estimate the disturbance. Applying the backstepping transformation and the disturbance estimation, the feedback control of the closed-loop system is proposed to compensate for the instability of the system itself and cancel the matched disturbance. By the C0-semigroup method and the Lyapunov method, the well-posedness and the input-to-state stability (ISS) of the
closed-loop systems are proved, respectively. The validity of the theoretical results is verified by numerical simulations. |