The Active Disturbance Rejection Control to Stabilization for Multi-Dimensional Wave Equation With Boundary Control Matched Disturbance
The Active Disturbance Rejection Control to Stabilization for Multi-Dimensional Wave Equation With Boundary Control Matched Disturbance
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DOI：
10.1109/tac.2014.2335511
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发表时间：
2015
影响因子：
6.8
通讯作者：
B. Guo;Hua-cheng Zhou
中科院分区：
文献类型：
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作者：
B. Guo;Hua-cheng Zhou
在本文中，我们考虑具有依赖于时间和空间变量的边界控制匹配干扰的多维波动方程的边界镇定问题。研究中采用了自抗扰控制（ADRC）方法。设计了一个扩张状态观测器，基于通过无穷多个测试函数从原始多维系统得到的无穷多个常微分方程来估计干扰。在反馈回路中，干扰与同位镇定控制器一起被消除。闭环中的所有子系统都被证明是渐近稳定的。特别地，时变高增益首次应用于由偏微分方程描述的系统，以实现完全抑制干扰的目的，并减少文献中由恒定高增益导致的峰值。通过该系统呈现了自抗扰控制在处理多维偏微分方程干扰方面的全貌。进行了数值实验以说明收敛性和峰值降低的效果。
In this paper, we consider boundary stabilization for a multi-dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables. The active disturbance rejection control (ADRC) approach is adopted in investigation. An extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi-dimensional system by infinitely many test functions. The disturbance is canceled in the feedback loop together with a collocated stabilizing controller. All subsystems in the closed-loop are shown to be asymptotically stable. In particular, the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature. The overall picture of the ADRC in dealing with the disturbance for multi-dimensional partial differential equation is presented through this system. The numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction.