边界含有界扰动的一维波动方程的滑模控制及自抗扰控制  

The Sliding Mode Control and Active Disturbance Rejection Control of One-Dimensional Wave Equation with Boundary Control Disturbance

作　　者：杨坤一[1] YANG Kunyi(College of Science,North China University of Technology,Beijing 100144)

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《系统科学与数学》2025年第3期696-707,共12页Journal of Systems Science and Mathematical Sciences

基　　金：北京市自然科学基金(1232006)资助课题.

摘　　要：文章考虑一维波动方程,一端Dirichlet边界条件,另一端边界控制含有界扰动.首先,文章构造滑模面,对系统设计滑模控制器,证明了闭环系统的稳定性.然后,文章构造高增益预估器,设计自抗扰控制器,并证明了闭环系统的稳定性.最后,对于施加滑模控制和自抗扰控制的闭环系统,进行数值模拟,验证了稳定的滑模控制器和自抗扰控制器的有效性.This paper considers the one-dimensional wave equation,with the Dirichlet boundary condition in the one end,and the control with the boundary disturbance in the other end.Firstly,this paper is devoted to design the sliding mode surface,and impose the sliding mode control further,and then this paper proves the stability of the closed-loop system.Secondly,this paper constructs the high-gain estimator,and then designs the active disturbance rejection control.The stability of the closed-loop system has been proven.Finally,this paper simulates the states of the closed-loop systems after imposing the sliding mode control and the active disturbance rejection control.The numerical simulation results show that both of the sliding mode control and the active disturbance rejection control are effective to make the original open-loop system stable.

关 键 词：波动方程 扰动 滑模控制 自抗扰控制 稳定性 

分 类 号：O231.2[理学—运筹学与控制论]