带宽幂次受限的一类不确定非线性系统的输出跟踪  

Output Tracking for a Class of Uncertain Nonlinear Systems with Limited Bandwidth Power

作　　者：郭宝珠 高璐 GUO Bao-zhu;GAO Lu(School of Mathematics and Physics,North China Electrical Power University,Beijing 102206,China)

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《数学的实践与认识》2024年第5期153-170,共18页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12131008)。

摘　　要：自抗扰控制中的扩张状态观测器的高增益问题一直是个理论难题.文章通过降低增益幂次部分解决这个问题.讨论了具有内部未建模动态和外部干扰的标准积分串联型n阶非线性系统的输出跟踪问题.首先设计带宽幂次受限的扩张状态观测器,用于在线估计目标系统的状态和总扰动,由此实时补偿总扰动,并设计出基于扩张状态观测器的输出反馈控制.所设计的输出反馈控制能实现整个闭环系统的输出跟踪和干扰抑制.闭环系统被证明是收敛的,并且跟踪误差能渐近收敛到任意给定的小的范围内.与经典的线性或者非线性的扩张状态观测器相比,增益的最高幂次从原来的n+1降低到了2.数值仿真的结果证明了设计控制的有效性.The challenge posed by the high-gain issue in the extended state observer of active disturbance rejection control has long been a formidable obstacle.In this study,we explore output tracking for a specific category of n-th order nonlinear systems characterized by internal uncertainties and external disturbances.Firstly,we design a high-gain extended state observer with limited bandwidth power,aimed at real-time estimation of both the system state and the total disturbances.We then introduce a feedback control mechanism rooted in the extended state observer,wherein the total disturbance is compensated by its estimated value.Our analysis demonstrates the practical convergence of the closed-loop system:specifically,the tracking error can be made to converge to any arbitrarily small neighborhood of the origin.A noteworthy improvement in this approach is the significant reduction in gain power for the extended state observer.Compared to the traditional extended state observer,our method reduces the gain power from n+1 to just 2.This substantial decrease promises more stable and efficient system performance.To validate the efficacy of our proposed control method,we present numerical simulations that offer compelling evidence of its practicality and effectiveness.

关 键 词：自抗扰控制 非线性系统 输出跟踪 不确定性 

分 类 号：O231[理学—运筹学与控制论]