摘要
采用自适应的方法研究了带有分布谐波扰动的一维波方程的误差反馈调节问题.假设谐波扰动的频率已知,振幅未知,量测输出为左边界位移与跟踪信号之间的跟踪误差及误差导数.首先,通过构造调节器方程将原始系统变为辅助系统,将分布的谐波干扰变为边界扰动信号.其次,仅利用可量测的误差信号设计自适应状态观测器及未知参数的更新律,从而估计出辅助系统的状态及谐波干扰、参考信号的未知振幅.最后,通过再次构造辅助系统将非同位的干扰与控制变至同一端,为被控系统设计边界误差反馈调节器,利用可逆的backstepping变换证明闭环系统存在唯一的有界解,跟踪误差渐近趋于零.
In this paper,the adaptive method is applied to study the error feedback regulation problem for a one-dimensional wave equation with distributed harmonic disturbance.It is assumed that the frequency of the disturbance is known but the amplitude is unknown,the tracking error between the output with the left boundary displacement and reference signal and its derivative are measured.Firstly,the original system is transformed into an auxiliary system by constructing a regulator equation,and the distributed harmonic disturbance is transformed into a boundary disturbance signal.Secondly,we design an adaptive error-based state observer to estimate the state of auxiliary system and the amplitude of harmonic disturbance and reference signal,and the unknown parameter update law is obtained.Finally,we make the disturbance and control collocated by constructing an auxiliary system again and propose a boundary error feedback regulator for the controlled system.It is proved that the closed-loop system has a unique bounded solution via the invertible backstepping transformation and the tracking error tends to zero asymptotically.
作者
李志媛
金凤飞
Li Zhiyuan;Jin Fengfei(School of Mathematics and Statistics,Shandong Normal University,250358,Jinan,China)
出处
《山东师范大学学报(自然科学版)》
CAS
2021年第1期54-65,共12页
Journal of Shandong Normal University(Natural Science)
基金
国家自然科学基金资助项目(62073203).
关键词
一维波方程
误差反馈
参数估计
自适应控制
1D wave equation
error feedback
parameter estimation
adaptive control