跟踪微分器和时变高增益观测器的应用

发布时间：2018-03-26 09:13

  本文选题：线性跟踪微分器　切入点：正态分布　出处：《山西大学》2015年硕士论文

【摘要】：近年来,在微分控制理论中对微分信号的提取、微分方程边界控制的研究吸引了大量的学者.因为量测的信号一般会受到噪声干扰,为了排除噪声的干扰,跟踪微分器的设计是相当的重要.对于解决微分方程边界控制问题学者们使用的技术方法有许多,例如鲁棒控制,自适应控制,滑模控制,李雅普诺夫方法等.然而,自抗扰控制技术尤为重要.本文主要研究以下两个问题：第一个问题是在较弱的条件下,使用一个线性跟踪微分器跟踪干扰信号并提取其微分.首先,应用特征根法得到跟踪微分器系统的解.其次,对跟踪信号的收敛性进行理论证明.最后,给出数值模拟结果.第二个问题是具有边界扰动的变系数n维波动方程的稳定性,在研究中应用了自抗扰控制方法.首先,使用时变高增益观测器代替常数高增益观测器很好地解决了峰值问题.其次,应用半群理论得到了变系数n维波动方程解的存在性和唯一性.最后,设计时变高增益观测器估计出边界扰动并通过状态反馈将其抵消使得系统稳定.本文主要分为三章：第一章为绪论,简单介绍了各种微分器对微分信号跟踪的收敛性以及观测器对波动方程边界控制问题的研究现状,并且阐明了本文的主要研究内容.在第二章第一节中,先说明经典微分器的数学含义,然后给出本文所用的线性跟踪微分器其中R0是参数,u(t)是被跟踪的输入信号.在第二节中,应用特征根法得到跟踪微分器系统的解并对跟踪信号的收敛性进行理论证明.在第三节中,给出了数值模拟结果.在第三章第一节中,先给出本章用到的基本概念和相关记号.在第二节中,利用半群理论研究下面具有边界扰动的变系数n维波动方程解的存在性和唯一性.其中v(x,t)为控制输入,假设扰动d(t)有界,即存在正常数M0,使得对一切t≥0,有|d(t)|≤M.最后通过巧妙的设计如下时变高增益观测器估计出边界扰动并通过状态反馈将其抵消使得系统稳定.
[Abstract]:In recent years, the study of differential signal extraction and differential equation boundary control in differential control theory has attracted a large number of scholars. The design of tracking differentiator is very important. There are many technical methods used by scholars to solve boundary control problems of differential equations, such as robust control, adaptive control, sliding mode control, Lyapunov method, etc. However, In this paper, the following two problems are studied: the first problem is to track the interference signal and extract its differential with a linear tracking differentiator under weak conditions. The characteristic root method is used to obtain the solution of the tracking differentiator system. Secondly, the convergence of the tracking signal is proved theoretically. Finally, the numerical simulation results are given. The second problem is the stability of the n-dimensional wave equation with variable coefficients with boundary perturbation. In this paper, the active disturbance rejection control method is applied. Firstly, the time-varying high gain observer is used instead of the constant high gain observer to solve the peak value problem. The existence and uniqueness of solutions for n-dimensional wave equations with variable coefficients are obtained by using semigroup theory. The time-varying high gain observer is designed to estimate the boundary disturbance and cancel it by state feedback. This paper is divided into three chapters: chapter 1 is an introduction. This paper briefly introduces the convergence of differential signal tracking by various differentiators and the research status of observer for boundary control of wave equation, and clarifies the main research contents of this paper. First, the mathematical meaning of the classical differentiator is explained, and then the linear tracking differentiator used in this paper is given, where R0 is the parameter of the input signal to be tracked. The characteristic root method is used to obtain the solution of the tracking differentiator system and the convergence of the tracking signal is proved theoretically. In the third section, the numerical simulation results are given. In the second section, the existence and uniqueness of the solution of the n-dimensional wave equation with boundary perturbation are studied by using the semigroup theory. That is, there exists a normal number M _ 0 such that for all t 鈮，

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