本文選題：線性跟蹤微分器　切入點(diǎn)：正態(tài)分布　出處：《山西大學(xué)》2015年碩士論文

【摘要】：近年來,在微分控制理論中對(duì)微分信號(hào)的提取、微分方程邊界控制的研究吸引了大量的學(xué)者.因?yàn)榱繙y(cè)的信號(hào)一般會(huì)受到噪聲干擾,為了排除噪聲的干擾,跟蹤微分器的設(shè)計(jì)是相當(dāng)?shù)闹匾?對(duì)于解決微分方程邊界控制問題學(xué)者們使用的技術(shù)方法有許多,例如魯棒控制,自適應(yīng)控制,滑�？刂�,李雅普諾夫方法等.然而,自抗擾控制技術(shù)尤為重要.本文主要研究以下兩個(gè)問題：第一個(gè)問題是在較弱的條件下,使用一個(gè)線性跟蹤微分器跟蹤干擾信號(hào)并提取其微分.首先,應(yīng)用特征根法得到跟蹤微分器系統(tǒng)的解.其次,對(duì)跟蹤信號(hào)的收斂性進(jìn)行理論證明.最后,給出數(shù)值模擬結(jié)果.第二個(gè)問題是具有邊界擾動(dòng)的變系數(shù)n維波動(dòng)方程的穩(wěn)定性,在研究中應(yīng)用了自抗擾控制方法.首先,使用時(shí)變高增益觀測(cè)器代替常數(shù)高增益觀測(cè)器很好地解決了峰值問題.其次,應(yīng)用半群理論得到了變系數(shù)n維波動(dòng)方程解的存在性和唯一性.最后,設(shè)計(jì)時(shí)變高增益觀測(cè)器估計(jì)出邊界擾動(dòng)并通過狀態(tài)反饋將其抵消使得系統(tǒng)穩(wěn)定.本文主要分為三章：第一章為緒論,簡(jiǎn)單介紹了各種微分器對(duì)微分信號(hào)跟蹤的收斂性以及觀測(cè)器對(duì)波動(dòng)方程邊界控制問題的研究現(xiàn)狀,并且闡明了本文的主要研究?jī)?nèi)容.在第二章第一節(jié)中,先說明經(jīng)典微分器的數(shù)學(xué)含義,然后給出本文所用的線性跟蹤微分器其中R0是參數(shù),u(t)是被跟蹤的輸入信號(hào).在第二節(jié)中,應(yīng)用特征根法得到跟蹤微分器系統(tǒng)的解并對(duì)跟蹤信號(hào)的收斂性進(jìn)行理論證明.在第三節(jié)中,給出了數(shù)值模擬結(jié)果.在第三章第一節(jié)中,先給出本章用到的基本概念和相關(guān)記號(hào).在第二節(jié)中,利用半群理論研究下面具有邊界擾動(dòng)的變系數(shù)n維波動(dòng)方程解的存在性和唯一性.其中v(x,t)為控制輸入,假設(shè)擾動(dòng)d(t)有界,即存在正常數(shù)M0,使得對(duì)一切t≥0,有|d(t)|≤M.最后通過巧妙的設(shè)計(jì)如下時(shí)變高增益觀測(cè)器估計(jì)出邊界擾動(dòng)并通過狀態(tài)反饋將其抵消使得系統(tǒng)穩(wěn)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，

本文編號(hào)：1667260