本文選題：離散系統(tǒng) + 指數(shù)衰減�。� 參考：《青島科技大學(xué)》2017年碩士論文

【摘要】：隨著社會(huì)不斷進(jìn)步和科學(xué)技術(shù)快速發(fā)展,計(jì)算機(jī)性能和控制技術(shù)水平得到不斷的提高,離散系統(tǒng)的研究在控制理論領(lǐng)域中也愈加受到眾多學(xué)者的關(guān)注。在實(shí)際工程中,時(shí)滯現(xiàn)象所涉及的領(lǐng)域較為廣泛,幾乎所有實(shí)際控制系統(tǒng)中都普遍帶有時(shí)滯現(xiàn)象,時(shí)滯的存在通常會(huì)造成系統(tǒng)性能變差。此外,控制系統(tǒng)工作時(shí)或多或少會(huì)受到外界的干擾,致使系統(tǒng)的動(dòng)態(tài)性能和穩(wěn)態(tài)性能變差。因此,針對(duì)離散系統(tǒng)的時(shí)滯問(wèn)題及擾動(dòng)問(wèn)題的分析具有重要意義。本文首先對(duì)離散系統(tǒng)進(jìn)行了簡(jiǎn)單的概述。接著對(duì)時(shí)滯系統(tǒng)進(jìn)行了綜述性地介紹,并介紹了這一領(lǐng)域內(nèi)對(duì)時(shí)滯現(xiàn)象的研究方法以及研究動(dòng)態(tài)。對(duì)最優(yōu)控制的理論知識(shí)以及其發(fā)展?fàn)顩r加以概述,闡述了含有時(shí)滯系統(tǒng)的最優(yōu)控制理論的發(fā)展現(xiàn)狀。最后,對(duì)振動(dòng)領(lǐng)域中的振動(dòng)控制問(wèn)題加以概述,重點(diǎn)介紹了振動(dòng)主動(dòng)控制技術(shù),并對(duì)振動(dòng)主動(dòng)控制方法的研究進(jìn)展及其最優(yōu)控制問(wèn)題加以闡述。其次,針對(duì)選取的離散系統(tǒng),研究了狀態(tài)變量中含有時(shí)滯的最優(yōu)控制問(wèn)題。通過(guò)加入指數(shù)衰減得到一個(gè)新的離散系統(tǒng),針對(duì)該離散系統(tǒng)對(duì)最優(yōu)控制問(wèn)題展開研究。本文提出通過(guò)引入靈敏度參數(shù),將原系統(tǒng)的最優(yōu)控制問(wèn)題轉(zhuǎn)變成一個(gè)既不含有超前項(xiàng)也不含有時(shí)滯項(xiàng)的兩點(diǎn)邊值(TPBV)問(wèn)題,通過(guò)級(jí)數(shù)求和得到最優(yōu)控制律。最后通過(guò)實(shí)驗(yàn)仿真表明該算法的可行性。接著,分析研究了引入指數(shù)衰減的含有隨機(jī)擾動(dòng)的離散系統(tǒng)。首先對(duì)隨機(jī)噪聲擾動(dòng)項(xiàng)進(jìn)行卡爾曼濾波估計(jì),其次通過(guò)分離原理對(duì)原系統(tǒng)進(jìn)行分析,進(jìn)而得到最優(yōu)控制律。最后通過(guò)MATLAB仿真表明該方法的可行性。最后選取含有柔性基礎(chǔ)的懸臂梁振動(dòng)模型為研究對(duì)象,對(duì)基于指數(shù)衰減性能的含有外界擾動(dòng)的離散系統(tǒng)的最優(yōu)控制問(wèn)題進(jìn)行研究。根據(jù)振動(dòng)力學(xué)知識(shí),可以推導(dǎo)獲得含有柔性基礎(chǔ)懸臂梁的振動(dòng)微分方程,再結(jié)合壓電方程得到含有柔性基礎(chǔ)懸臂梁系統(tǒng)的狀態(tài)空間表達(dá)式。將該連續(xù)系統(tǒng)離散化得到的離散系統(tǒng)就是我們要研究的含有持續(xù)擾動(dòng)的離散系統(tǒng)。采用含擾動(dòng)離散系統(tǒng)的最優(yōu)控制對(duì)該系統(tǒng)進(jìn)行研究,并通過(guò)實(shí)驗(yàn)仿真驗(yàn)證其可行性。
[Abstract]:With the continuous progress of society and the rapid development of science and technology, the performance of computer and the level of control technology have been continuously improved, and the study of discrete systems has been paid more and more attention by many scholars in the field of control theory. In practical engineering, the delay phenomenon involves a wide range of fields, almost all practical control systems generally have time delay phenomenon, the existence of time delay will usually lead to the system performance deterioration. In addition, the control system is more or less disturbed by external disturbance, which makes the dynamic and steady-state performance of the control system worse. Therefore, it is of great significance to analyze the time-delay problem and perturbation problem of discrete systems. In this paper, a brief overview of discrete systems is given. Then, this paper gives a general introduction to the time-delay system, and introduces the research methods and the research trends of the time-delay phenomenon in this field. The theoretical knowledge of optimal control and its development are summarized, and the development of optimal control theory with time delay is expounded. Finally, the vibration control problems in the field of vibration are summarized, the active vibration control technology is introduced, and the research progress of the active vibration control method and its optimal control are described. Secondly, the optimal control problem with time delay in state variables is studied for the selected discrete systems. A new discrete system is obtained by adding exponential attenuation, and the optimal control problem of the discrete system is studied. In this paper, by introducing sensitivity parameters, the optimal control problem of the original system is transformed into a two-point boundary value TPBV problem with neither lead term nor delay term. The optimal control law is obtained by summing up the series. Finally, the feasibility of the algorithm is demonstrated by experimental simulation. Then, the discrete systems with stochastic perturbations with exponential attenuation are studied. Firstly, the stochastic noise disturbance is estimated by Kalman filter, and then the optimal control law is obtained by analyzing the original system by the separation principle. Finally, the feasibility of the method is demonstrated by MATLAB simulation. Finally, the vibration model of cantilever beam with flexible foundation is selected as the research object, and the optimal control problem of discrete system with external disturbance based on exponential attenuation performance is studied. According to the knowledge of vibration dynamics, the vibration differential equation of cantilever beam with flexible foundation can be derived, and the state space expression of cantilever beam system with flexible foundation can be obtained by combining piezoelectric equation. The discrete system obtained by discretization of the continuous system is a discrete system with persistent perturbations that we are going to study. The optimal control of the discrete system with disturbance is used to study the system, and the feasibility of the system is verified by experimental simulation.
【學(xué)位授予單位】：青島科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP13

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本文編號(hào)：1815965