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】：隨著社會不斷進步和科學(xué)技術(shù)快速發(fā)展,計算機性能和控制技術(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。在實際工程中,時滯現(xiàn)象所涉及的領(lǐng)域較為廣泛,幾乎所有實際控制系統(tǒng)中都普遍帶有時滯現(xiàn)象,時滯的存在通常會造成系統(tǒng)性能變差。此外,控制系統(tǒng)工作時或多或少會受到外界的干擾,致使系統(tǒng)的動態(tài)性能和穩(wěn)態(tài)性能變差。因此,針對離散系統(tǒng)的時滯問題及擾動問題的分析具有重要意義。本文首先對離散系統(tǒng)進行了簡單的概述。接著對時滯系統(tǒng)進行了綜述性地介紹,并介紹了這一領(lǐng)域內(nèi)對時滯現(xiàn)象的研究方法以及研究動態(tài)。對最優(yōu)控制的理論知識以及其發(fā)展狀況加以概述,闡述了含有時滯系統(tǒng)的最優(yōu)控制理論的發(fā)展現(xiàn)狀。最后,對振動領(lǐng)域中的振動控制問題加以概述,重點介紹了振動主動控制技術(shù),并對振動主動控制方法的研究進展及其最優(yōu)控制問題加以闡述。其次,針對選取的離散系統(tǒng),研究了狀態(tài)變量中含有時滯的最優(yōu)控制問題。通過加入指數(shù)衰減得到一個新的離散系統(tǒng),針對該離散系統(tǒng)對最優(yōu)控制問題展開研究。本文提出通過引入靈敏度參數(shù),將原系統(tǒng)的最優(yōu)控制問題轉(zhuǎn)變成一個既不含有超前項也不含有時滯項的兩點邊值(TPBV)問題,通過級數(shù)求和得到最優(yōu)控制律。最后通過實驗仿真表明該算法的可行性。接著,分析研究了引入指數(shù)衰減的含有隨機擾動的離散系統(tǒng)。首先對隨機噪聲擾動項進行卡爾曼濾波估計,其次通過分離原理對原系統(tǒng)進行分析,進而得到最優(yōu)控制律。最后通過MATLAB仿真表明該方法的可行性。最后選取含有柔性基礎(chǔ)的懸臂梁振動模型為研究對象,對基于指數(shù)衰減性能的含有外界擾動的離散系統(tǒng)的最優(yōu)控制問題進行研究。根據(jù)振動力學(xué)知識,可以推導(dǎo)獲得含有柔性基礎(chǔ)懸臂梁的振動微分方程,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)擾動的離散系統(tǒng)。采用含擾動離散系統(tǒng)的最優(yōu)控制對該系統(tǒng)進行研究,并通過實驗仿真驗證其可行性。
[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)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP13

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本文編號：1815965