本文選題：部分極點(diǎn)配置 + 無(wú)溢出性　； 參考：《成都理工大學(xué)》2017年碩士論文

【摘要】：極點(diǎn)配置問(wèn)題是控制結(jié)構(gòu)系統(tǒng)中的重要問(wèn)題之一。一般情況下,在控制系統(tǒng)矩陣中極點(diǎn)的位置決定著系統(tǒng)的穩(wěn)定性能,而極點(diǎn)配置法是比較常用的改變系統(tǒng)動(dòng)態(tài)性能的重要方法。這類問(wèn)題在實(shí)際工程項(xiàng)目前期的構(gòu)造分析中有重要用途,比如在彈簧和橋梁系統(tǒng)中,一般測(cè)量得到的系統(tǒng)矩陣中有一小部分極點(diǎn)可能會(huì)使得系統(tǒng)產(chǎn)生共振現(xiàn)象,從而導(dǎo)致整個(gè)系統(tǒng)的穩(wěn)定性和反應(yīng)速度等性能下降。極點(diǎn)配置問(wèn)題的關(guān)鍵就是通過(guò)選取適當(dāng)?shù)臓顟B(tài)反饋矩陣,使得閉環(huán)控制系統(tǒng)中的矩陣所期望的極點(diǎn)配置到事先給定的位置上,從而保證整個(gè)系統(tǒng)具有良好的動(dòng)態(tài)特性,即部分極點(diǎn)配置問(wèn)題。部分極點(diǎn)配置問(wèn)題的核心是對(duì)影響整個(gè)系統(tǒng)性能因素的分析和控制,狀態(tài)反饋、時(shí)滯現(xiàn)象、解的優(yōu)化等因素,這些問(wèn)題有待進(jìn)一步展開(kāi)研究。本文主要研究部分極點(diǎn)配置問(wèn)題的理論與方法,文中首先介紹了線性系統(tǒng)狀態(tài)反饋的部分極點(diǎn)配置問(wèn)題,總結(jié)了二階線性系統(tǒng)狀態(tài)反饋的部分極點(diǎn)配置問(wèn)題的理論與方法,研究、設(shè)計(jì)出相關(guān)算法并給出了數(shù)值實(shí)例,然后研究高階線性系統(tǒng)狀態(tài)反饋的部分極點(diǎn)配置問(wèn)題的理論與方法,給出了求解算法并結(jié)合數(shù)值實(shí)例說(shuō)明了算法的有效性。接下來(lái)重點(diǎn)研究了受時(shí)滯影響的部分極點(diǎn)配置問(wèn)題,基于總結(jié)前人關(guān)于二階時(shí)滯系統(tǒng)極點(diǎn)配置問(wèn)題的研究方法,然后在有關(guān)二階控制系統(tǒng)的方法基礎(chǔ)上,提出了一種求解高階時(shí)滯系統(tǒng)的部分極點(diǎn)配置問(wèn)題的改進(jìn)算法,該方法中直接進(jìn)行計(jì)算,沒(méi)有使用響應(yīng)矩陣和求解Sylvester方程,避免了比較復(fù)雜的計(jì)算過(guò)程,能更簡(jiǎn)單有效的解決問(wèn)題,最后針對(duì)最優(yōu)部分極點(diǎn)配置問(wèn)題來(lái)研究,主要通過(guò)求反饋矩陣的最小范數(shù)解來(lái)優(yōu)化問(wèn)題,分別給出了求解二階和高階系統(tǒng)的最優(yōu)部分極點(diǎn)配置問(wèn)題的最小范數(shù)解的算法設(shè)計(jì)。
[Abstract]:Pole assignment is one of the most important problems in control system. In general, the position of the poles in the control system matrix determines the stability of the system, and pole assignment is an important method to change the dynamic performance of the system. Such problems have important applications in the structural analysis of the early stage of a practical engineering project. For example, in spring and bridge systems, a small number of poles in the system matrix obtained from general measurements may cause resonance in the system. As a result, the stability and reaction speed of the whole system are reduced. The key of pole assignment problem is to select appropriate state feedback matrix, so that the desired poles of the matrix in the closed-loop control system can be configured to a given position in advance, so as to ensure that the whole system has good dynamic characteristics. That is, the problem of partial pole assignment. The core of the partial pole assignment problem is the analysis and control of the factors affecting the performance of the whole system, the state feedback, the phenomenon of time delay, the optimization of the solution, and so on. These problems need to be further studied. In this paper, the theory and method of partial pole assignment problem are studied. Firstly, the partial pole assignment problem of linear system state feedback is introduced, and the theory and method of partial pole assignment problem of second order linear system state feedback are summarized. The related algorithm is designed and a numerical example is given. Then the theory and method of partial pole assignment problem with state feedback for high order linear systems are studied. The algorithm is given and the effectiveness of the algorithm is illustrated by a numerical example. Then, the partial pole assignment problem affected by time delay is studied, based on summarizing the previous research methods of pole assignment problem for second order delay systems, and then on the basis of the second order control system method. In this paper, an improved algorithm for solving partial pole assignment problem for high-order time-delay systems is proposed. In this method, the response matrix and Sylvester equation are not used to solve the problem, and the complicated calculation process is avoided. The problem can be solved more simply and effectively. Finally, the problem of optimal partial pole assignment is studied, and the problem is optimized by finding the minimum norm solution of the feedback matrix. The algorithm design for the minimum norm solution of the optimal partial pole assignment problem for the second order and higher order systems is given respectively.
【學(xué)位授予單位】：成都理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O231

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本文編號(hào)：2097254