本文關(guān)鍵詞： 極點(diǎn)配置 參數(shù)化方法 矩陣攝動(dòng)理論 魯棒性　出處：《東北電力大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：線性系統(tǒng)的魯棒控制問題一直是控制領(lǐng)域研究的熱點(diǎn)內(nèi)容。通過設(shè)計(jì)反饋控制器使系統(tǒng)按照期望的規(guī)律運(yùn)動(dòng)是控制系統(tǒng)設(shè)計(jì)的基本方法。在實(shí)際的控制系統(tǒng)設(shè)計(jì)中,必須保證系統(tǒng)滿足期望的穩(wěn)態(tài)性能和暫態(tài)性能,利用特征結(jié)構(gòu)配置的參數(shù)化方法設(shè)計(jì)狀態(tài)或輸出反饋控制器可以方便地實(shí)現(xiàn)這一目標(biāo)。但是,實(shí)際系統(tǒng)都工作在不斷變化的環(huán)境中,不可避免地會(huì)受到外界擾動(dòng)和參數(shù)變化的影響,給系統(tǒng)建模帶來不確定性,從而嚴(yán)重影響系統(tǒng)設(shè)計(jì)的穩(wěn)態(tài)特性和動(dòng)態(tài)響應(yīng)特性。解決這個(gè)問題最好的方法就是對(duì)系統(tǒng)進(jìn)行魯棒性設(shè)計(jì),對(duì)控制律和魯棒性能指標(biāo)進(jìn)行不斷地探究和創(chuàng)新。基于上述問題,本文針對(duì)一階線性系統(tǒng),進(jìn)行的主要研究?jī)?nèi)容及取得的主要成果總結(jié)如下:首先介紹了通過矩陣的Jordan分解與系統(tǒng)初值的選取來獲得期望的狀態(tài)與輸出控制的方法。研究了狀態(tài)反饋與輸出反饋極點(diǎn)配置的參數(shù)化方法,通過對(duì)Sylvester矩陣方程的求解,得到控制器的完全參數(shù)化表達(dá)式,通過適當(dāng)?shù)剡x取自由參數(shù)來獲得滿足控制要求的控制器。但是受限于自由參數(shù)的數(shù)量,系統(tǒng)有時(shí)會(huì)出現(xiàn)無解的情況,針對(duì)這種情況,本文給出了一種狀態(tài)反饋下近似求解的優(yōu)化指標(biāo),從而求得近似解。由此得到啟發(fā),可以通過增加自由參數(shù)的數(shù)量來避免這種近似求解情況。本文在特征向量矩陣參數(shù)化結(jié)果的基礎(chǔ)上,進(jìn)一步研究了如何通過引入新的可調(diào)參數(shù)來增加系統(tǒng)的自由度,以便更有利于實(shí)現(xiàn)期望的系統(tǒng)特性。然后在參數(shù)化方法的基礎(chǔ)上,利用參數(shù)化結(jié)果為系統(tǒng)設(shè)計(jì)提供的自由度,對(duì)系統(tǒng)進(jìn)行魯棒性設(shè)計(jì)。本文通過矩陣攝動(dòng)理論的分析,推導(dǎo)出了一種新的魯棒指標(biāo)。該魯棒指標(biāo)的原理不同于以往常用的譜條件數(shù),它并不是關(guān)于特征向量的函數(shù),所以其計(jì)算過程簡(jiǎn)單且效率高,因此更適合大系統(tǒng)�？紤]到該指標(biāo)的優(yōu)點(diǎn),進(jìn)一步研究了大系統(tǒng)的魯棒分散控制問題,利用該魯棒指標(biāo)可以很容易地將閉環(huán)極點(diǎn)配置在特定的區(qū)域。同時(shí)使得閉環(huán)特征值對(duì)外界擾動(dòng)和參數(shù)變化具有最小的靈敏度。本文通過對(duì)參數(shù)化方法的研究得出了閉環(huán)特征值、特征向量與反饋增益矩陣的參數(shù)化表達(dá)式之間的相互關(guān)系。總結(jié)了相關(guān)算法,并通過數(shù)值算例表明了方法的有效性。在參數(shù)化方法的基礎(chǔ)上,利用所提供的的自由度,研究基于矩陣攝動(dòng)理論的新型魯棒指標(biāo),解決了魯棒分散控制問題。通過數(shù)值算例與仿真與以往方法進(jìn)行對(duì)比,表明了新指標(biāo)優(yōu)越性。
[Abstract]:The robust control problem of linear systems is always a hot topic in the field of control. It is the basic method to design the control system by designing feedback controller to make the system move according to the expected law. Middle. The desired steady-state and transient performance of the system must be guaranteed. It is convenient to design the state or output feedback controller using the parameterized method of eigenstructure configuration. The actual system is working in the changing environment, which will inevitably be affected by the external disturbance and parameter change, which brings uncertainty to the system modeling. Therefore, the steady-state and dynamic response characteristics of the system design are seriously affected. The best way to solve this problem is to design the system robustness. The control law and robust performance index are constantly explored and innovated. Based on the above problems, this paper aims at the first order linear system. The main research contents and main results obtained are summarized as follows:. Firstly, the method of obtaining desired state and output control by Jordan decomposition of matrix and the selection of system initial value is introduced, and the parameterization method of state feedback and output feedback pole assignment is studied. The complete parameterized expression of the controller is obtained by solving the Sylvester matrix equation. By properly selecting the free parameters to obtain the controller which meets the control requirements, but limited by the number of free parameters, the system will sometimes have no solution, in view of this situation. In this paper, an optimization index for approximate solution under state feedback is given, and the approximate solution is obtained. This approximate solution can be avoided by increasing the number of free parameters. This paper is based on the parameterized results of eigenvector matrix. In this paper, we further study how to increase the degree of freedom of the system by introducing new adjustable parameters in order to achieve the desired system characteristics. Then, based on the parameterization method. Using the degree of freedom provided by the parameterized results, the robust design of the system is carried out. In this paper, the matrix perturbation theory is used to analyze the robustness of the system. A new robust index is derived. The principle of the robust index is different from the usual spectral condition number. It is not a function of the eigenvector, so the calculation process is simple and efficient. Therefore, it is more suitable for large scale systems. Considering the advantages of this index, the robust decentralized control problem of large scale systems is further studied. By using the robust index, the closed-loop poles can be easily disposed in a specific region. At the same time, the closed-loop eigenvalues have the minimum sensitivity to external disturbances and parameter changes. In this paper, the parameterization method is studied. The closed-loop eigenvalues are given. The correlation between the eigenvector and the parameterized expression of the feedback gain matrix. The correlation algorithm is summarized, and the effectiveness of the method is demonstrated by a numerical example. Using the degree of freedom provided, a new robust index based on matrix perturbation theory is studied, and the problem of robust decentralized control is solved. The numerical example is compared with the simulation method, and the superiority of the new index is shown.
【學(xué)位授予單位】：東北電力大學(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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