一類線性時變系統(tǒng)的狀態(tài)觀測器設(shè)計方法
發(fā)布時間：2018-12-28 15:26
【摘要】：該論文主要研究控制領(lǐng)域中的線性時變系統(tǒng)的狀態(tài)觀測器設(shè)計問題,其目的在于經(jīng)由狀態(tài)重構(gòu)解決實際工程中系統(tǒng)狀態(tài)量由于種種原因無法完全或部分獲得的問題。區(qū)別于在狀態(tài)觀測器理論方面已經(jīng)趨于成熟的線性定常系統(tǒng),線性時變系統(tǒng)的研究相對困難并且具有挑戰(zhàn)性,所發(fā)表出的理論成果較少,并且更接近于實際工程,故而是近幾年的研究熱點。下面闡述該論文的主要研究內(nèi)容。該論文的設(shè)計思路是對于原有的線性時變系統(tǒng),首先對其進(jìn)行線性非奇異變換以使得變換后的系統(tǒng)具有某種特殊形式,而后對變換后的系統(tǒng)進(jìn)行狀態(tài)觀測器設(shè)計,并最終達(dá)到重構(gòu)原有系統(tǒng)狀態(tài)的設(shè)計要求。針對此思路能夠得知設(shè)計工作主要劃分為兩個部分,即線性非奇異變換以及狀態(tài)觀測器設(shè)計。首先,該論文提出線性時變系統(tǒng)基于方塊展開的狀態(tài)觀測器設(shè)計。線性非奇異變換后的系統(tǒng)中系數(shù)矩陣皆為分塊形式,并且其中包含較多的零陣以及單位陣。而后對變換后的系統(tǒng)進(jìn)行全維,降維以及Luenberger狀態(tài)函數(shù)觀測器設(shè)計,給出各自的動態(tài)方程,系數(shù)矩陣求解方法以及算法步驟等。其次,該論文提出線性時變系統(tǒng)基于行展開的狀態(tài)觀測器設(shè)計。線性非奇異變換矩陣由原有系統(tǒng)能觀測性矩陣中線性無關(guān)的行經(jīng)過運算得到。變換后的系統(tǒng)仍為分塊形式,不同點在于其各個子塊中均包含較多的零元。而后對變換后的系統(tǒng)進(jìn)行全維狀態(tài)觀測器設(shè)計。上述基于一種設(shè)計思路,兩種設(shè)計方法得到的各個狀態(tài)觀測器均由仿真驗證其可行性以及有效性。并且針對兩種設(shè)計方法該論文給出對比,從而在具體實際工程中能夠加以選擇。最后,該論文還對線性時變系統(tǒng)中閉環(huán)系統(tǒng)的分離原理問題進(jìn)行了初步研究,得到該論文所設(shè)計出的狀態(tài)觀測器均符合分離原理的結(jié)論。該論文主要研究成果是對線性時變系統(tǒng)的狀態(tài)觀測器設(shè)計此研究課題在理論層面上的推進(jìn)與添補(bǔ)。所設(shè)計出的狀態(tài)觀測器其優(yōu)點在于可以避免求解復(fù)雜的矩陣微分方程,并且將部分運算轉(zhuǎn)化到線性定常系統(tǒng)中。這樣極大地降低與簡化了計算復(fù)雜度以及計算量。故而也有其實際工程層面的意義。
[Abstract]:This paper focuses on the design of state observer for linear time-varying systems in the field of control. The purpose of this paper is to solve the problem that the system state variables can not be obtained completely or partially in practical engineering because of various reasons. Different from the linear time-invariant systems which have become mature in the theory of state observer, the study of linear time-varying systems is relatively difficult and challenging, and the published theoretical results are less and closer to the actual engineering. Therefore, it is a hot research topic in recent years. The main research contents of this paper are described below. The design idea of this paper is to design the original linear time-varying system by linear nonsingular transformation to make the transformed system have some special form, and then to design the state observer for the transformed system. Finally, the design requirements of reconstructing the original system state are achieved. According to this idea, the design work can be divided into two parts: linear nonsingular transformation and state observer design. Firstly, the design of state observer for linear time-varying systems based on block expansion is proposed. In the linear nonsingular transformation system, the coefficient matrices are all partitioned, and they contain more zero matrices and unit matrices. Then, the full dimension, reduced order and Luenberger state function observer are designed for the transformed system, and their dynamic equations, coefficient matrix solutions and algorithm steps are given. Secondly, this paper presents the design of state observer based on row expansion for linear time-varying systems. The linear nonsingular transformation matrix is derived from the linear independent rows in the observability matrix of the original system. The transformed system is still in block form, the difference is that each subblock of the system contains more zeros. Then the full-order state observer is designed for the transformed system. Based on a design idea, the feasibility and validity of each state observer obtained by the two design methods are verified by simulation. Two design methods are compared in this paper, so that they can be selected in practical projects. Finally, the separation principle of closed-loop systems in linear time-varying systems is studied preliminarily, and it is concluded that the state observers designed in this paper are in accordance with the separation principle. The main achievement of this paper is the design of state observer for linear time-varying systems. The advantage of the designed state observer is that it can avoid solving complex matrix differential equations and transform partial operations into linear time-invariant systems. This greatly reduces and simplifies the computational complexity and computational complexity. Therefore, it also has its practical engineering significance.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP13
本文編號：2394124
[Abstract]:This paper focuses on the design of state observer for linear time-varying systems in the field of control. The purpose of this paper is to solve the problem that the system state variables can not be obtained completely or partially in practical engineering because of various reasons. Different from the linear time-invariant systems which have become mature in the theory of state observer, the study of linear time-varying systems is relatively difficult and challenging, and the published theoretical results are less and closer to the actual engineering. Therefore, it is a hot research topic in recent years. The main research contents of this paper are described below. The design idea of this paper is to design the original linear time-varying system by linear nonsingular transformation to make the transformed system have some special form, and then to design the state observer for the transformed system. Finally, the design requirements of reconstructing the original system state are achieved. According to this idea, the design work can be divided into two parts: linear nonsingular transformation and state observer design. Firstly, the design of state observer for linear time-varying systems based on block expansion is proposed. In the linear nonsingular transformation system, the coefficient matrices are all partitioned, and they contain more zero matrices and unit matrices. Then, the full dimension, reduced order and Luenberger state function observer are designed for the transformed system, and their dynamic equations, coefficient matrix solutions and algorithm steps are given. Secondly, this paper presents the design of state observer based on row expansion for linear time-varying systems. The linear nonsingular transformation matrix is derived from the linear independent rows in the observability matrix of the original system. The transformed system is still in block form, the difference is that each subblock of the system contains more zeros. Then the full-order state observer is designed for the transformed system. Based on a design idea, the feasibility and validity of each state observer obtained by the two design methods are verified by simulation. Two design methods are compared in this paper, so that they can be selected in practical projects. Finally, the separation principle of closed-loop systems in linear time-varying systems is studied preliminarily, and it is concluded that the state observers designed in this paper are in accordance with the separation principle. The main achievement of this paper is the design of state observer for linear time-varying systems. The advantage of the designed state observer is that it can avoid solving complex matrix differential equations and transform partial operations into linear time-invariant systems. This greatly reduces and simplifies the computational complexity and computational complexity. Therefore, it also has its practical engineering significance.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP13
【參考文獻(xiàn)】
相關(guān)期刊論文 前1條
1 段廣仁,吳愛國;廣義線性系統(tǒng)的干擾解耦觀測器設(shè)計[J];控制理論與應(yīng)用;2005年01期
，本文編號：2394124
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