【摘要】：在一些實(shí)際的工程領(lǐng)域中存在著多個(gè)數(shù)量級(jí)差別較大的狀態(tài)變量,這是造成系統(tǒng)的動(dòng)態(tài)變化速度差異巨大的根源,從而使得系統(tǒng)具有跨尺度特性,這種以跨尺度為主要特征的動(dòng)態(tài)系統(tǒng)可歸納為奇異攝動(dòng)系統(tǒng)的框架下進(jìn)行研究。奇異攝動(dòng)系統(tǒng)的控制和分析是控制理論的研究熱點(diǎn),主要包括系統(tǒng)穩(wěn)定性、魯棒性、優(yōu)化、控制等。而在故障診斷及容錯(cuò)控制方面的研究和文獻(xiàn)卻相對(duì)較少。從研究方法上來(lái)講,以往的研究多采用模型降階法、快慢分解法、廣義系統(tǒng)法,因此本文從整體的角度,采用一體化設(shè)計(jì)思路,針對(duì)奇異攝動(dòng)系統(tǒng)的故障診斷和容錯(cuò)控制問(wèn)題提出了新的研究方法并得到有意義的結(jié)論,主要內(nèi)容概括如下:1.研究了基于動(dòng)態(tài)輸出反饋的極限奇異攝動(dòng)系統(tǒng)(廣義系統(tǒng))的最優(yōu)干擾抑制問(wèn)題。首先基于廣義系統(tǒng)的相關(guān)理論推導(dǎo)出PI(比例-積分)觀測(cè)器存在的充分條件。考慮到并不是所有的狀態(tài)變量和外部干擾信號(hào)能夠直接測(cè)量,提出了新的PI觀測(cè)器設(shè)計(jì)方法,設(shè)計(jì)了全階和降階兩種觀測(cè)器,通過(guò)求解簡(jiǎn)單的矩陣方程即可得到觀測(cè)器的設(shè)計(jì)參數(shù)。在此基礎(chǔ)上基于線性二次型性能指標(biāo)提出最優(yōu)干擾抑制律,即可保證閉環(huán)系統(tǒng)允許時(shí)在最壞的干擾下,其性能指標(biāo)達(dá)到最小。在數(shù)值算例中,通過(guò)比較原狀態(tài)信號(hào)、干擾信號(hào)和觀測(cè)器狀態(tài)信號(hào)、反饋控制信號(hào)的比較說(shuō)明觀測(cè)器的設(shè)計(jì)合理,最優(yōu)干擾抑制律是有效的。2.研究了奇異攝動(dòng)系統(tǒng)的故障診斷和最優(yōu)容錯(cuò)控制問(wèn)題,這里考慮的是系統(tǒng)的故障為動(dòng)態(tài)特性已知的一類線性奇異攝動(dòng)系統(tǒng)。首先將原系統(tǒng)和故障系統(tǒng)聯(lián)立為增廣系統(tǒng),然后依據(jù)奇異攝動(dòng)系統(tǒng)的相關(guān)理論,提出全維PI觀測(cè)器存在條件。在此基礎(chǔ)上再進(jìn)一步考慮閉環(huán)系統(tǒng)的最優(yōu)性,設(shè)計(jì)了狀態(tài)反饋控制器保證系統(tǒng)漸近穩(wěn)定,并且能夠使得給定的線性二次最優(yōu)性能指標(biāo)最小,最后通過(guò)數(shù)值算例說(shuō)明結(jié)論的有效性及正確性。
[Abstract]:In some practical engineering fields, there are many state variables with great difference in magnitude, which is the root of the great difference in the dynamic change speed of the system, which makes the system have cross-scale characteristics. This kind of dynamic system with cross-scale as the main characteristic can be summarized into the framework of singular perturbed system. The control and analysis of singular perturbed systems is a hot research topic in control theory, including system stability, robustness, optimization, control and so on. However, the research and literature on fault diagnosis and fault-tolerant control are relatively few. From the point of view of research methods, the model reduction method, fast and slow decomposition method and singular system method are mostly used in the previous research. Therefore, from the overall point of view, this paper adopts the integrated design idea. A new research method for fault diagnosis and fault-tolerant control of singular perturbed systems is proposed and meaningful conclusions are obtained. the main contents are summarized as follows: 1. The optimal interference suppression problem for limit singular perturbed systems (singular systems) based on dynamic output feedback is studied. Firstly, based on the theory of singular systems, the sufficient conditions for the existence of PI (proportional integral) observer are derived. Considering that not all state variables and external interference signals can be measured directly, a new PI observer design method is proposed, and two kinds of observers, full order and reduced order, are designed. The design parameters of the observer can be obtained by solving the simple matrix equation. On this basis, the optimal interference suppression law is proposed based on the linear quadratic performance index, which can ensure the minimum performance of the closed-loop system under the worst interference. In the numerical example, the comparison of the original state signal, the interference signal and the observer state signal and the feedback control signal shows that the design of the observer is reasonable and the optimal interference suppression law is effective. 2. In this paper, the problem of fault diagnosis and optimal fault tolerance control for singular perturbed systems is studied. in this paper, the fault of the system is considered as a class of linear singular perturbed systems with known dynamic characteristics. Firstly, the original system and the fault system are combined into the augmented system, and then according to the theory of the singular perturbed system, the existence condition of the full-dimensional PI observer is proposed. On this basis, the optimality of the closed-loop system is further considered, and the state feedback controller is designed to ensure the asymptotic stability of the system, and the given linear quadratic optimal performance index can be minimized. Finally, a numerical example is given to illustrate the validity and correctness of the conclusion.
【學(xué)位授予單位】：北方工業(yè)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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