【摘要】：隨著計算機(jī)科學(xué)的快速發(fā)展,分?jǐn)?shù)階理論已經(jīng)在流體力學(xué)、信號分析以及電力電子等諸多領(lǐng)域開始得到應(yīng)用。分?jǐn)?shù)階微積分是整數(shù)階微積分的擴(kuò)展,即微積分的階次是分?jǐn)?shù)。由于分?jǐn)?shù)階系統(tǒng)具有記憶性和遺傳性,因此對系統(tǒng)動態(tài)過程的描述更為合理和精確。另外,分?jǐn)?shù)階控制器本身提供了更多的調(diào)節(jié)參數(shù),并且參數(shù)整定的選擇范圍更廣。分?jǐn)?shù)階微積分的特性以及在理論研究的不斷突破,這使得分?jǐn)?shù)階控制的應(yīng)用方面也得到了越來越多的重視。在實(shí)際應(yīng)用中,對于系統(tǒng)而言,并非所有的狀態(tài)變量都能夠容易測得。因此,分?jǐn)?shù)階微分系統(tǒng)觀測器的設(shè)計,具有重要的理論意義與應(yīng)用價值,也是分?jǐn)?shù)階控制理論在實(shí)際工程應(yīng)用中一個亟待解決的問題。本論文對分?jǐn)?shù)階濾波器以及分?jǐn)?shù)階觀測器方面進(jìn)行研究。主要進(jìn)行的工作有:(1)提出一種分?jǐn)?shù)階觀測器的設(shè)計方法。針對一類非線性系統(tǒng),通過引入連續(xù)頻率分布等價模型以及利用間接李雅普諾夫方法,獲得全維觀測器動態(tài)誤差系統(tǒng)漸近穩(wěn)定的充分條件,并結(jié)合LMI工具求解觀測器增益。(2)提出分?jǐn)?shù)階濾波器設(shè)計方法。離散化近似處理是對分?jǐn)?shù)階濾波器數(shù)字實(shí)現(xiàn)的關(guān)鍵,離散化近似處理方法即是對于分?jǐn)?shù)階生成函數(shù)和展開方法上的選擇。利用幾種常見的離散化方法進(jìn)行濾波器設(shè)計。分析各種離散法的性能,比較出符合濾波器設(shè)計的要求。分析出濾波器的階次選擇。(3)針對電動扭矩加載系統(tǒng)的數(shù)學(xué)模型,在分?jǐn)?shù)階濾波器的基礎(chǔ)上設(shè)計分?jǐn)?shù)階抗干擾觀測器,同時驗(yàn)證對抗干擾以及抗擾動的性能。然后與傳統(tǒng)的PI控制進(jìn)行對比顯示分?jǐn)?shù)階干擾觀測器的優(yōu)越性。
[Abstract]:With the rapid development of computer science, fractional order theory has been applied in many fields, such as fluid mechanics, signal analysis, power electronics and so on. Fractional calculus is an extension of integer calculus, that is, the order of calculus is fraction. Because of the memory and heredity of the fractional system, the description of the dynamic process of the system is more reasonable and accurate. In addition, the fractional controller itself provides more adjustment parameters, and the selection range of parameter tuning is wider. The characteristics of fractional calculus and the continuous breakthrough in theoretical research have made more and more attention to the application of fractional order control. In practical application, not all state variables can be easily measured for the system. Therefore, the design of fractional differential system observer has important theoretical significance and application value, and it is also an urgent problem to be solved in practical engineering application of fractional control theory. In this paper, the fractional filter and fractional observer are studied. The main work is as follows: (1) A design method of fractional observer is proposed. For a class of nonlinear systems, the sufficient conditions for the asymptotic stability of the full-order observer dynamic error system are obtained by introducing the continuous frequency distribution equivalent model and the indirect Leonov method, and the observer gain is solved by combining the LMI tool. (2) the fractional filter design method is proposed. Discrete approximate processing is the key to the digital realization of fractional filter. Discrete approximate processing method is the choice of fractional generation function and expansion method. Several common discretization methods are used to design the filter. The performance of various discrete methods is analyzed, and the requirements of filter design are compared. The order selection of the filter is analyzed. (3) aiming at the mathematical model of the electric torque loading system, the fractional anti-interference observer is designed on the basis of the fractional filter, and the performance of anti-interference and anti-disturbance is verified at the same time. Then compared with the traditional PI control, the advantages of the fractional disturbance observer are shown.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TN713

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