前提匹配的T-S模糊時滯系統(tǒng)穩(wěn)定性分析和控制器設(shè)計
發(fā)布時間：2018-09-13 13:19
【摘要】：眾所周知,時滯現(xiàn)象廣泛存在于各個工程領(lǐng)域當(dāng)中。時滯的存在不僅是導(dǎo)致系統(tǒng)不穩(wěn)定的重要因素之一,還會影響系統(tǒng)的性能。而且目前很多的工程領(lǐng)域涉及到的復(fù)雜的系統(tǒng)都是非線性的,所以,對非線性時滯系統(tǒng)穩(wěn)定性的研究尤為重要,這也正是現(xiàn)代控制理論研究的熱點問題之一。特別地,可以以任意精度逼近一個非線性系統(tǒng)的Takagi-Sugeno(T-S)模糊模型提出后,把專家的實踐經(jīng)驗和線性系統(tǒng)的理論知識相結(jié)合,得到了研究復(fù)雜非線性時滯系統(tǒng)行之有效的方法;這個方法也受到了國內(nèi)外學(xué)者的普遍關(guān)注。隨著線性矩陣不等式(LMI)理論的提出,可以把復(fù)雜非線性時滯系統(tǒng)穩(wěn)定性的研究轉(zhuǎn)化為求解一系列線性矩陣不等式的問題,進一步推動了T-S模糊時滯系統(tǒng)的發(fā)展。因此,對時滯T-S系統(tǒng)穩(wěn)定性的研究,不僅具有重要的理論意義,更具有重要的實際意義。正是基于這樣的背景之下,本文選擇了模糊時滯系統(tǒng)穩(wěn)定性和控制器設(shè)計方面的研究。目前,從相關(guān)文獻的研究中可以得出,主流的方法依然使用的是時域分析法:本文就是基于T-S模糊模型,建立適當(dāng)?shù)睦钛牌罩Z夫泛函(LKF),在對李氏泛函求導(dǎo)之后,通過積分不等式的放縮和矩陣不等式的變換,將其轉(zhuǎn)化成一系列線性矩陣不等式的形式,采用求解線性矩陣不等式的方法得到時滯T-S系統(tǒng)穩(wěn)定性的充分條件以及控制器設(shè)計的相關(guān)準(zhǔn)則。現(xiàn)在已有報道的文獻中,基于狀態(tài)反饋的T-S模糊時滯系統(tǒng)穩(wěn)定性的相關(guān)研究比較多,在降低保守性方面也取得了豐碩的成果;但靜態(tài)輸出反饋(SOF)和動態(tài)輸出反饋(DOF)領(lǐng)域研究的文獻有限,在降低保守性方面也沒有特別好的處理方法;同時,也沒有一套系統(tǒng)的方法既能夠降低狀態(tài)反饋的保守性,又能降低輸出反饋的保守性。所以,本文重點研究了三類問題:一是定常時滯T-S系統(tǒng)的狀態(tài)反饋和靜態(tài)輸出反饋的穩(wěn)定性和控制器設(shè)計問題;二是具有反饋記憶的常時滯T-S系統(tǒng)的狀態(tài)反饋和靜態(tài)輸出反饋的穩(wěn)定性和控制器設(shè)計問題;三是時變時滯T-S系統(tǒng)的動態(tài)輸出反饋鎮(zhèn)定和動態(tài)輸出反饋H_∞控制器設(shè)計問題。對于以上問題,本文在定理證明過程中引入了調(diào)節(jié)矩陣L,通過對L矩陣中某些參數(shù)的設(shè)定,對穩(wěn)定性條件進行調(diào)節(jié),以達到降低保守性的目的。對于狀態(tài)反饋問題,在轉(zhuǎn)化成線性矩陣不等式的過程中,采用了基于引理9的方法;對于輸出反饋問題,在矩陣不等式變換的過程中,引入了調(diào)節(jié)參數(shù)β,通過對β值的恰當(dāng)選取,得到保守性更低的穩(wěn)定條件。最后,對于常時滯T-S系統(tǒng)穩(wěn)定性的研究,本文通過具體實例得出了相關(guān)定理的結(jié)果,并與現(xiàn)有很多文獻的結(jié)果進行了對比說明;針對一些復(fù)雜實例進行了仿真,同時描繪出了相關(guān)的閉環(huán)系統(tǒng)和開環(huán)系統(tǒng)的狀態(tài)響應(yīng)曲線。對于時變時滯T-S系統(tǒng)動態(tài)輸出反饋穩(wěn)定性的研究,本文則是通過具體的案例進行了仿真,得出了仿真結(jié)果的圖表;同時也繪制出了閉環(huán)系統(tǒng)和開環(huán)系統(tǒng)的狀態(tài)響應(yīng)曲線進行比較。通過案例分析結(jié)果的對比和仿真圖表的比較,得出了以下一些結(jié)論:(1)時域分析法,即基于T-S模糊模型,運用李雅普諾夫穩(wěn)定判據(jù)、通過不等式放縮與變換、最終轉(zhuǎn)化成一系列LMIs進行求解,是解決復(fù)雜非線性系統(tǒng)穩(wěn)定性和控制器設(shè)計問題非常有效的方法。(2)在穩(wěn)定性分析的過程中,引入調(diào)節(jié)矩陣L,設(shè)置L中合適的參數(shù)值,在某種程度上可以降低保守性;同時,這個方法也具有很好的通用性。(3)對于狀態(tài)反饋的時滯T-S系統(tǒng),基于引理9的處理方法可以簡化獲取LMIs形式穩(wěn)定條件的過程,同時也能降低保守性。(4)在研究輸出反饋問題(包括靜態(tài)和動態(tài))時,引入恰當(dāng)?shù)膮?shù)β,也可以有效降低保守性。
[Abstract]:As we all know, time-delay phenomenon exists widely in various engineering fields. The existence of time-delay is not only one of the important factors that lead to the instability of the system, but also affects the performance of the system. Especially, the Takagi-Sugeno (T-S) fuzzy model of a nonlinear system can be approximated with arbitrary accuracy. By combining the expert's practical experience with the theoretical knowledge of the linear system, an effective method for studying the complex nonlinear time-delay system is obtained. With the development of linear matrix inequality (LMI) theory, the stability of complex nonlinear time-delay systems can be transformed into solving a series of linear matrix inequalities, which further promotes the development of T-S fuzzy time-delay systems. Based on this background, this paper chooses to study the stability of fuzzy time-delay systems and the design of controllers. At present, from the research of related literature, it can be concluded that the mainstream method is still using the time-domain analysis method: this paper is based on T-S fuzzy. After deriving the LKF, the integral inequality is reduced and transformed into a series of linear matrix inequalities. By solving the linear matrix inequalities, the sufficient conditions for the stability of T-S systems with time-delay and the controller design are obtained. There are many studies on the stability of T-S fuzzy time-delay systems based on state feedback, and plentiful results have been achieved in reducing the conservatism. However, the research on static output feedback (SOF) and dynamic output feedback (DOF) is limited, and there is no special research on reducing the conservatism. There is no systematic method to reduce the conservatism of state feedback and output feedback. Therefore, this paper focuses on three types of problems: the stability of state feedback and static output feedback of T-S systems with time-delay and the design of controllers; and the stability of feedback and output feedback with feedback memory. Stability and controller design of state feedback and static output feedback for T-S systems with constant delays; dynamic output feedback stabilization and H_uuuuuuuuuuuuuuuuuuuuu For the state feedback problem, the method based on lemma 9 is adopted in the process of transforming it into linear matrix inequalities; for the output feedback problem, the adjustment parameter beta is introduced in the process of matrix inequality transformation, and the appropriate selection of the value beta is obtained. Finally, for the stability study of T-S systems with constant time-delay, the results of the relevant theorems are obtained through specific examples, and compared with the results of many existing literatures. For the study of dynamic output feedback stability of T-S systems with time-varying delays, the simulation results are obtained through a specific case, and the state response curves of closed-loop and open-loop systems are compared. Some conclusions are drawn as follows: (1) Time domain analysis method, which is based on T-S fuzzy model, applies Lyapunov stability criterion, transforms inequality into a series of LMIs to solve the problem. It is a very effective method to solve the stability and controller design problems of complex nonlinear systems. (2) In the process of stability analysis, Lyapunov stability criterion is used. By introducing the adjusting matrix L and setting the appropriate parameter value in L, conservatism can be reduced to a certain extent. At the same time, this method also has good generality. (3) For the state feedback T-S system with time delay, the processing method based on lemma 9 can simplify the process of obtaining the LMIs form stability conditions, and also can reduce the conservatism. (4) In the study of transmission. When the feedback problem (including static and dynamic) is introduced, the proper parameter beta can also effectively reduce the conservatism.
【學(xué)位授予單位】：西華大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP13
[Abstract]:As we all know, time-delay phenomenon exists widely in various engineering fields. The existence of time-delay is not only one of the important factors that lead to the instability of the system, but also affects the performance of the system. Especially, the Takagi-Sugeno (T-S) fuzzy model of a nonlinear system can be approximated with arbitrary accuracy. By combining the expert's practical experience with the theoretical knowledge of the linear system, an effective method for studying the complex nonlinear time-delay system is obtained. With the development of linear matrix inequality (LMI) theory, the stability of complex nonlinear time-delay systems can be transformed into solving a series of linear matrix inequalities, which further promotes the development of T-S fuzzy time-delay systems. Based on this background, this paper chooses to study the stability of fuzzy time-delay systems and the design of controllers. At present, from the research of related literature, it can be concluded that the mainstream method is still using the time-domain analysis method: this paper is based on T-S fuzzy. After deriving the LKF, the integral inequality is reduced and transformed into a series of linear matrix inequalities. By solving the linear matrix inequalities, the sufficient conditions for the stability of T-S systems with time-delay and the controller design are obtained. There are many studies on the stability of T-S fuzzy time-delay systems based on state feedback, and plentiful results have been achieved in reducing the conservatism. However, the research on static output feedback (SOF) and dynamic output feedback (DOF) is limited, and there is no special research on reducing the conservatism. There is no systematic method to reduce the conservatism of state feedback and output feedback. Therefore, this paper focuses on three types of problems: the stability of state feedback and static output feedback of T-S systems with time-delay and the design of controllers; and the stability of feedback and output feedback with feedback memory. Stability and controller design of state feedback and static output feedback for T-S systems with constant delays; dynamic output feedback stabilization and H_uuuuuuuuuuuuuuuuuuuuu For the state feedback problem, the method based on lemma 9 is adopted in the process of transforming it into linear matrix inequalities; for the output feedback problem, the adjustment parameter beta is introduced in the process of matrix inequality transformation, and the appropriate selection of the value beta is obtained. Finally, for the stability study of T-S systems with constant time-delay, the results of the relevant theorems are obtained through specific examples, and compared with the results of many existing literatures. For the study of dynamic output feedback stability of T-S systems with time-varying delays, the simulation results are obtained through a specific case, and the state response curves of closed-loop and open-loop systems are compared. Some conclusions are drawn as follows: (1) Time domain analysis method, which is based on T-S fuzzy model, applies Lyapunov stability criterion, transforms inequality into a series of LMIs to solve the problem. It is a very effective method to solve the stability and controller design problems of complex nonlinear systems. (2) In the process of stability analysis, Lyapunov stability criterion is used. By introducing the adjusting matrix L and setting the appropriate parameter value in L, conservatism can be reduced to a certain extent. At the same time, this method also has good generality. (3) For the state feedback T-S system with time delay, the processing method based on lemma 9 can simplify the process of obtaining the LMIs form stability conditions, and also can reduce the conservatism. (4) In the study of transmission. When the feedback problem (including static and dynamic) is introduced, the proper parameter beta can also effectively reduce the conservatism.
【學(xué)位授予單位】：西華大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP13
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