飽和約束下輸入時(shí)滯Hamilton系統(tǒng)的魯棒鎮(zhèn)定
發(fā)布時(shí)間：2018-08-25 16:31
【摘要】：在實(shí)際應(yīng)用中,如通信系統(tǒng),電力網(wǎng)絡(luò)和工程系統(tǒng)中經(jīng)常出現(xiàn)飽和、狀態(tài)或者輸入時(shí)滯以及各種不確定的現(xiàn)象.這些因素的存在往往會(huì)導(dǎo)致系統(tǒng)穩(wěn)定性的急劇惡化.近幾十年來,控制界產(chǎn)生了大量有關(guān)飽和約束下時(shí)滯系統(tǒng)的穩(wěn)定和控制研究成果.然而,大部分成果是有關(guān)線性系統(tǒng)的,在非線性系統(tǒng)領(lǐng)域的研究結(jié)果相對(duì)較少.作為一類特殊而重要的非線性系統(tǒng),PCH(Port-Controlled Hamiltonian)系統(tǒng)具有豐富的實(shí)際應(yīng)用背景,比如電力系統(tǒng)、通訊系統(tǒng)、機(jī)械系統(tǒng)等實(shí)際系統(tǒng)都可以抽象成PCH系統(tǒng)的形式.其中的Hamilton函數(shù)可以看成具體系統(tǒng)的總能量,而且在一定條件下可以作為系統(tǒng)的Lyapunov函數(shù).因此,在Hamilton系統(tǒng)框架下,解決具有飽和與時(shí)滯的非線性系統(tǒng)的控制問題具有重要意義.本文主要針對(duì)PCH系統(tǒng)在受飽和約束的情況下,研究該系統(tǒng)輸入為常數(shù)時(shí)滯和時(shí)變時(shí)滯兩種情況下的魯棒控制設(shè)計(jì)問題.眾所周知,研究系統(tǒng)魯棒控制迫在眉睫的問題是,如何設(shè)計(jì)控制器使閉環(huán)系統(tǒng)在輸入飽和、時(shí)滯和不確定存在的情況下保持穩(wěn)定.本文主要利用L-K(Lyapunov Krasovskii)泛函方法和Wirtinger不等式方法得出保守性相對(duì)較小的結(jié)果.本文的主要內(nèi)容如下:(i)具有飽和的時(shí)滯無關(guān)和時(shí)滯相關(guān)的Hamilton系統(tǒng)的鎮(zhèn)定.首先,針對(duì)飽和的輸入常時(shí)滯的Hamilton系統(tǒng),借助Wirtinger不等式,得到了使系統(tǒng)穩(wěn)定的充分條件.然后,考慮變時(shí)滯的情況,由于變時(shí)滯問題的復(fù)雜性,我們引入另一種形式的Wirtinger不等式,得出了使系統(tǒng)穩(wěn)定的充分條件.最后,將得到的結(jié)果應(yīng)用于電力系統(tǒng)中,驗(yàn)證所得結(jié)論的正確性.(ii)具有不確定的飽和輸入時(shí)滯Hamilton系統(tǒng)的魯棒鎮(zhèn)定.在這一部分,我們考慮系統(tǒng)的不確定為非參數(shù)不確定,而且該不確定因素是屬于一個(gè)凸有界多面體域.然后,參照Convex Combination的方法簡化系統(tǒng)中的飽和項(xiàng)再使用傳統(tǒng)的控制器,最終利用Wirtinger不等式得出了非參數(shù)不確定的飽和輸入時(shí)滯Hamilton系統(tǒng)的魯棒鎮(zhèn)定結(jié)論.最后,結(jié)論的可行性通過一個(gè)數(shù)值例子得以驗(yàn)證.
[Abstract]:In practical applications, such as communication systems, power networks and engineering systems, saturation, state or input delays and various uncertainties often occur. The existence of these factors often leads to the rapid deterioration of system stability. In recent decades, there have been a lot of researches on the stability and control of time-delay systems under saturation constraints. However, most of the results are related to linear systems, and there are relatively few results in the field of nonlinear systems. As a special and important nonlinear system, Port-Controlled Hamiltonian (Port-Controlled Hamiltonian) system has rich practical application background, such as power system, communication system, mechanical system and other practical systems can be abstracted into the form of PCH system. The Hamilton function can be regarded as the total energy of the system, and it can be regarded as the Lyapunov function of the system under certain conditions. Therefore, it is of great significance to solve the control problem of nonlinear systems with saturation and delay under the framework of Hamilton system. In this paper, the robust control design problem for PCH systems with constant and time-varying delays is studied. As we all know, the urgent problem to study the robust control of the system is how to design a controller to keep the closed-loop system stable in the presence of input saturation, time delay and uncertainty. In this paper, we mainly use L-K (Lyapunov Krasovskii) functional method and Wirtinger inequality method to get the result that the conservatism is relatively small. The main contents of this paper are as follows: (i) has saturated delay-independent and delay-dependent Hamilton systems. Firstly, for saturated Hamilton systems with constant time-delay input, sufficient conditions for the stability of the systems are obtained by means of Wirtinger inequality. Then, considering the case of variable delay, due to the complexity of the problem of variable delay, we introduce another form of Wirtinger inequality, and obtain sufficient conditions for the stability of the system. Finally, the obtained results are applied to power systems to verify the correctness of the obtained results. (ii) has robust stabilization of uncertain saturated input time-delay Hamilton systems. In this part we consider the uncertainty of the system as nonparametric uncertainty and the uncertainty belongs to a convex bounded polyhedron domain. Then, referring to Convex Combination's method, the saturation term in the system is simplified and the traditional controller is used. Finally, by using the Wirtinger inequality, the robust stabilization results of the nonparametric uncertain saturated time-delay Hamilton systems are obtained. Finally, the feasibility of the conclusion is verified by a numerical example.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O231
本文編號(hào)：2203472
[Abstract]:In practical applications, such as communication systems, power networks and engineering systems, saturation, state or input delays and various uncertainties often occur. The existence of these factors often leads to the rapid deterioration of system stability. In recent decades, there have been a lot of researches on the stability and control of time-delay systems under saturation constraints. However, most of the results are related to linear systems, and there are relatively few results in the field of nonlinear systems. As a special and important nonlinear system, Port-Controlled Hamiltonian (Port-Controlled Hamiltonian) system has rich practical application background, such as power system, communication system, mechanical system and other practical systems can be abstracted into the form of PCH system. The Hamilton function can be regarded as the total energy of the system, and it can be regarded as the Lyapunov function of the system under certain conditions. Therefore, it is of great significance to solve the control problem of nonlinear systems with saturation and delay under the framework of Hamilton system. In this paper, the robust control design problem for PCH systems with constant and time-varying delays is studied. As we all know, the urgent problem to study the robust control of the system is how to design a controller to keep the closed-loop system stable in the presence of input saturation, time delay and uncertainty. In this paper, we mainly use L-K (Lyapunov Krasovskii) functional method and Wirtinger inequality method to get the result that the conservatism is relatively small. The main contents of this paper are as follows: (i) has saturated delay-independent and delay-dependent Hamilton systems. Firstly, for saturated Hamilton systems with constant time-delay input, sufficient conditions for the stability of the systems are obtained by means of Wirtinger inequality. Then, considering the case of variable delay, due to the complexity of the problem of variable delay, we introduce another form of Wirtinger inequality, and obtain sufficient conditions for the stability of the system. Finally, the obtained results are applied to power systems to verify the correctness of the obtained results. (ii) has robust stabilization of uncertain saturated input time-delay Hamilton systems. In this part we consider the uncertainty of the system as nonparametric uncertainty and the uncertainty belongs to a convex bounded polyhedron domain. Then, referring to Convex Combination's method, the saturation term in the system is simplified and the traditional controller is used. Finally, by using the Wirtinger inequality, the robust stabilization results of the nonparametric uncertain saturated time-delay Hamilton systems are obtained. Finally, the feasibility of the conclusion is verified by a numerical example.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O231
【參考文獻(xiàn)】
相關(guān)期刊論文 前2條
1 ;Stability for a class of nonlinear time-delay systems via Hamiltonian functional method[J];Science China(Information Sciences);2012年05期
2 ;L_2 DISTURBANCE ATTENUATION FOR A CLASS OF TIME-DELAY HAMILTONIAN SYSTEMS[J];Journal of Systems Science & Complexity;2011年04期
，本文編號(hào)：2203472
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