饱和约束下输入时滞Hamilton系统的鲁棒镇定

发布时间：2018-08-25 16:31

【摘要】：在实际应用中,如通信系统,电力网络和工程系统中经常出现饱和、状态或者输入时滞以及各种不确定的现象.这些因素的存在往往会导致系统稳定性的急剧恶化.近几十年来,控制界产生了大量有关饱和约束下时滞系统的稳定和控制研究成果.然而,大部分成果是有关线性系统的,在非线性系统领域的研究结果相对较少.作为一类特殊而重要的非线性系统,PCH(Port-Controlled Hamiltonian)系统具有丰富的实际应用背景,比如电力系统、通讯系统、机械系统等实际系统都可以抽象成PCH系统的形式.其中的Hamilton函数可以看成具体系统的总能量,而且在一定条件下可以作为系统的Lyapunov函数.因此,在Hamilton系统框架下,解决具有饱和与时滞的非线性系统的控制问题具有重要意义.本文主要针对PCH系统在受饱和约束的情况下,研究该系统输入为常数时滞和时变时滞两种情况下的鲁棒控制设计问题.众所周知,研究系统鲁棒控制迫在眉睫的问题是,如何设计控制器使闭环系统在输入饱和、时滞和不确定存在的情况下保持稳定.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对较小的结果.本文的主要内容如下:(i)具有饱和的时滞无关和时滞相关的Hamilton系统的镇定.首先,针对饱和的输入常时滞的Hamilton系统,借助Wirtinger不等式,得到了使系统稳定的充分条件.然后,考虑变时滞的情况,由于变时滞问题的复杂性,我们引入另一种形式的Wirtinger不等式,得出了使系统稳定的充分条件.最后,将得到的结果应用于电力系统中,验证所得结论的正确性.(ii)具有不确定的饱和输入时滞Hamilton系统的鲁棒镇定.在这一部分,我们考虑系统的不确定为非参数不确定,而且该不确定因素是属于一个凸有界多面体域.然后,参照Convex Combination的方法简化系统中的饱和项再使用传统的控制器,最终利用Wirtinger不等式得出了非参数不确定的饱和输入时滞Hamilton系统的鲁棒镇定结论.最后,结论的可行性通过一个数值例子得以验证.
[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.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O231

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