线性时滞系统的反馈镇定时滞界研究

发布时间：2018-01-13 03:00

本文关键词：线性时滞系统的反馈镇定时滞界研究　出处：《山东大学》2017年博士论文　论文类型：学位论文

【摘要】：时滞现象不但广泛存在于实际工程系统中,并且还会降低系统的控制性能.近几十年来,控制领域的学者给予时滞系统广泛的关注,并系统地研究了系统稳定性分析和控制器设计等问题,获得了丰富的研究成果.而对反馈镇定所容许的时滞界则研究较少,并且也缺乏对系统性能,系统本质特征以及输入时滞之间关系的定量分析.但是对系统的反馈镇定性的分析,特别是对时滞系统本质局限性的研究,尤为重要.本文以含输入时滞线性系统为研究对象,考察在不确定时滞约束下,系统的反馈镇定性能局限,着重于对时滞界上界的求解,以便揭示反馈镇定性,系统内在特征,输入时滞,以及控制策略之间的联系.时滞界问题是时滞系统的一个本质局限,被认为是数学系统和控制理论中的公开难题之一.本文的创新点主要包括如下几点内容:1.针对含多个不稳定极点的定常输入时滞线性系统,利用提出的双线性变换方法,将原无穷维优化问题转化为一个有限维的优化问题.基于频域方法和最优化理论,给出了采用线性时不变控制器时,系统能保持镇定的时滞界的上界.结果表明系统的反馈镇定性能由被控对象的不稳定极点和输入时滞共同决定,同时不稳定极点越大,反馈镇定的时滞界就越小.所得到的定量关系表达式,为控制系统设计提供了理论指导.特别地,我们的结果与已有文献结果是一致的,并且对其进行了推广.2.将时滞界问题由仅考虑系统含定常输入时滞的类型,推广到时变时滞的一般情形.针对时变输入时滞线性系统,首先利用参数代数Riccati方程和Ha1anay型不等式,研究了系统能被状态反馈镇定时,时变时滞应满足的条件.该条件仅与时变时滞函数平方的积分有关,可允许时变时滞是不连续的,对时滞的上界也没有限制.其次,又利用模型变换和小增益定理,得到了时变时滞的一些时滞界.结果表明系统的反馈镇定性能,由闭环系统的传递函数和输入时滞共同确定.多个数值算例验证了所提出方法的有效性.3.针对多输入多输出线性时滞系统,利用以上的类似方法,得到一些反馈镇定时滞界结果.研究表明系统的反馈镇定性能与被控对象不稳定极点,极点方向,以及输入时滞等有关.这些结果与已有文献的结果相一致,并且还包含了一些已有结果.4.将单一输入时滞的趋同时滞界问题,推广到含双输入时滞情形.针对一类含双输入时滞的线性多自主体系统,利用频域方法和代数图理论,得到系统可趋同的时滞界结果.研究结果表明多自主体系统的可趋同性能不仅依赖于被控对象的固有特性,如不稳定极点等,还与网络拓扑和输入时滞有关,而且结果还定量地揭示了输入时滞是如何对可趋同性产生影响的。
[Abstract]:Delay phenomena not only exist widely in practical engineering systems, but also reduce the control performance of systems. In recent decades, researchers in the field of control have paid much attention to time-delay systems. The stability analysis and controller design of the system are studied systematically, and a lot of research results are obtained. However, there are few researches on the time-delay bound of feedback stabilization, and there is also a lack of performance to the system. Quantitative analysis of the essential characteristics of the system and the relationship between input delays. However, the analysis of feedback stabilization of the system, especially the study of the essential limitations of time-delay systems. In this paper, we take linear systems with input time delay as the research object, investigate the limitation of feedback stabilization performance under uncertain time-delay constraints, and focus on the solution of upper bound of time-delay bound in order to reveal the feedback stabilization. The relationship among the characteristics, input delays, and control strategies within the system. The time-delay bound problem is an essential limitation of time-delay systems. It is considered to be one of the open problems in mathematical systems and control theory. The innovation of this paper mainly includes the following points: 1. For linear systems with constant input time delay with multiple unstable poles. By using the bilinear transformation method, the original infinite dimensional optimization problem is transformed into a finite dimensional optimization problem. Based on the frequency-domain method and optimization theory, the linear time-invariant controller is given. The results show that the feedback stabilization performance of the system is determined by both the unstable poles and the input delays, and the larger the unstable poles are. The time delay bound of feedback stabilization is smaller. The quantitative relation expressions obtained provide theoretical guidance for the design of control systems. In particular, our results are consistent with those obtained in previous literatures. The delay bound problem is extended from the type of time-varying input delay to the general case of time-varying delay, and the time-varying input time-delay linear system is extended to the time-varying input time-delay linear system. Firstly, by using parametric algebraic Riccati equation and Ha1anay type inequality, we study the time when the system can be stabilized by state feedback. This condition is only related to the integral of the square of the time-varying delay function, and the time-varying delay is allowed to be discontinuous, and there is no limitation on the upper bound of the time-varying delay. Secondly, this condition is related to the integral of the square of the time-varying delay function. By using model transformation and small gain theorem, some time-varying delay bounds are obtained. The results show the feedback stabilization performance of the system. The transfer function of the closed-loop system and the input delay are determined together. Several numerical examples show the effectiveness of the proposed method. 3. For the multi-input multi-output linear time-delay system, the similar method is used. Some feedback stabilization delay bound results are obtained. It is shown that the feedback stabilization performance of the system is related to the unstable poles, pole directions, and input delays of the plant under control. These results are consistent with those obtained in previous literatures. The convergence delay bound problem with a single input delay is extended to a class of linear multi-agent systems with double input delays. By using frequency-domain method and algebraic graph theory, the time-delay bound results of system convergence are obtained. The results show that the homogeneity of multi-agent systems depends not only on the inherent characteristics of the controlled object, such as unstable poles, etc. It is also related to the network topology and the input delay, and the results also quantitatively reveal how the input delay affects the convergence.
【学位授予单位】：山东大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13

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