【作者】 高金凤；

【导师】 俞立；

【作者基本信息】 浙江工业大学 ， 控制理论与控制工程， 2003， 硕士

【摘要】 实际工业过程控制系统中一般会存在时滞现象，这种时滞在工业装置尺寸较大的情形下体现地尤其明显。如石油化工和冶金工业过程中的容量滞后和传输延时基本上是不可避免的，几十分钟的纯滞后现象也不算稀奇。另外有些大惯性环节、复杂的在线分析仪等等也会导致时延现象。而滞后特性往往会严重影响到控制系统的性能指标甚至使系统不稳定性。所以时滞系统的研究具有重要的理论和实际意义。 另一方面，控制设计所基于的数学模型一般仅仅是被控对象的近似，所以在控制系统中要想完全准确地建立被控对象的数学模型几乎是不可能的。因为外部工作环境的物理和化学变化以及不可测量的干扰因素使得我们得到的对象模型跟实际对象的特性之间存在一定的差距，这种差距可以视为系统模型的不确定性。而且多数情况下我们可以获知此不确定性大小的某种度量，那么在系统稳定性分析和设计控制器时考虑这个不确定性的度量，即鲁棒控制方法是处理系统模型不确定性的有效方法。 本文主要针对一类普遍存在的非线性系统即Lurie系统，采用状态空间的方法展开研究。特别地，在已有文献的基础上，考虑实际工业过程系统中存在的时滞与不确定性情况，基于Lyapunov稳定性理论，采用线性矩阵不等式这一有效的工具，分别给出Lurie直接型与间接型时滞系统的鲁棒绝对稳定性条件和稳定化控制器的设计方法。根据控制器设计与时滞的关系，分为时滞独立鲁棒控制和时滞相关鲁棒控制，考虑到时滞独立鲁棒控制的保守性，本文研究结论给出的是时滞相关的稳定性条件和鲁棒稳定化控制器。具体内容如下:1.针对当前LMI解决控制问题的优越性和简便性这一现状。本文第三 章详细介绍了线性矩阵不等式的基本概念和用于求解线性矩阵不 等式的软件工具箱Matlablmi的三个求解器，对线性矩阵不等式在 控制系统中的应用作了详细的综述，主要分析了其在当前的两个研 究热点即不确定系统的鲁棒控制与鲁棒滤波中的运用。同时探讨了 LMI在时滞系统与非线性系统方面的研究现状。然后列举了一些具 有代表性的采用LMI求解控制问题的最新结果。为了说明线性矩阵 不等式的求解过程，文中给出了一个保性能控制的例子，并且附上 详细的解题程序。2.针对具有范数有界不确定参数的Lur记时滞系统，分别给出了Lurie 直接型系统时滞相关的鲁棒绝对稳定性条件和稳定化控制器以及 Lurie间接型系统时滞相关的鲁棒绝对稳定性条件，结论均采用线 性矩阵不等式的形式给出，通过和最近的其他充分性方法比较最大 的时滞界，表明本文方法大大减少了保守性。更多还原

【Abstract】 There often exist time-delay phenomena in most practical industrial processes control systems, especially in the case of large size of industrial device. For example, petroleum chemical engineering systems and metallurgy systems can be modeled as time-delay systems for their content lag and transmission delay. And it isn’t a rare phenomenon for several ten minutes of delay. In addition to these, some large-lag links and complicated on-line analyzer etc can also result in time-delay. Systems stability and performance are always influenced badly by lag. So the study of delay systems always attracts considerable attention in the control theory.On the other hand, Because of the changing of the physics and chemistry for outside environment and other unmeasurable disturbances, the model under which the controller is designed is usually different to the real plant owing to model reduction. So it is always impossible to obtain accurate mathematics model for the practical controlled plant. And the difference of which some measure can be given usually can be described as the uncertainties in the model arguments. Robust control considering suchuncertainties when analyzing stability and designing controller is a effective way to deal with the uncertain parameters.In this paper, state-space method is adopted to study a class of ubiquitous nonlinear systems, namely Lurie systems. Based on the existed results, this paper considers two kinds of simultaneous cases, that is time-delay and uncertainties, to get the solution of uncertain Lurie time-delay system by means of Lyapunov stability theory and LMI toolbox. At the same time, the robust absolute stability conditions and the design method of robust controllers of Lurie direct-type and indirect-type delay systems are given.The design methods of robust stabilizing controller and guaranteeing certain robust performance controller for Lurie-type delay systems with norm-bounded uncertainties are studied by delay independent method and delay dependent method. In this paper we adopt the delay dependent method for the conservativeness of delay independent method. The main contents are as follows:1. For the advantages and simplicity of LMI toolbox in resolving control problems currently, the chapter 3 of this paper introduces some basic concepts about Linear Matrix Inequalities (LMIs). Three solvers of LMI toolbox of the software Matlab is also presented. A review on the theory and application research for LMI in control systems is described in detail, mainly including robust control and robust filtering ofuncertain systems. At the same time, some nonlinear systems and time-delay systems are discussed. And then, a list of the latest results of some representative control problems via the LMI approach is introduced. Finally, an example is presented to illustrate the procedure of solving LMIs, and the associated programme is also given.2. The problems of robust stability for a class of Lurie direct or indirect systems with time-delay and norm-bounded uncertainties are discussed using delay dependent method. Method of linear matrix inequality is adopted to resolve the problems. Comparing with the other sufficient conditions, the maximum delay obtained in this paper is less conservative.更多还原