【作者】 蒋培刚；

【导师】 褚健；

【作者基本信息】 浙江大学 ， 控制理论与控制工程， 2001， 博士

【摘要】 在实际工业过程控制中要想完全准确地建立控制对象的数学模型是不可能的，通过模型降阶近似，非线性特性的线性化近似，以及忽略对象难以建模的动态特性，外部工作环境的变化和各种不可测干扰之后所得到的对象模型跟实际对象的特性存在一定的差距，这种差距往往可以看成是系统模型的一种不确定性。通常，我们对于这些不确定性并不是一无所知的，而是能给出这些不确定性大小的某种度量，在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。另一方面，在实际的工业过程中，大惯性环节，传输过程，复杂的在线分析仪等等不可避免地会导致滞后现象，而这些滞后特性往往会严重影响控制系统的稳定性以及系统的性能指标，因此时滞系统地研究同样具有重要的理论和实际工程意义，而且历来是控制理论研究的热点之一。本文主要研究用状态空间模型描述的线性不确定时滞系统的鲁棒控制问题。 本文的研究工作主要基于Lyapunov稳定性定理，Razumikhin稳定性定理以及凸集的有关理论，并采用了线性矩阵不等式，矩阵分析以及凸规划等工具。本文针对具有范数有界不确定参数或凸多面体不确定参数的线性不确定时滞系统，采用时滞无关和时滞依赖两种不同的方法研究其鲁棒稳定性分析，鲁棒镇定控制器设计以及具有各种鲁棒性能约束的控制器设计问题。主要研究内容包括： 1．针对具有范数有界不确定参数和凸多面体不确定参数的线性不确定 时滞系统，分别给出了它们时滞无关鲁棒二次可镇定的充分必要条件 以及相应的控制器设计方法，结果以线性矩阵不等式的形式给出。通 过跟其他充分性方法比较最大的允许不确定界，表明本文的方法大大 减小了保守性。 2．针对具有范数有界不确定参数和凸多面体不确定参数的线性不确定 时滞系统，分别给出了它们时滞无关指定鲁棒H~∞性能约束可镇定的 充分必要条件以及相应的控制器设计方法，结果以线性矩阵不等式的n 浙 江 大 学 博 士 学 位 论 文 形式给出。同其他方法相比，本文给出的方法简结明了，而且保守性 低。 3．用时滞依赖方法分别研究了具有范数有界不确定参数和凸多面体不 确定参数并同时具有状态和控制滞后的线性不确定时滞的鲁棒镇定 问题。并给出了几种处理非线性矩阵不等式约束下线性矩阵不等式求 解问题的不同方法。 4．讨论了具有范数有界不确定参数线性不确定时滞系统的指定衰减度 鲁棒稳定的一个充分性判据以及设计状态反馈控制器使得闭环系统 具有指定鲁棒衰减度的方法。所得结果都是时滞依赖的。 5．研究了具有范数有界不确定参数线性不确定时滞系统的时滞依赖最 优保成本控制问题。构造了闭环系统二次型性能指标的一个鲁棒界， 并给出了一个搜索最优控制器使得闭环系统鲁棒成本上界最小的凸 规划方法。 6．针对一类具有扇形饱和特性执行器和具有范数有界不确定参数的不 确定时滞系统，研究其状态反馈鲁棒可镇定条件以及相应的控制器设 计方法问题，分别给出了时滞无关和时滞依赖的结果。 7．针对一类具有扇形饱和特性执行器和具有范数有界不确定参数的不 确定时滞系统，研究其状态反馈鲁棒厂”控制问题。给出了时滞无关 的指定鲁棒H“性能约束可镇定的充分条件以及相应的控制器设计 方法。 最后是全文的总结以及展望。更多还原

【Abstract】 It is always impossible to obtain accurate mathematics model for the practical industrial process control. The model under which the controller is designed is usually different to the real plant owing to model reduction, linear approximations and the ignoring of the dynamics difficulty for modeling, the changing of the operating environment and other unmeasurable disturbances. The difference which some measure can be given usually can be described as the uncertainties in the model arguments. Robust control, the control method considering such uncertainties when designing controller is a effective way to deal with the uncertain parameters. In the other hand, because of transmission process, large-lag links and complicated on-line analyzer etc, a large number of industrial processes (in metal engineering, chemical engineering systems, biomedical systems and so on) can be modeled as time-delay systems. Systems stability and performance are always dominated by the delay phenomena, so the study of delay systems always attracts considerable attention in the control theory literature, in this paper, kinds of robust control problem for linear uncertain time-delay systems are studied in detail. Based on Lyapunov stability theory, Razumikhin stability theory and convex set theory, linear matrix inequality, matrix analyzing methods and convex programming are adopted in this paper. Robust stability criteria, the design methods of robust stabilizing controller and guaranteeing certain robust performance controller for linear time-delay system with norm-bounded uncertainties or convex polyhedron uncertainties are studied in this paper by delay independent method and delay dependent method. The main contents are as follows: Iv 1. For linear time-delay systems with norm-bounded uncertainties or convex polyhedron uncertainties, a sufficient and necessary delay independent robust quadratically stabilizable condition and the corresponding robust stabilizing controller designing methods are given in the terms of linear matrix inequalities. The results in this paper deduce a lager allowed upper bound of uncertainties comparing to previous results. 2. For linear time-delay systems with norm-bounded uncertainties or convex polyhedron uncertainties, a sufficient and necessary delay independent condition of quadratic stabilizability under certain robust H~? performance constraint and the corresponding robust stabilizing controller designing methods are given in the terms of linear matrix inequalities. The methods presented in this paper are more concise and less conservative comparing to the previous results. 3. The problem of robust stabilization for a class of linear systems with state and control delay, norm-bounded uncertainties or convex polyhedron uncertainties is discussed using delay dependent method. Methods of solving linear matrix inequalities under nonlinear matrix inequality constraint are also presented. 4. For a class of linear time-delay systems with norm-bounded uncertainties, the concept of system attenuance is introduced. A definite attenuance robust stability criteria, a sufficient condition for the existence of definite attenuance memoryless state feedback control law and the corresponding method of controller design are derived. The results are de更多还原