论文标题:不确定关联系统分散鲁棒控制理论及其应用研究
Decentralized Robust Control Theory and Its Application for Interconnected Uncertain Systems
论文作者 陈宁
论文导师 桂卫华,论文学位 博士,论文专业 控制理论与控制工程
论文单位 中南大学,点击次数 72,论文页数 129页File Size4830k
2002-06-01论文网 http://www.lw23.com/lunwen_74223427/ 关联大系统;分散鲁棒控制;H∞控制;不确定性;状态反馈:输出反馈;无源化控制;输出跟踪;线性矩阵不等式;时滞
large-scale interconnected system;decentralized robust control;Ha∞control;uncertainties;state feedback;output feedback;passive control;output track;LMI;time delay
本论文研究关联大系统的分散鲁棒控制理论及应用，在概述了分散鲁棒控制理论的发展及现状的基础上，对具有不确定性关联大系统的分散鲁棒状态反馈与输出反馈、分散无源化控制、时滞大系统分散H_∞控制和分散输出跟踪控制以及在锌湿法冶炼过程中的应用问题做了详细的研究。主要包括以下七个部分： (1)首先，针对一类仅含状态不确定性的关联系统，提出一种基于线性矩阵不等式(LMI)的分散H_∞状态反馈控制的设计方法。在此基础上，研究并提出了当控制器在规定范围内的一部分失效时的分敞H_∞可靠控制问题，提出了能保证闭环系统可靠稳定和具有一定H_∞性能的分散可靠控制器的设计方法。其次，从子系统水平上研究了一类状态、控制和关联矩阵均具有不确定性的关联大系统的分散控制问题，获得了能分散状态反馈镇定的充分条件。分别给出了数值例子，说明了算法的有效性。 (2)研究状态和控制均存在不确定性的关联大系统基于状态观测器的分散鲁棒H_∞控制问题，提出了一种基于观测器的分散动态输出反馈控制器的设计方法。所设计的控制器能使闭环系统对可容许的不确定性分散二次镇定，且满足一定的H_∞性能。得到了基于LMI条件的分散状态观测器的设计算法。给出了算例，说明了状态观测器的设计步骤。 (3)给出了一种新的分散H_∞输出反馈控制器的参数化方法，并提出了求解分散H_∞输出反馈控制器的交叉迭代算法。该算法通过固定非线性矩阵不等式中的某些变量，使非线性矩阵不等式成为LMI，从而使求解一个具有非线性矩阵不等式约束的最小化问题变为两个具有LMI约束的最小化问题，通过交叉迭代求解这两个最小化问题，即可获得分散H_∞输出反馈控制器。仿真示例表明，该法收敛性良好，计算方法直观、简单，便于实际应用。在此基础上，研究了一类具有仿射结构不确定性的关联大系统，不确定性假定为在多面体内，线性地依赖于时变参数。提出了分散强鲁棒H_∞性能准则，给出了保证由输入到输出的L_2诱导范数来量测的不确定性大系统鲁棒性能的分散输出反馈控制器存在的充分条件及迭代算法。通过数值例子，说明了算法的有效性。 (4)将无源性概念引进到关联大系统的分散无源化控制问题中，研究了具有范数界不确定性的大系统的分散鲁棒无源化控制问题。给出了存在一个分散动态输出反馈控制器使得闭环系统渐近稳定且严格无源的充分条件。详细的仿 摘要真示例说明了理论的可行性。 (5)针对控制输入、状态及关联矩阵同时存在不同时滞的不确定性时滞大系统，提出了分散H。状态反馈控制器的设计方法。基于LMI解的存在性，应用Lyapunov稳定性原理设计一类分散线性无一记忆状态反馈控制器，使被控系统渐近稳定，并满足一定Hco性能水平。 (6)研究了在满足匹配条件和具有数值界可不满足匹配条件的两类不确定性时的关联时滞系统的分散鲁棒输出跟踪控制问题，得到了使两类时滞大系统渐近跟踪给定参考输入的LMI条件，提出了具有较小反馈增益控制律的LMI设计方法。该方法克服了Riccati方程方法需预先调整多个参数，计算复杂，应用不便的问题。 (7)研究了锌湿法冶炼过程中浸出工序的分散H。控制。通过对浸出工艺过程的反应机理的深入研究，建立了整个浸出过程的数学模型。在此基础上，提出了锌湿法冶炼浸出过程的分散H。鲁棒控制器的设计方法，并进行了控制系统的仿真研究，给出系统稳定性和性能的仿真曲线，说明了设计方法的可行性。
This paper discusses decentralized robust control theory and its applications for large-scale interconnected systems. Beginning with the overview of the development and the present situation of decentralized robust control theory, the paper focuses on the decentralized state feedback and output feedback control for large-scale uncertain systems, decentralized passive control, decentralized H∞, control and decentralized output tracking control for large-scale system with time-delay, and the application to the process of zinc hydrometallurgy. The research consists of the following seven sections:Section 1 firstly proposes a design approach for decentralized H∞ control using state feedback for large-scale uncertain system based on the linear matrix inequalities(LMIs). And then, the studies come to decentralized reliable H∞ control problem when possible actuator failures occur within prespecified subset of actuators, and a design approach for the existence of a decentralized robust reliable H∞, controller is presented. After that, the decentralized H∞, control problem for a class of interconnected uncertain systems with time varying but norm-bounded parametric uncertainties is addressed and a sufficient condition which makes the closed-loop system decentralized asymptotically stable with disturbance attenuation is derived. Examples are given to demonstrate the effectiveness of the design approaches.Section 2 studies the decentralized robust H∞, observer-based control for a class of interconnected uncertain systems with time-varying uncertainties both in state and control matrices. A design method is derived for decentralized observer-based controller, which makes the closed-loop system quadratically stable with an H∞-norm bound for any admissible uncertainties. We obtain a design algorithm for decentralized observer-based controller on the basis of LMI conditions. Finally, a numerical example is given to demonstrate the design procedure for the decentralized Ho∞ observer-based feedback controller.Section 3 proposes a new parameterization approach to decentralized H∞ output feedback controller and a cross iterative algorithm for decentralized H∞ output feedback control design. By fixing some of the optimization variables of nonlinear matrix inequality, the decentralized output feedback problem can be converted to linear matrix inequality. Then the decentralized control problem turns to be some convex optimizations. The example shows the excellent convergence, directness and simplicity of computation, and convenience in application. Based on the research, the decentralized H∞ output feedback control is studied for large-scale systems with structured uncertainties. The uncertainty is assumed to be polytopic. With the strong robust H∞ performance criterion proposed, a sufficient condition and an iterative algorithm for theAbstractexistence of dynamic output feedback H controllers are given in terms of linear matrix inequalities. Also a given example shows the effectiveness of the algorithm.Section 4 studies the decentralied passive control of a class of large-scale systems with norm-bounded uncertainties by means of applying the notion of passivation to the decentralized control problem of large-scale systems and a sufficient condition for interconnected uncertain system to be asymptotically stable with strict passivity is given in terms of linear matrix inequality. A detailed simulation example is given to illustrate the theoretical developments.Section 5 proposes a decentralized H controller design approach for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. It is based on the existence of the solution to the LMI and the application of the Lyapunov stability theorem. The designed controller enables the closed-loop system decentralized asymptotically stable and satisfies the H performance attenuation.Section 6 discusses the decentralized robust tracking control problem for interconnected time-d
|
