参数不确定时滞系统的稳定性分析及鲁棒控制器设计.pdf

硕士学位论文硕士学位论文参数不确定时滞系统的稳定性分析及鲁棒参数不确定时滞系统的稳定性分析及鲁棒参数不确定时滞系统的稳定性分析及鲁棒参数不确定时滞系统的稳定性分析及鲁棒控制器设计控制器设计控制器设计控制器设计STABILITYSTABILITYSTABILITYSTABILITYANLYSISANLYSISANLYSISANLYSIS ANDANDANDAND ROBUSTROBUSTROBUSTROBUSTCONTROLLERCONTROLLERCONTROLLERCONTROLLER DESIGNDESIGNDESIGNDESIGN OFOFOFOFTHETHETHETHEPARAMETERSPARAMETERSPARAMETERSPARAMETERS UNCERTAINUNCERTAINUNCERTAINUNCERTAINTIME-DELAYTIME-DELAYTIME-DELAYTIME-DELAYSYSTEMSSYSTEMSSYSTEMSSYSTEMS李佳李佳哈尔滨工业大学哈尔滨工业大学20122012 年年 7 7 月月国内图书分类号：TP273学校代码：10213国际图书分类号：681.5密级：公开工学硕士学位论文工学硕士学位论文参数不确定时滞系统的稳定性分析及鲁棒参数不确定时滞系统的稳定性分析及鲁棒参数不确定时滞系统的稳定性分析及鲁棒参数不确定时滞系统的稳定性分析及鲁棒 控制器设计控制器设计控制器设计控制器设计硕 士 研 究 生：李佳导师：王茂教授申请学位：工学硕士学科：控制科学与工程所在单位：航天学院答辩日期：2012 年 7 月 3 日授予学位单位：哈尔滨工业大学Classified Index: TP273 U.D.C: 681.5Dissertation for the Doctoral Degree in EngineeringSTABILITYANLYSIS AND ROBUST CONTROLLER DESIGN OF THE PARAMETERS UNCERTAIN TIME-DELAY SYSTEMSCandidateCandidateCandidateCandidate：：：：Li JiaSupervisorSupervisorSupervisorSupervisor：：：：Prof. Wang MaoAcademicAcademicAcademicAcademic DegreeDegreeDegreeDegree AppliedAppliedAppliedApplied forforforfor：：：：Master of EngineeringSpecialitySpecialitySpecialitySpeciality：：：：Control science and EngineeringAffiliationAffiliationAffiliationAffiliation：：：：Department of aeronauticsDateDateDateDate ofof ofof DefenceDefenceDefenceDefence：：：：July, 3th, 2012Degree-Conferring-InstitutionDegree-Conferring-InstitutionDegree-Conferring-InstitutionDegree-Conferring-Institution：：：： Harbin Institute of Technology哈尔滨工业大学工学硕士学位论文I摘摘摘摘 要要要要在自动控制系统中，时滞现象是广泛存在的。

由于时滞项的存在，控 制系统的稳定性、时域性能、频域性能等都会受到相应的影响，所以研究时 滞系统对于控制系统的分析与设计具有深刻的意义 本文主要利用线性矩阵 不等式的相关理论，研究了时滞系统的稳定性问题、∞H控制问题以及保成 本控制问题 利用改进的 Lyapunov 函数提出新的稳定性判据，设计了∞H控制器和保成本控制器，并且通过数值仿真证明了方法的可行性及优越性论文首先归纳总结了时滞系统的研究现状、线性矩阵不等式的分析方 法 简单介绍了时滞系统相关的基本知识、 系统模型， 以及之前研究的方法、 提出的定理，为后文改进算法提供理论基础 其次研究了时滞系统的稳定性问题针对三种典型的时滞系，即时滞独 立系统、时滞依赖系统以及参数不确定时滞系统，分别给出了系统的稳定性 判据，并且转化为线性矩阵不等式典型的可行性问题来求解提出的稳定性判据具有较小的保守性，仿真结果证明了此方法的优越性 然后研究了时滞系统的∞H控制问题分别设计了无记忆状态反馈控制 器和动态输出反馈控制器， 使得闭环控制系统是渐近稳定的， 并且系统的∞H范数小于某个给定值 通过线性矩阵不等式可行性问题解得控制器的参数矩 阵，数值仿真验证了控制器设计方法的有效性。

最后研究了时滞系统的保成本控制 保成本控制是对时滞系统性能的优化处理，在实际系统中具有重要的应用价值 本文设计了无记忆状态反馈控 制器使得闭环系统是渐近稳定的， 同时使得系统的二次成本函数具有最小的 上界 在求解过程中， 利用线性矩阵不等式可行性问题得到控制器参数矩阵， 并且给出实际战斗机例子，仿真过程证明了这种方法的有效性关键词关键词：时滞系统；线性矩阵不等式；∞H控制；保成本控制哈尔滨工业大学工学硕士学位论文IIAbstractAbstractAbstractAbstractIt is a common thing that time delay phenomena exists in the control systems. Due to the existence of the time-delay item, the stability of the control system, time domain performance, frequency-domain performance will be influenced ,So it is very important to study the time-delay systems for theanalysis and design of the control system .This paper mainly by using the linear matrix inequality related theory, study the stability of the system with time-delay, control problems and guaranteed cost control problem,The paper puts forward the stability conditions, design the corresponding controller, and the numerical simulation results prove the feasibility of the method and the superiority. First of all, this paper summarizes the current research of systems with timedelay, the linear matrix inequality (LMI) method of analysis. Then Introduced the basic knowledge of systems with time delay, system model. The paper focuses on the method of previous studies, proposed the , the improved theorem. Second, this paper studies the stability of the system with time-delay. Divided into three kinds of typical systems with time delay, delay-dependent system, delay- independent system system and parameter uncertain time-delay system.The stability criterion are given, and into the linear matrix inequality the feasibility problems to solve. The improved algorithm has smaller conservative, in the process of simulation proved the validity of the proposed method. Andthen,theresearchofthedelaysystem∞Hcontrolproblem.Respectively memoryless state feedback controller and dynamic output feedback controller are designed , the closed-loop control system is asymptotically stable,and the performance of system is less than a given value norm. Through the linear matrix inequality , the parameters of the matrix to controller is solved, the numerical simulation results prove the superiority of the controller design method. Finally,this paper studies the guaranteed cost control systems with time delay. Memoryless state feedback controller is designed so that the closed-loop system is asymptotically stable, and the second cost∞Hfunction has the upperbound of the smallest. Guaranteed cost control systems with time delay has important application value of the performance optimization. In the solving哈尔滨工业大学工学硕士学位论文IIIprocess, by using the linear matrix inequality feasibility problems,controller parameter matrices is got, and gives a real fighter example, the simulation results prove the validity of the proposed methodKeyKeyKeyKey wordswordswordswords: time-delay systems ,linear matrix inequality ,∞Hcontrol ,guaranteed cost control哈尔滨工业大学工学硕士学位论文IV目目目目 录录录录摘摘摘摘 要要要要...........................。