非高斯随机分布系统控制与故障检测方法的研究
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摘要
传统随机控制主要研究系统输出均值和方差的统计特性。近十多年来,随机控制的研究领域出现一个新的分支,即非高斯随机分布系统控制理论,它突破了传统随机控制研究仅限于系统随机变量服从高斯分布假设,正在逐步发展成为一个较为完善的建模和控制理论框架,并已成为控制理论及应用研究领域内一个新的研究方向。目前,非高斯随机分布系统的研究主要集中于非高斯随机分布系统控制、非高斯随机分布系统的故障检测与诊断等问题,且这些问题都需要进一步研究和发展。
本论文主要针对非高斯随机分布系统尚未涉及的非高斯随机分布系统保性能控制、有待深入研究的故障检测与故障等内容进行了研究,同时也涉及到容错控制的研究。通过这些研究,可进一步补充、完善非高斯随机分布系统理论。本论文的主要工作如下：
1.非高斯连续随机分布系统具有记忆功能保性能控制的研究。针对非高斯连续随机分布系统的保守性问题,提出具有记忆状态反馈保性能控制算法,并采用凸优化技术对保性能控制算法进行优化,实现系统输出概率密度函数追踪目标概率密度函数,并满足规定的保性能指标
2.非高斯不确定连续随机分布系统神经保性能控制的研究。针对非高斯不确定连续随机分布系统的保守性问题,引入附加增益,并在保性能控制器设计时采用神经控制器调控附加增益,以降低系统的保守性
3.非高斯连续随机分布系统跟踪控制的研究。利用权值向量的约束条件,将非高斯连续随机分布系统跟踪控制和干扰抑制问题转换成基于H∞优化的PID控制问题,解决了系统输出概率密度函数跟踪控制和干扰抑制问题,并在线性矩阵不等式的基础上,得到H∞优化PID控制器存在的条件以及设计算法。
4.非高斯连续随机分布系统故障检测与诊断的研究。采用有理平方根B样条逼近建立系统输出概率密度函数模型(静态模型),利用系统控制输入和静态模型权值之间的动态关系建立系统动态权值模型。之后,引入自适应参数,通过参数的调整来增强残差对故障的敏感度,进而提出了一种新的非线性自适应观测器故障诊断算法,并对系统的稳定性和收敛性进行了分析。
5.非高斯奇异连续随机分布系统故障检测与诊断的研究。采用平方根B样条逼近来建立系统输出概率密度函数模型,利用系统控制输入和静态模型权值之间的动态关系建立系统动态权值模型。之后,非线性观测器被设计用来检测和诊断系统的故障,通过在算法中引入可调参数,提高了残差信号对故障的灵敏度,并通过通过线性矩阵不等式给出非高斯奇异连续随机分布系统稳定性条件。
6.非高斯连续时滞随机分布系统故障检测与诊断的研究。采用RBF神经网络逼近来建立系统输出概率密度函数模型,利用系统控制输入和系统静态模型权值之间的动态关系建立系统动态权值模型。之后,提出了一种参数自适应调整的故障检测与诊断算法,通过引进一个可调参数使残差信号对故障较为敏感。当故障发生时,该算法能够通过自适应调整算法调整参数,有效提高了故障的检测效果。
7.非高斯连续随机分布系统容错控制的研究。采用RBF神经网络逼近建立系统输出概率密度函数模型,利用系统控制输入和系统静态模型权值之间的动态关系建立系统动态权值模型。之后,在系统存在故障和扰动的情况下,提出H∞优化PID容错控制算法,以补偿或者拒绝故障、衰减扰动,实现系统输出概率密度函数追踪目标概率密度函数,并确保非高斯随机分布系统的鲁棒性和稳定性,从而提高系统容错控制效果
总体而言,本论文在非高斯随机分布系统控制理论框架的基础上,结合非线性控制、鲁棒控制、稳定性分析以及故障检测与诊断等多种理论和技术,研究了非高斯随机分布系统的控制、故障检测与诊断以及容错控制等问题,并在现有研究基础上,提出了新的理论和方法,对非高斯随机分布系统理论的完善和发展有着十分积极的作用
Traditional control techniques for stochastic systems are mainly concerned with mean and variance of the variable. In recent years, the stochastic control have formulated a new branch,which is called the stochastic distribute control, where the systems has its input as a deterministic variable and its output as the probability density function (PDF) of the systems output. The research for the stochastic distribution control (SDC) broke through stochastic variables subjected to the assumption of the Gaussian distribution, which is a new topic in stochastic control research, and formulated a relatively complete modeling and control theory.
In the thesis, the control and fault detection and diagnosis for the non-Gaussian stochastic distribution systems will be described. In particular,The study of non-Gaus-sian stochastic distribution systems includes Tracking controll,Fault detection and diagnosis, Fault tolerant control. The theory of non-Gaussian stochastic distribution systems can been further supplement, improve through the article.the The main research work and contributions of this thesis are listed as follows:
1.A guaranteed cost control for non-Gaussian stochastic distribution systems. Attention is focused on a memory state feedback control law based on linear matrix inequality (LMI) with model transformation such that the closed-loop systems is asymptotically stable and the guaranteed cost index is not more than a specified upper bound,which ensure that the systems output PDF follows the target PDF.
2.Neuro-controller designing for guaranteed cost control of non-Gaussian uncertain stochastic distribution dontrol systems.neural controller for the guaranteed cost problem is vestigated. Based on LMI design,a class of a state feedback controller with a gain perturbations is structured,meanwhile,neural controller is used to tune the additive gain perturbations such that the guaranteed cost is reduced,and sufficient conditions for the existence of guaranteed cost controller are derived.
3.Robust tracking control for the non-Gaussian stochastic distribution systems. We considers the design problem of a novel PID control based on Hoo for the non-Gaussian stochastic distribution systems.the PDF tracking control is transformed into a contrained tracking control problem for weight vector by B-spline expansion with modeling errors and the nonlinear weight model with exogenous disturbances. A design approaches PID control based on Hoo are provied to fulfil the PDF tracking problem. Based on LMI,the existence condition of Hoo controller is obtained.
4.Observer-based fault detection and diagnosis for non-Gaussian stochastic disribution systems.a new type of fault detection and diagnosis (FDD) problem for non-gausian stochastic distribution systems via the output PDFs) is investigated. The PDF can be approximated by using rational square-root B-spline expansion,via this expansions to represent the dynamics weighting systems between the systems input and the weights related to the output PDF. a nonlinear adaptive observer-based fault detection and diagnosis algorithm is present by introducing the adaptive tuning rule such that the residual is as sensitive as possible to the fault. Stability and convergency analysis is performed in fault detection and fault diagnosis analysis for the error dynamic systems.
5.Fault detection and diagnosis for non-Gaussian singular stochastic distribution systems.The outputs of singular stochastic systems are described by PDF based on square root B-spline expansions. Then, non-linear observers are designed for the FDD. The conditions of stability of the correlative error estimation systemss are given by using LMI.
6.Fault detection and diagnosis for non-Gaussian stochastic distribution systems with time delays. A RBF neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings. In this work, a nonlinear adaptive observer-based fault detection and diagnosis algorithm is presented by introducing the tuning parameter so that the residual is as sensitive as possible to the fault.
7.Fault tolerant control for non-Gaussian stochastic distribution systems. Different from the conventional FTC methods, the measured information is the output PDFs rather than its instant values,where the RBFs neural network technique is introduced so that the output PDF can be formulated by the dynamic weights. Then based on Hoo techniques and PID controller, the concerned FTC problem can be transferred into a classical nonlinear FTC problem subject to a nonlinear systemss with both of modeling error and the fault. In terms of LMI techniques, a new control method is given so that the fault can be compensated or rejected.
On the whole,this thesis investigates a series of new methods of tracking control and Fault detection and diagnosis for non-Gaussian stochastic distribution systems based on a variety of classical research methods in nonlinear control,stability analysis fields and Fault detection and diagnosis. It is noted that the above results have Important theoretical significance In research for the non-Gaussian stochastic distribution systems.
本论文主要针对非高斯随机分布系统尚未涉及的非高斯随机分布系统保性能控制、有待深入研究的故障检测与故障等内容进行了研究,同时也涉及到容错控制的研究。通过这些研究,可进一步补充、完善非高斯随机分布系统理论。本论文的主要工作如下：
1.非高斯连续随机分布系统具有记忆功能保性能控制的研究。针对非高斯连续随机分布系统的保守性问题,提出具有记忆状态反馈保性能控制算法,并采用凸优化技术对保性能控制算法进行优化,实现系统输出概率密度函数追踪目标概率密度函数,并满足规定的保性能指标
2.非高斯不确定连续随机分布系统神经保性能控制的研究。针对非高斯不确定连续随机分布系统的保守性问题,引入附加增益,并在保性能控制器设计时采用神经控制器调控附加增益,以降低系统的保守性
3.非高斯连续随机分布系统跟踪控制的研究。利用权值向量的约束条件,将非高斯连续随机分布系统跟踪控制和干扰抑制问题转换成基于H∞优化的PID控制问题,解决了系统输出概率密度函数跟踪控制和干扰抑制问题,并在线性矩阵不等式的基础上,得到H∞优化PID控制器存在的条件以及设计算法。
4.非高斯连续随机分布系统故障检测与诊断的研究。采用有理平方根B样条逼近建立系统输出概率密度函数模型(静态模型),利用系统控制输入和静态模型权值之间的动态关系建立系统动态权值模型。之后,引入自适应参数,通过参数的调整来增强残差对故障的敏感度,进而提出了一种新的非线性自适应观测器故障诊断算法,并对系统的稳定性和收敛性进行了分析。
5.非高斯奇异连续随机分布系统故障检测与诊断的研究。采用平方根B样条逼近来建立系统输出概率密度函数模型,利用系统控制输入和静态模型权值之间的动态关系建立系统动态权值模型。之后,非线性观测器被设计用来检测和诊断系统的故障,通过在算法中引入可调参数,提高了残差信号对故障的灵敏度,并通过通过线性矩阵不等式给出非高斯奇异连续随机分布系统稳定性条件。
6.非高斯连续时滞随机分布系统故障检测与诊断的研究。采用RBF神经网络逼近来建立系统输出概率密度函数模型,利用系统控制输入和系统静态模型权值之间的动态关系建立系统动态权值模型。之后,提出了一种参数自适应调整的故障检测与诊断算法,通过引进一个可调参数使残差信号对故障较为敏感。当故障发生时,该算法能够通过自适应调整算法调整参数,有效提高了故障的检测效果。
7.非高斯连续随机分布系统容错控制的研究。采用RBF神经网络逼近建立系统输出概率密度函数模型,利用系统控制输入和系统静态模型权值之间的动态关系建立系统动态权值模型。之后,在系统存在故障和扰动的情况下,提出H∞优化PID容错控制算法,以补偿或者拒绝故障、衰减扰动,实现系统输出概率密度函数追踪目标概率密度函数,并确保非高斯随机分布系统的鲁棒性和稳定性,从而提高系统容错控制效果
总体而言,本论文在非高斯随机分布系统控制理论框架的基础上,结合非线性控制、鲁棒控制、稳定性分析以及故障检测与诊断等多种理论和技术,研究了非高斯随机分布系统的控制、故障检测与诊断以及容错控制等问题,并在现有研究基础上,提出了新的理论和方法,对非高斯随机分布系统理论的完善和发展有着十分积极的作用
Traditional control techniques for stochastic systems are mainly concerned with mean and variance of the variable. In recent years, the stochastic control have formulated a new branch,which is called the stochastic distribute control, where the systems has its input as a deterministic variable and its output as the probability density function (PDF) of the systems output. The research for the stochastic distribution control (SDC) broke through stochastic variables subjected to the assumption of the Gaussian distribution, which is a new topic in stochastic control research, and formulated a relatively complete modeling and control theory.
In the thesis, the control and fault detection and diagnosis for the non-Gaussian stochastic distribution systems will be described. In particular,The study of non-Gaus-sian stochastic distribution systems includes Tracking controll,Fault detection and diagnosis, Fault tolerant control. The theory of non-Gaussian stochastic distribution systems can been further supplement, improve through the article.the The main research work and contributions of this thesis are listed as follows:
1.A guaranteed cost control for non-Gaussian stochastic distribution systems. Attention is focused on a memory state feedback control law based on linear matrix inequality (LMI) with model transformation such that the closed-loop systems is asymptotically stable and the guaranteed cost index is not more than a specified upper bound,which ensure that the systems output PDF follows the target PDF.
2.Neuro-controller designing for guaranteed cost control of non-Gaussian uncertain stochastic distribution dontrol systems.neural controller for the guaranteed cost problem is vestigated. Based on LMI design,a class of a state feedback controller with a gain perturbations is structured,meanwhile,neural controller is used to tune the additive gain perturbations such that the guaranteed cost is reduced,and sufficient conditions for the existence of guaranteed cost controller are derived.
3.Robust tracking control for the non-Gaussian stochastic distribution systems. We considers the design problem of a novel PID control based on Hoo for the non-Gaussian stochastic distribution systems.the PDF tracking control is transformed into a contrained tracking control problem for weight vector by B-spline expansion with modeling errors and the nonlinear weight model with exogenous disturbances. A design approaches PID control based on Hoo are provied to fulfil the PDF tracking problem. Based on LMI,the existence condition of Hoo controller is obtained.
4.Observer-based fault detection and diagnosis for non-Gaussian stochastic disribution systems.a new type of fault detection and diagnosis (FDD) problem for non-gausian stochastic distribution systems via the output PDFs) is investigated. The PDF can be approximated by using rational square-root B-spline expansion,via this expansions to represent the dynamics weighting systems between the systems input and the weights related to the output PDF. a nonlinear adaptive observer-based fault detection and diagnosis algorithm is present by introducing the adaptive tuning rule such that the residual is as sensitive as possible to the fault. Stability and convergency analysis is performed in fault detection and fault diagnosis analysis for the error dynamic systems.
5.Fault detection and diagnosis for non-Gaussian singular stochastic distribution systems.The outputs of singular stochastic systems are described by PDF based on square root B-spline expansions. Then, non-linear observers are designed for the FDD. The conditions of stability of the correlative error estimation systemss are given by using LMI.
6.Fault detection and diagnosis for non-Gaussian stochastic distribution systems with time delays. A RBF neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings. In this work, a nonlinear adaptive observer-based fault detection and diagnosis algorithm is presented by introducing the tuning parameter so that the residual is as sensitive as possible to the fault.
7.Fault tolerant control for non-Gaussian stochastic distribution systems. Different from the conventional FTC methods, the measured information is the output PDFs rather than its instant values,where the RBFs neural network technique is introduced so that the output PDF can be formulated by the dynamic weights. Then based on Hoo techniques and PID controller, the concerned FTC problem can be transferred into a classical nonlinear FTC problem subject to a nonlinear systemss with both of modeling error and the fault. In terms of LMI techniques, a new control method is given so that the fault can be compensated or rejected.
On the whole,this thesis investigates a series of new methods of tracking control and Fault detection and diagnosis for non-Gaussian stochastic distribution systems based on a variety of classical research methods in nonlinear control,stability analysis fields and Fault detection and diagnosis. It is noted that the above results have Important theoretical significance In research for the non-Gaussian stochastic distribution systems.
引文
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