奇异摄动系统的故障诊断和最优容错控制
发布时间：2019-06-06 00:22
【摘要】：在一些实际的工程领域中存在着多个数量级差别较大的状态变量,这是造成系统的动态变化速度差异巨大的根源,从而使得系统具有跨尺度特性,这种以跨尺度为主要特征的动态系统可归纳为奇异摄动系统的框架下进行研究。奇异摄动系统的控制和分析是控制理论的研究热点,主要包括系统稳定性、鲁棒性、优化、控制等。而在故障诊断及容错控制方面的研究和文献却相对较少。从研究方法上来讲,以往的研究多采用模型降阶法、快慢分解法、广义系统法,因此本文从整体的角度,采用一体化设计思路,针对奇异摄动系统的故障诊断和容错控制问题提出了新的研究方法并得到有意义的结论,主要内容概括如下:1.研究了基于动态输出反馈的极限奇异摄动系统(广义系统)的最优干扰抑制问题。首先基于广义系统的相关理论推导出PI(比例-积分)观测器存在的充分条件。考虑到并不是所有的状态变量和外部干扰信号能够直接测量,提出了新的PI观测器设计方法,设计了全阶和降阶两种观测器,通过求解简单的矩阵方程即可得到观测器的设计参数。在此基础上基于线性二次型性能指标提出最优干扰抑制律,即可保证闭环系统允许时在最坏的干扰下,其性能指标达到最小。在数值算例中,通过比较原状态信号、干扰信号和观测器状态信号、反馈控制信号的比较说明观测器的设计合理,最优干扰抑制律是有效的。2.研究了奇异摄动系统的故障诊断和最优容错控制问题,这里考虑的是系统的故障为动态特性已知的一类线性奇异摄动系统。首先将原系统和故障系统联立为增广系统,然后依据奇异摄动系统的相关理论,提出全维PI观测器存在条件。在此基础上再进一步考虑闭环系统的最优性,设计了状态反馈控制器保证系统渐近稳定,并且能够使得给定的线性二次最优性能指标最小,最后通过数值算例说明结论的有效性及正确性。
[Abstract]:In some practical engineering fields, there are many state variables with great difference in magnitude, which is the root of the great difference in the dynamic change speed of the system, which makes the system have cross-scale characteristics. This kind of dynamic system with cross-scale as the main characteristic can be summarized into the framework of singular perturbed system. The control and analysis of singular perturbed systems is a hot research topic in control theory, including system stability, robustness, optimization, control and so on. However, the research and literature on fault diagnosis and fault-tolerant control are relatively few. From the point of view of research methods, the model reduction method, fast and slow decomposition method and singular system method are mostly used in the previous research. Therefore, from the overall point of view, this paper adopts the integrated design idea. A new research method for fault diagnosis and fault-tolerant control of singular perturbed systems is proposed and meaningful conclusions are obtained. the main contents are summarized as follows: 1. The optimal interference suppression problem for limit singular perturbed systems (singular systems) based on dynamic output feedback is studied. Firstly, based on the theory of singular systems, the sufficient conditions for the existence of PI (proportional integral) observer are derived. Considering that not all state variables and external interference signals can be measured directly, a new PI observer design method is proposed, and two kinds of observers, full order and reduced order, are designed. The design parameters of the observer can be obtained by solving the simple matrix equation. On this basis, the optimal interference suppression law is proposed based on the linear quadratic performance index, which can ensure the minimum performance of the closed-loop system under the worst interference. In the numerical example, the comparison of the original state signal, the interference signal and the observer state signal and the feedback control signal shows that the design of the observer is reasonable and the optimal interference suppression law is effective. 2. In this paper, the problem of fault diagnosis and optimal fault tolerance control for singular perturbed systems is studied. in this paper, the fault of the system is considered as a class of linear singular perturbed systems with known dynamic characteristics. Firstly, the original system and the fault system are combined into the augmented system, and then according to the theory of the singular perturbed system, the existence condition of the full-dimensional PI observer is proposed. On this basis, the optimality of the closed-loop system is further considered, and the state feedback controller is designed to ensure the asymptotic stability of the system, and the given linear quadratic optimal performance index can be minimized. Finally, a numerical example is given to illustrate the validity and correctness of the conclusion.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
本文编号：2493928
[Abstract]:In some practical engineering fields, there are many state variables with great difference in magnitude, which is the root of the great difference in the dynamic change speed of the system, which makes the system have cross-scale characteristics. This kind of dynamic system with cross-scale as the main characteristic can be summarized into the framework of singular perturbed system. The control and analysis of singular perturbed systems is a hot research topic in control theory, including system stability, robustness, optimization, control and so on. However, the research and literature on fault diagnosis and fault-tolerant control are relatively few. From the point of view of research methods, the model reduction method, fast and slow decomposition method and singular system method are mostly used in the previous research. Therefore, from the overall point of view, this paper adopts the integrated design idea. A new research method for fault diagnosis and fault-tolerant control of singular perturbed systems is proposed and meaningful conclusions are obtained. the main contents are summarized as follows: 1. The optimal interference suppression problem for limit singular perturbed systems (singular systems) based on dynamic output feedback is studied. Firstly, based on the theory of singular systems, the sufficient conditions for the existence of PI (proportional integral) observer are derived. Considering that not all state variables and external interference signals can be measured directly, a new PI observer design method is proposed, and two kinds of observers, full order and reduced order, are designed. The design parameters of the observer can be obtained by solving the simple matrix equation. On this basis, the optimal interference suppression law is proposed based on the linear quadratic performance index, which can ensure the minimum performance of the closed-loop system under the worst interference. In the numerical example, the comparison of the original state signal, the interference signal and the observer state signal and the feedback control signal shows that the design of the observer is reasonable and the optimal interference suppression law is effective. 2. In this paper, the problem of fault diagnosis and optimal fault tolerance control for singular perturbed systems is studied. in this paper, the fault of the system is considered as a class of linear singular perturbed systems with known dynamic characteristics. Firstly, the original system and the fault system are combined into the augmented system, and then according to the theory of the singular perturbed system, the existence condition of the full-dimensional PI observer is proposed. On this basis, the optimality of the closed-loop system is further considered, and the state feedback controller is designed to ensure the asymptotic stability of the system, and the given linear quadratic optimal performance index can be minimized. Finally, a numerical example is given to illustrate the validity and correctness of the conclusion.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
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