上海交通大学学报

上海交通大学学报（自然版）

• 自动化技术、计算机技术 • 上一篇    下一篇

非线性分布参数系统鲁棒故障检测观测器设计

刘平岳，吴淮宁
  

  1. (北京航空航天大学 控制一体化技术国家级科技重点实验室,北京 100191)
  • 收稿日期:2010-10-12 修回日期:1900-01-01 出版日期:2011-02-28 发布日期:2011-02-28

Robust Fault Detection Observer Design for Nonlinear Distributed Parameter Systems

LIU Pingyue，WU Huaining
  

  1. (National Key Laboratory of Science and Technology on Holistic Control,
    Beihang University, Beijing 100191, China)
  • Received:2010-10-12 Revised:1900-01-01 Online:2011-02-28 Published:2011-02-28

摘要： 针对一类由偏微分方程(PDE)描述的非线性分布参数系统的鲁棒故障检测观测器(FDO)设计问题进行了研究.采用模态分解法将PDE系统变换成一个等价的无穷维常微分方程(ODE)系统，并根据空间微分算子的特征谱，将无穷维ODE系统表达成有限维慢子系统与无穷维快子系统相耦合的形式.基于慢子系统模型设计有限维FDO，使得无故障残差系统在容许的未知非线性动态和快子系统动态影响下依然渐近稳定，并设计相应的检测门限，以实现故障检测.仿真结果验证了所提方法的有效性.

关键词: 分布参数系统, 模态分解法, 故障检测, 鲁棒性, 观测器

Abstract: This paper addresses the problem of robust fault detection observer (FDO) design for a class of nonlinear distributed parameter systems described by partial differential equations (PDEs). Firstly, applying modal decomposition techniques, the PDE system can be transformed to an equivalent infinitedimensional ordinary differential equations (ODE) system. Based on the spectrum of spatial differential operator, the ODE system can be represented by a finitedimensional slow subsystem and a coupled infinitedimensional fast subsystem. Subsequently, a finitedimensional FDO is designed based on the slow subsystem such that the normal residual system is asymptotically stable for all admissible unknown nonlinear dynamics and fast subsystem dynamics. Then, the corresponding timevarying threshold is proposed to implement fault detection. Finally, numerical simulations are performed to demonstrate the effectiveness of the developed FDO design methodology.

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