Robust fault detection and reconfiguration in sampled-data uncertain distributed processes
Robust fault detection and reconfiguration in sampled-data uncertain distributed processes
复制标题
采样数据不确定分布式过程中的鲁棒故障检测和重构
DOI：
10.1109/cdc.2011.6160873
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
N. El‐Farra
中科院分区：
文献类型：
--
作者：
Zhiyuan Yao;N. El‐Farra
针对由抛物型偏微分方程描述的空间分布过程，在时变外部扰动、控制执行器故障和测量采样率约束下，研究了基于模型的鲁棒故障检测和容错控制问题。利用一个近似的有限维系统来捕获偏微分方程组的主要动态，设计了一个基于观测器的输出反馈控制器，在没有故障的情况下，在闭环系统状态上具有任意小的最终界来增强鲁棒稳定性。然后在控制器中嵌入有限维样本间模型预测器，以向观测器提供采样时间之间的测量输出的估计，并且使用每个采样时间的测量输出来更新模型的状态。通过将采样数据有限维闭环系统描述为离散-连续组合系统，得到了闭环系统鲁棒稳定的充要条件，并利用该条件明确地刻画了采样率、模型不确定性程度、扰动大小、闭环系统状态可达最终界的大小以及执行器/传感器位置的选择之间的权衡。基于这一分析，得到了故障检测残差的时变报警阈值，以及确定保持鲁棒闭环系统稳定性的可行后退执行器集合的执行器重构律。最后，通过一个典型的扩散-反应过程的应用，说明了结果的正确性。
This paper focuses on robust model-based fault detection and fault-tolerant control of spatially distributed processes described by parabolic partial differential equations (PDEs) subject to time-varying external disturbances, control actuator faults and measurement sampling rate constraints. Using an approximate finite-dimensional system that captures the dominant dynamics of the PDE, an observer-based output feedback controller is initially designed to enforce robust stability with an arbitrarily small ultimate bound on the closed-loop state in the absence of faults. A finite-dimensional inter-sample model predictor is then embedded within the controller to provide the observer with estimates of the measured output between the sampling times, and the state of the model is updated using the measured output at each sampling time. By formulating the sampled-data finite-dimensional closed-loop system as a combined discrete-continuous system, a necessary and sufficient condition for robust closed-loop stability is obtained and used to explicitly characterize the tradeoffs between the sampling rate, the degree of model uncertainty, the disturbance size, the size of the achievable ultimate bound on the closed-loop state, and the choice of actuator/sensor locations. Based on this analysis, a time-varying alarm threshold on the fault detection residual is obtained, together with an actuator reconfiguration law that determines the set of feasible fall-back actuators that preserve robust closed-loop stability. Finally, the result is illustrated through an application to a representative diffusion-reaction process.