带马尔科夫参数时滞容错控制系统稳定性分析

在主动容错控制系统 (AFTCS, Active Fault Tolerant Control System)中,故障检测与隔离(FDI,Fault Detection and Isolation)装置是核心部分,对系统故障诊断过程建模并研究其对整个系统的影响是十分重要的内容.考虑控制系统传感器到控制器之间由网络传输造成的常时滞,用两个马尔科夫随机过程分别描述系统的故障过程和故障诊断过程,建立多马尔科夫参数的系统模型;进而研究故障诊断装置对系统稳定性的影响,基于矩阵直积的方法,给出了不依赖延时的系统均方随机稳定的充分条件,为故障诊断方法的选择和评估提供了依据;最后给出了计算实例,根据稳定性条件,得出了在保持系统稳定的前提下,时滞、误检率和漏检率应满足的条件.

Stability of time-delay fault tolerant control systems with markovian parameters

FDI (fault detection and isolation) is a crucial part in AFTCS (active fault tolerant control system), so how to model the FDI process and evaluate its influence upon the system is very important. Considering constant networked-induced time delay between sensor and controller in the transmission, two homogeneous Markov stochastic processes with different state spaces were defined: one represented system components failures and the other represented the decisions of the FDI process upon which the state feedback control law was reconfigured. Further, the stability of the control system with state feedback was discussed. A delay-independent sufficient condition based on Kronecker product approach for checking the mean square stochastic stability of this class of systems was established. Simulation examples were given to demonstrate the theoretical results. Simulation results gave the relation of time-delay, false alarm rate and missed detection rate to guarantee the system stability.