基于降维观测器与多胞体方法的执行器故障检测

Actuator Fault Detection based on Combination of Reduced-order Observer and Zonotope Method

摘要:

针对具有执行器故障且状态方程和输出方程同时受到外部扰动影响的离散系统，研究了降维观测器设计方法和基于多胞体理论的区间估计方法，并在此基础上提出了基于区间估计的执行器故障检测方法。首先，通过适当的状态等价变换，将原系统分解成2个降维子系统，使得一个子系统可以直接解耦干扰。然后，在无执行器故障发生的前提下，基于对干扰解耦的子系统，提出了一种降维观测器设计方法，实现了原系统状态的渐近收敛估计。其次，针对具有干扰的子系统，设计了Luenberger型观测器，并结合多胞体理论，提出了一种对可测输出的区间估计方法。之后，基于可测输出的区间估计，提出了一种残差的构造方法，以此提出了一种执行器故障检测新方法。最后，给出了仿真设计和分析，验证了方法的有效性。

Abstract:

For the discrete-time system with actuator fault， and the state equation and output equation are affected by external disturbance， the reduced-order observer design method and interval estimation method based on the zonotope theory are studied， and an interval-observer-based actuator fault detection method is proposed. First， the original system is decomposed into two reduced-order subsystems by an appropriate state equivalent transformation， so that one subsystem can directly decouple the disturbance. Then， under the assumption that system has no actuator fault， a reduced-order observer design method is proposed for the subsystem without disturbance to obtain the asymptotic convergence state estimation of the original system. Next， a Luenberger observer is designed for another subsystem， and by combining it with the zonotope theory， an interval estimation method for measurable output is proposed. Afterwards， based on the interval estimation of the measurable output， a new actuator fault detection method is proposed by constructing a new residual. Finally， a simulation example is given and analyzed to verify the effectiveness of the method.