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摘 要:为降低诊断算法的计算量,优化算法参数,设计了一种基于降维观测器的最优故障诊断算法。首先,利用正交原理,将故障状态与系统状态进行解耦,从而构造了用于故障估计且无需进行矩阵分块运算的降维观测器;其次,基于对偶原理,将诊断算法的增益优化问题转化为诊断误差方程对偶系统的最优控制律设计问题,从而实现了对故障的最小方差估计。然后,利用诊断结果设计了基于故障补偿思想的容错控制律,以此实现了系统与故障的隔离。最后,通过数值仿真验证了所提方法的有效性。结果表明,对于二阶系统,该诊断算法可在7s内快速收敛到故障真实值。
Abstract: In order to reduce the computational complexity of the diagnostic algorithm and optimize the parameters of the algorithm, an optimal fault diagnosis algorithm based on the reduced-dimensional observer is designed. Firstly, the orthogonality principle is used to decouple the fault state and the system state, so that a dimensionality reduction observer is constructed for fault estimation without matrix partitioning. Second, based on the duality principle, the gain optimization problem of the diagnostic algorithm The optimal control law design of the dual system is transformed into the diagnostic error equation, so as to achieve the minimum variance estimation of the fault. Then, the fault-tolerant control law based on the fault compensation idea is designed by using the diagnosis results, in order to achieve the system and fault isolation. Finally, the effectiveness of the proposed method is verified by numerical simulation. The results show that for the second-order system, the diagnostic algorithm can quickly converge to the true value of the fault within 7s.