基于观测器的LPV系统故障检测方法

Fault Detection Based on Observer for a Class of LPV Systems

针对一类线性参数变化(LPV)连续系统的故障检测问题,通过构造合适的输出观测器,获得残差生成器,并通过优化设计步骤,实现对干扰的有效抑制和对故障的灵敏检测。利用依赖参数的Lyapunov函数,在保证残差生成器稳定性的基础上,给出观测器存在的充分条件。应用投影定理,借助附加矩阵解除了基于参数的Lyapunov函数矩阵与系统矩阵的耦合,得到以线性矩阵不等式(LMI)形式表示的求解条件。对于参数变化系统,基于LMI的求解条件为无穷维问题,借助基函数和参数网格化方法,使其转变为可求解的问题。仿真结果表明,应用该方法可以在一定程度上抑制干扰,并能灵敏有效地实现故障检测。

In view of the fault detection of a class of linear parameter varying （LPV）systems, an observcer to acquire an effective residual generator is constructed. Based on the residual generator, a series of optimization steps are proposed to enhance the sensitivity to faults and restrain the disturbance of unknown inputs as well. The sufficient condition for the existence of the observer is established in terms of the parameter-dependent Lyapunov functions. Using the projection Lemma and with the help of some attached matrices, the parameter-dependent Lyapunov functions matrices and the system matrices are decoupled so that the linear matrix inequality （LMI） conditions are obtained. Moreover, the basis functions and the gridding technique are involved to solve the infinite-dimensional linear matrix inequality caused by the LPV. A numerical example shows the effectiveness of the proposed method.