This paper proposes a new approach for the leak diagnosis problem in pipelines based on the use of a Kalman filter for Linear Parameter Varying (LPV) systems. Such a filter considers the availability of flow and pressure measurements at each end of the pipeline. The proposed methodology relies on an LPV model derived from the nonlinear description of the pipeline. For the Kalman filter design purposes, the LPV model is transformed into a polytopic representation. Then, using such a representation, the LPV Kalman filter is designed by solving a set of Linear Matrix Inequalities (LMIs) offline. In the online implementation, the observer gain is calculated as an interpolation of those gains previously computed at the vertices of the polytopic model. The main advantages of this approach are: a) the embedding of the nonlinearities in the varying parameters allows the quasi-LPV system to be obtained which is equivalent to the original nonlinear one, and; b) the use of the well-known LMIs to compute the Kalman gain allows the extension to the LPV case. Those aspects are the main advantages with respect to the classic design of the Extended Kalman Filter (EKF) that requires a linearization procedure and the solution of the Ricatti equation at each iteration. To illustrate the potential of this method, a test bed plant built at Cinvestav-Guadalajara is used. Additionally, the results presented are compared with those results obtained through the classical EKF showing that LPV Kalman observer outperforms the classical EKF.

本文基于对线性参数变化 ( LPV ) 系统使用卡尔曼滤波器，提出了一种解决管道泄漏诊断问题的新方法。这种过滤器考虑了管道每一端的流量和压力测量的可用性。所提出的方法依赖于从管道的非线性描述中导出的LPV模型。出于卡尔曼滤波器设计的目的，LPV模型被转换为多面体表示。然后，使用这样的表示，通过求解一组线性矩阵不等式 ( LMIs)来设计LPV卡尔曼滤波器） 离线。在在线实现中，观察者增益被计算为先前在多面体模型顶点处计算的那些增益的插值。这种方法的主要优点是： a)在可变参数中嵌入非线性允许获得与原始非线性系统等效的准 LPV系统，以及；b) 使用众所周知的LMI来计算卡尔曼增益允许扩展到LPV情况。这些方面是扩展卡尔曼滤波器 ( EKF)经典设计的主要优势) 需要一个线性化过程和 Ricatti 方程在每次迭代时的解。为了说明这种方法的潜力，使用了在 Cinvestav-Guadalajara 建造的试验台工厂。此外，将呈现的结果与通过经典EKF获得的结果进行比较，表明LPV卡尔曼观测器优于经典EKF。