Exponential Boundary Observers for Pressurized Water Pipe

12th European Workshop on Advanced Control and Diagnosis

Som, Idellette Judith Hermine^1 ; Cocquempot, Vincent^1 ; Aitouche, Abdel^2

CRIStAL: Research Center in Computer Science, Signal and Automatic Control of Lille, Lille 1 University, France^1

CRIStAL: Research Center in Computer Science, Signal and Automatic Control of Lille, HEI: Hautes Etudes d'Ingénieur, France^2

关键词: Boundary variables;    Finite difference scheme;    Hyperbolic equations;    Leakage detection;    Linear Matrix Inequalities (LMIs);    Lipschitz property;    Mathematical tools;    State transformation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/659/1/012024/pdf
DOI  :  10.1088/1742-6596/659/1/012024

来源: IOP

【 摘 要 】

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.