Second-order sliding mode algorithms for the reconstruction of leaks

A framework for leak reconstruction in pipelines using second-order sliding mode is presented. Two cases are considered. In the case of a single leak, the necessary and sufficient condition that allows estimating the position of the leak is determined and discussed. Under such a condition, an algorithm that determines the position and flow of the leak in finite-time is introduced. In the case of two leaks with known positions, a finite-time estimation of the leaks flow is obtained. Experimental results for this second case are presented, together with a comparison of the performance of first and second-order sliding mode algorithms.