On the Discrete Time Stepwise Safe Switching Soft Sensor Design for Water Distribution Networks

Nikolaos D. Kouvakas, Fotis N. Koumboulis, Maria P. Tzamtzi, Dimitrios G. Fragkoulis, Klimis K. Katsiavrias, Konstantinos Katsiavrias, John Dimitropoulos

A discrete-time, model-based soft sensor is developed to estimate free chlorine concentration in selected sections of a water distribution network (WDN). The study considers a benchmark network with a star-like geometry, which is initially described by a set of nonlinear ordinary differential equations. The hydraulic subsystem is approximated in static form, such that steady-state flows is consistent with boundary heads and demands that drive the chlorine transport–reaction dynamics. Around a set of preselected operating points, linear approximants are obtained and the respective exact discrete-time state-space representations are derived under zero-order-hold interpolations. Based on this model, a bank of full-order Luenberger-type discrete-time observers is constructed, constituting the base of the the proposed soft sensor. The observer gains are determined through a multicriterion design procedure that combines discrete-time pole-placement requirements with a normbased minimization objective. Simulation results on the benchmark network indicate high-fidelity chlorine estimation, with deviations limited to brief intervals during operating transitions.