Monitoring of Chlorine Concentration in Drinking Water Distribution Systems Using an Interval Estimator

Abstract

This paper describes the design of an interval observer for the estimation of unmeasured quality state variables in drinking water distribution systems. The estimator utilizes a set bounded model of uncertainty to produce robust interval bounds on the estimated state variables of the water quality. The bounds are generated by solving two differential equations. Hence the numerical efficiency is sufficient for on-line monitoring of the water quality. The observer is applied to an exemplary water network and its performance is validated by simulations.

Adaptive control technique for a propagation bioprocess carried out inside a fixed bed reactor

“…where  5 X and  5 X represent the estimates of lower and upper bounds of unmeasured variable X 5 provided by the interval observer (12) and 5  is on-line provided by the OBE (18). In the OBE equations, the variable 5 X is replaced by the arithmetic mean of its lower and upper estimated bounds, that is, 1 X becomes 2 / ) ( Case 1.…”

“…Under these conditions and based on properties of cooperative systems [17], a robust interval observer for the system (7) is given as follows [10,18]: …”

“…Finally, the full adaptive control algorithm for fixed bed bioprocess (4), (5) is made up by combination of the observer equations (10), (11), (15)-(17) and parameter estimator equations (18) with the control law (13) written as:…”

Robust‐Adaptive Control Strategies for a Time Delay Bioelectrochemical Process Using Interval Observers

“…Then, based on the asymptotic observer (20), (21), under hypotheses H1′-H6, a robust interval observer for the system (17) is given as follows [16,26]:…”

A biochemical multi-species quality model of a drinking water distribution system for simulation and design

“…It is not the main goal of the research to obtain a model which could be easily calibrated and directly applied to solve problems related to monitoring or control of DWDS quality, but good care of model parameter validity and some means of obtaining them are necessary and as such this is addressed in this work. The main goal of the paper is to capture the class of dynamics that resembles the DWDS environment and by doing so will serve as a tool for deriving and verifying simplified model structures more suitable for solving tasks related to DWDS on-line monitoring, control (e.g., Łangowski and Brdys, 2007;Nowicki et al, 2012). The authors assume that, if the derived simplified structure can be tuned to handle tasks in the environment simulated by utilising the derived 'full scale' model, it is very likely to obtain similar results in practice.…”