Optimisation of chlorine dosing for water disribution system using model-based predictive control
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An ideal drinking water distribution system (DWDS) must supply safe drinking water with free chlorine residual (FCR) in the form of HOCI and OCIֿ at a required concentration level. Meanwhile the FCR is consumed in the bulk liquid phase and at the DWDS pipes wall as the result of chemical reactions. Because of these, an optimized chlorine dosing for the DWDS using model-based predictive control (MBPC) is developed through the steps of modelling the FCR transport along the main pipes of the DWDS, designing chlorine dosing and implementing a multiple-input multiple-output system control scheme in Matlab 7.0.1 software. Discrete time-space models (DTSM) that can be used to predict free chlorine residual (FCR) concentration along the pipes of the DWDS over time is developed using explicit finite difference method (EFDM). Simulations of the DTSM using step and rectangular pulse input show that the effect of water flow rate velocity is much stronger than the effect of chlorine effective diffusivity coefficient on the FCR distribution and decay process in the DWDS main pipes. Therefore, the FCR axial diffusion in single pipes of the DWDS can be neglected. Investigating the effect of injection time, initial chlorine distribution, and overall chlorine decay rate constant involved in the process have provided a thorough understanding of chlorination and the effectiveness of all the parameters. This study proposed a model-based chlorine dosing design (MBCDD) based on a conventional-optimum design process (CODP) (Aurora, 2004), which is created for uncertain water demand based on the DTSM simulation.In the MBCDD, the constraints must be met by designing distances between chlorine boosters and optimal value of the initial chlorine distribution in order to maintain the controlled variable (CV), i.e. FCR concentration with a certain degree of robustness to the variations of water flow rate. The MBCDD can cope with the simulated DWDS (SDWDS) with the conditions; the main pipe is 12 inch diameter size with the pipe length of 8.5 km, the first consumers taking the water from the point of 0.83 km, the assumed pipe wall chlorine decay rate constant of 0.45 m/day, and the value of chlorine overall decay rate constants follow Rosman's model (1994), by proposing a set of rules for selecting the locations for additional chlorine dosing boosters, and setting the optimal chlorine dosing concentrations for each booster in order to maintain a relatively even FCR distribution along the DWDS, which is robust against volumetric water supply velocity (VWS) variations. An example shows that by implementing this strategy, MBCDD can control the FCR along the 8.5 km main pipe of 12 inch diameter size with the VWS velocity from 0.2457 to 2.457 km/hr and with the assumed wall and bulk decay constants of 0.45 and 0.55 m/day, respectively. An adaptive chlorine dosing design (ACDD) as another CODP of chlorine dosing which has the same concept with the MBCDD without the rule of critical velocity is also proposed in this study. The ACDD objective is to obtain the optimum value of initial chlorine distribution for every single change in the VWS. Simulation of the ACDD on the SDWDS shows that the ACDD can maintain the FCR concentration within the required limit of 0.2-0.6 mg/1.To enable water quality modelling for studying the effectiveness of chlorine dosing and injection in the form of mass flow rate of pure gaseous chlorine as manipulated variable (MV), a multiple-input multiple-output (MIMO) system is developed in Simulink for Matlab 7.0.1 software by considering the disturbances of temperature and circuiting flow. The MIMO system can be used to design booster locations and distribution along a main pipe of the DWDS, to monitor the FCR concentration at the point just before injection (mixing) and between two boosters, and to implement feedback and open-loop control. This study also proposed a decentralized model-based control (DMBC) based on the MBCDD-ACDD and centralized model predictive control (CMPC) in order to optimize MV to control the CV along the main pipe of the DWDS in the MIMO system from the FCR concentration at just after the chlorine injection (CVin) to the FCR concentration (CVo) before the next chlorine injection with the constraints of 0.2-0.6 ppm for both the CVin and CVo. A comparison of the performances of decentralized PI (DPI) control, DMBC and CMPC, shows that the performances of the DMBC and CMPC in controlling the MIMO system are almost the same, and they both are significantly better than the DPI control performance. In brief, model-based predictive control (MBPC), in this case a decentralized model-based control (DMBC) and a centralized predictive control (CMPC), enable optimization of chlorine dosing for the DWDS.
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