Towards model predictive control: Online predictions of ammonium and nitrate removal by using a stochastic ASM

Peter Alexander Stentoft, Thomas Munk-Nielsen, Luca Vezzaro, Henrik Madsen, Peter Steen Mikkelsen, Jan Kloppenborg Møller

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Online model predictive control (MPC) of water resource recovery facilities (WRRFs) requires simple and fast models to improve the operation of energy-demanding processes, such as aeration for nitrogen removal. Selected elements of the activated sludge model number 1 modelling framework for ammonium and nitrate removal were included in discretely observed stochastic differential equations in which online data are assimilated to update the model states. This allows us to produce model-based predictions including uncertainty in real time while it also reduces the number of parameters compared to many detailed models. It introduces only a small residual error when used to predict ammonium and nitrate concentrations in a small recirculating WRRF facility. The error when predicting 2 min ahead corresponds to the uncertainty from the sensors. When predicting 24 hours ahead the mean relative residual error increases to ∼10% and ∼20% for ammonium and nitrate concentrations respectively. Consequently this is considered a first step towards stochastic MPC of the aeration process. Ultimately this can reduce electricity demand and cost for water resource recovery, allowing the prioritization of aeration during periods of cheaper electricity.

Original languageEnglish
JournalWater Science and Technology
Issue number1
Pages (from-to)51-62
Publication statusPublished - 2019


  • Activated sludge process (ASP)
  • Grey-box model
  • MPC
  • Prediction
  • Stochastic differential equations


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