Control of an ideal activated sludge process in wastewater treatment via an ODE–PDE model

Research output: Contribution to journalArticle


The activated sludge process (ASP), found in most wastewater treatment plants, consists basically of a biological reactor followed by a sedimentation tank, which has one inlet and two outlets. The purpose of the ASP is to reduce organic material and dissolved nutrients (substrate) in the incoming wastewater by means of activated sludge (microorganisms). The major part of the discharged flow through the bottom outlet of the sedimentation tank is recirculated to the reactor, so that the biomass is reused. Only two material components are considered; the soluble substrate and the particulate sludge. The biological reactions are modelled by two nonlinear ordinary differential equations and the continuous sedimentation process by two hyperbolic partial differential equations (PDEs), which have coefficients that are discontinuous functions in space due to the inlet and outlets. In contrast to previously published modelling-control aspects of the ASP, the theory for such PDEs is utilized. It is proved that the most desired steady-state solutions can be parameterized by a natural control variable; the ratio of the recirculating volumetric flow to the input flow. This knowledge is a key ingredient in a two-variable regulator, with which the effluent dissolved nutrients concentration and the concentration profile in the sedimentation tank are controlled. Theoretical results are supported by simulations.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics
  • Control Engineering
  • Computational Mathematics
  • Chemical Engineering
  • Water Engineering
  • Water Treatment


  • Partial differential equation, Regulator, Controller, Clarifier-thickener, Settler, Continuous sedimentation
Original languageEnglish
Pages (from-to)359-381
JournalJournal of Process Control
Issue number3
Publication statusPublished - 2013
Publication categoryResearch