Journal of Engineering Mathematics

, Volume 54, Issue 3, pp 225–259 | Cite as

Operating Charts for Continuous Sedimentation III: Control of Step Inputs

  • Stefan DiehlEmail author


The main purposes of a clarifier-thickener unit is that it should produce a high underflow concentration and a zero effluent concentration. The main difficulty in the control of the clarification-thickening process (by adjusting a volume flow) is that it is nonlinear with complex relations between concentrations and volume flows via the solution of a PDE – a conservation law with a source term and a space-discontinuous flux function. In order to approach this problem, control objectives for dynamic operation and strategies on how to meet these objectives are presented in the case when the clarifier-thickener unit initially is in steady state in optimal operation and is subjected to step input data. A complete classification of such solutions is given by means of an operating chart (concentration-flux diagram).


continuous sedimentation control operating charts step response thickener 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Diehl S. (2001). Operating charts for continuous sedimentation I: Control of steady states. J. Engng. Math. 41: 117–144zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Diehl S. (2005). Operating charts for continuous sedimentation II: Step responses. J. Engng. Math. 53: 139–185zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Stehfest H. (1984). An operational dynamic model of the final clarifier. Trans. Inst. Meas. Control 6(3): 160–164CrossRefGoogle Scholar
  4. 4.
    Keinath T.M. (1985). Operational dynamics and control of secondary clarifiers. J. Water Pollut. Control Fed. 57: 770–776Google Scholar
  5. 5.
    Bustos M.C., Paiva F. and Wendland W. (1990). Control of continuous sedimentation as an initial and boundary value problem. Math. Methods Appl. Sci. 12: 533–548MathSciNetCrossRefADSzbMATHGoogle Scholar
  6. 6.
    Barton N.G., Li C.-H. and Spencer J. (1992). Control of a surface of discontinuity in continuous thickeners. J. Austral. Math. Soc. Ser. B 33: 269–289MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Balslev P., Nickelsen C. and Lynggaard-Jensen A. (1994). On-line flux-theory based control of secondary clarifiers. Wat. Sci. Tech. 30: 209–218Google Scholar
  8. 8.
    Chancelier J.-Ph., Cohen de Lara M. and Pacard F. (1994). Analysis of a conservation PDE with discontinuous flux: A model of settler. SIAM J. Appl. Math. 54: 945–995MathSciNetCrossRefGoogle Scholar
  9. 9.
    Chancelier J.-Ph., Cohen de Lara M., Joannis C. and Pacard F. (1997). New insight in dynamic modelling of a secondary settler – II. Dynamical analysis. Wat. Res. 31: 1857–1866CrossRefGoogle Scholar
  10. 10.
    Diehl S. (1996). A conservation law with point source and discontinuous flux function modelling continuous sedimentation. SIAM J. Appl. Math. 56: 388–419zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Diehl S. and Jeppsson U. (1998). A model of the settler coupled to the biological reactor. Wat. Res. 32: 331–342CrossRefGoogle Scholar
  12. 12.
    Bürger R., Karlsen K.H. and Towers J.D. (2005). A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. SIAM. J. Appl. Math. 65: 882–940MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden

Personalised recommendations