Thursday , June 21 2018

Non-linear State Dependent Differential Riccati States Filter for Wastewater Treatment Process

Abdelhamid IRATNI
Centre Universitaire de Bordj Bou Arréridj
El-Anasser, 34265, Algeria

Industrial Control Centre, Department of Electronic and Electrical Engineering, University of Strathclyde

Laboratoire d’Automatique de Sétif, Department of Electrical Engineering, University of Ferhat Abbas
Sétif, Algeria

Abstract: The most important issues relating to monitoring, quality control and prediction models for environmental protection in the treatment plant waste water are based on the amount of information and measures that are available. The key step in controlling and monitoring the plant is to obtain an accurate and robust estimate of the states model. The paper focuses on estimating non-measurable physical states of wastewater treatment system, which are unavailable because of difficulties techniques or the high cost of physical sensors. The developed filter is dealing with the non-linearity describing the system. The Activated Sludge Process (ASP) as the biological technique most commonly used wastewater treatment, attracts much attention the research community. We developed for this class of processes a robust non-linear estimator known as “state-dependent differential Riccati filter (SDDRF). The sensor software is simple to implement and has a computational cost relatively low. The results are compared with the extended Kalman filter (EKF) to demonstrate the improved performance of the filter SDDRF. The filter allows the online monitoring of process variables, which are not directly measurable. The simulation results prove the advantage of using this approach.

Keywords: Wastewater system, nonlinear estimation, EKF, State dependent Riccati equation.

>>Full text
Abdelhamid IRATNI, Reza KATEBI, Mohammed MOSTEFAI, Non-linear State Dependent Differential Riccati States Filter for Wastewater Treatment Process, Studies in Informatics and Control, ISSN 1220-1766, vol. 20 (3), pp. 247-254, 2011.

1. Introduction

The wastewater systems have usually poor and inaccurate instrumentation because of their complexity and harsh environment. Hence, very little information is available for monitoring and control. This prevents the monitoring of effluent quality and, therefore, the pollution standards cannot be guaranteed. Although some recent physical sensors provide measurements online, but for many reasons, their cost, maintenance or difficulty in placing them have limited their installation and use. Hence the design and implementation of soft sensors are still relevant and useful. The aim of this work is to propose nonlinear estimator that can be easily implemented on a real process.

Estimator developed here is applied to a simple model of ASP reported in [1]. Application to a benchmark simulator proposed by the European group COST 624 [2] will be conducted in a second phase.

Some estimation techniques have been proposed for wastewater systems in the literature. These are as follows:

  • The extended Kalman filter is widely accepted and used in industry, but its convergence is difficult to prove, and the resulting estimates are highly dependent on the precision of model used [3], [4].
  • The extended asymptotic observer [5] is suggested for the biological processes when the parameters of the mode are not known, but the method is not suitable for real time implementation.
  • Observer-based intervals method [6] is proposed to design robust estimator but the method is based on linear models and hence not appropriate when the nonlinearities are dominant [7].

The purpose of this paper is to develop an observer sufficiently accurate to estimate the states of ASP for real time monitoring and control. The estimation algorithm is based on state dependent differential Riccati method. The proposed estimation has several useful features. It incorporates the well-known nonlinearities of the processes; it addresses the issues of high computational requirements and potentially relaxes the overly restrictive observability and controllability requirements.

The second objective of this paper is to produce a comparative study of EKF and the SDDRF with respect to estimation accuracy, robustness and computation load. The paper is organized as follow: the modeling of the continuous wastewater treatment is briefly described in Section 2. Section 3 is dedicated to the extended Kalman filter and state dependent differential Riccati filer algorithm. The comparison between the two filters is illustrated via simulation studies in Section 4. A general conclusion ends the paper.


  1. NEJJARI, F., B. DAHHOU, A. BENHAMMOU, G. ROUX, Non-linear Multivariable Adaptive Control of an Activated Sludge Wastewater Treatment Process, International Journal of Adaptive Control and Signal Processing, 13, 1999, pp. 347-365.
  2. COPP, J. B., The COST Simulation Benchmark: Description and Simulator Manual, (COST Action 624 & COST Action 682), Office for Official Publications of the European Communities, Luxembourg, 2002.
  3. KALMAN, R. E., R. S. BUCY, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, 1961, pp. 95-108.
  4. BENAZZI, F., R. KATEBI, J. WILKIE, Application of Extended Kalman Filter to Activated Sludge Process, EU Research Training Network (HPRN-CT-2001-00200), internal report, 2003.
  5. BASTIN, G., D. DOCHAIN, On-line Estimation and Adaptive Control of Bioreactors, Elsevier Publisher, 1990.
  6. HADJ-SADOK, M. Z., J. L. GOUZÉ, Estimation of Uncertain Models of Activated Sludge Processes with Interval Observers, Journal of Process Control 11. Elsevier Publisher, 2001.
  7. GOMEZ-QUINTERO, C. S., I. QUEINNEC, Robust Estimation for an Uncertain Linear Model of an Activated Sludge Process, 2002 IEEE International Conference on Control Applications, 2002, pp. 972-977.
  8. TAKACS, I., G. G. PATRY, D. NOLASCO, A Dynamic Model of the Clarification Thickening Process, Water Research, 25(10), 1991, pp. 1263-1271.
  9. HENZE, M., JR. GREDY, W. GUJER, G. MARAIS, T. MATSUO, Activated Sludge Model n°1, IAWQ Scientific and Technical report no 1. London, 1986.
  10. KATEBI, R., M. JOHNSON, J. WILKIE, Control and Instrumentation for Wastewater Treatment Plants, Springer edition, 1999.
  11. G. OLSSON, State of the Art in Sewage Treatment Plant Control, American Institute of Chemical Engineers, Symposium Series, 1976, pp. 52-76.
  12. DUZINKIEWICZ, K., A. BOROWA, K. MAZUR, M. GROCHOWSKI, M. A. BRDYS, K. JEZIOR, Leakage Detection and Localisation in Drinking Water Distribution Networks by MultiRegional PCA, Studies in Informatics and Control, Vol. 17(2), 2008, pp. 135-152.
  13. MAYBECK, P. S., Stochastic Models, Estimation and Control. New York: Academic Press, 1982.
  14. AZEMI, A., E. E. YAZ, Comparative Study of Several Nonlinear Stochastic Estimators, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, vol. 5, 1999, pp. 4549-4554.
  15. MRACEK, C. P., J. R. CLOUTIER, C. A. D’SOUZA, New Technique for Nonlinear Estimation, Proceedings of the IEEE Conference on Control Applications, 1996, pp. 338-342.