Modeling of Waste Water Treatment Plant via system ID & model reduction technique

This paper investigates the application of Model Order Reduction (MOR) technique to Waste Water Treatment Plant (WWTP) system. The mathematical model of WWTP is obtained by using System Identification. In this paper, Prediction Error Estimate of Linear or Nonlinear Model (PEM) is proposed as the System Identification method which is used to find the parameter of linear or nonlinear system in state-space model from an experimental input-output data WWTP. The result shows that the estimated model of WWTP is a high order system with good best fit with 91.56% and 80.19% compared to the original experimental model. To simplify the obtained model,the MOR technique is proposed to reduce the high order system to lower order system while still retaining the characteristics of the original system. In this paper, the balanced truncation and Frequency Weighted Model Reduction (FWMR) are proposed to obtain a lower order WWTP model. The result shows that by MOR techniques, the higher WWTP system can be simplified to lower order system with a low error of the reduced system. The result of reduced model will be represented in sigma graph and numerical value.

[1]  Victor Sreeram,et al.  Improved results on frequency weighted balanced truncation , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[2]  A. Antoulas,et al.  A Survey of Model Reduction by Balanced Truncation and Some New Results , 2004 .

[3]  Ching-An Lin,et al.  Model Reduction via Frequency Weighted Balanced Realization , 1990, 1990 American Control Conference.

[4]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

[5]  Norhaliza Abdul Wahab,et al.  Multivariable PID control design for activated sludge process with nitrification and denitrification , 2009 .

[6]  Victor Sreeram,et al.  An improved algorithm for frequency weighted balanced truncation , 2011, IEEE Conference on Decision and Control and European Control Conference.

[7]  Sanjay Lall,et al.  Error-bounds for balanced model-reduction of linear time-varying systems , 2003, IEEE Trans. Autom. Control..

[8]  H. Natsuyama.  System identification: methods and applications , 1974 .

[9]  Brian R. Gaines,et al.  General System Identification — Fundamentals and Results , 1978 .

[10]  D. Enns.  Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[11]  Pan Agathoklis,et al.  The use of model reduction techniques for designing IIR filters with linear phase in the passband , 1996, IEEE Trans. Signal Process..

[12]  V. Sreeram,et al.  Frequency weighted model reduction technique with error bounds , 2005, Proceedings of the 2005, American Control Conference, 2005..

[13]  Jang-Gyu Lee,et al.  Model reduction via frequency weighting approach , 2001, SICE 2001. Proceedings of the 40th SICE Annual Conference. International Session Papers (IEEE Cat. No.01TH8603).