OBSERVER BASED ADAPTIVE MODEL FOR A CLASS OF AEROBIC BATCH BIOREACTOR
The main issue of this work is to design a nonlinear observer (soft sensor) with finite convergence time for a class of batch bioreacting systems. Considering the necessity to fast response for monitoring and control issues for batch processes a finite time high order sliding-mode observer is considered. It is presented a theoretical analysis to provide a sketch of proof to demonstrate the convergence properties of the proposed observer and the finite time of convergence is calculated from the same analysis. A simple model for a batch aerobic wastewater bioreactor, experimentally corroborated, is proposed as application example and numerical experiments show the adequate observer performance compared to a standard nonlinear Luenberger observer.
Aguilar R., Martínez-Guerra R. and MayaYescas R. (2003) State Estimation for Partially Unknown Nonlinear Systems: A Class of Integral High Gain Observers. IEE Proceedings Control Theory and Applications 150 (3), 240-244.
Athans M., Falb P. (1966) Optimal Control: An introduction to theory and Applications. McGraw Hill, New York.
Bertoni G., Punta E. (2000) Chattering elimination with second order sliding-modes robust to Coulomb friction. Journal of Dynamics, Measurement and Control 122, 679-684.
Bhat S., Berstein D. (2000) Continuous finite time stability of continuous autonomous systems. SIAM Journal of Control and Optimization 38, 751-766.
Dávila J., Fridman L., Levant A. (2005) Second order sliding-mode observer for mechanical systems. IEEE Transactions on Automatic Control 50 (11), 1785-1789.
Dochain, D. and Vanrolleghem, P. (2001). Dynamic modeling and estimation in wastewater treatment process. IWA Publishing. U.K.
Eckefelder, W. (2000) Industrial water pollution control. Environmental Engineering Series. McGraw Hill. 3rd Ed.
Engel R., Kreisselmeier G. (2002). A continuoustime observer which converges in finite time. IEEE Transactions on Automatic Control 47 (7), 1202-1204.
Feki M. (2003) Observer-based exact synchronization of ideal and mismatched chaotic systems. Physics Letters A 309, 53-60.
Haimo V. (1986). Finite time controllers. SIAM Journal of Control and Optimization 24 (4), 760-770.
Heitzer, A., Hans-Peter E., Reichert, P. and Hamer, G. (1991). Utility of phenomenological models for describing temperature dependence of bacterial growth. Applied Environmental Microbiology 57, 2656-2665.
Hong Y., Huang J., Xu Y. (2001) On an output feedback finite-time stabilization problem.IEEE Transactions on Automatic Control 46 (2), 305-309.
Hong Y., Xu Y., Huang J. (2002) Finite-time control for robot manipulators. Systems and Control Letters 46, 243-253.
Kazantzis N., Kravaris C. (1998) Nonlinear observer design using Liapunov´s auxiliary theorem. Systtems and Control Letters 34, 241-247.
Levant A. (2001). Universal single-input-singleoutput (SISO) sliding-mode controllers with finite-time convergence. IEEE Transactions on Automatic Control 46 (9), 1447-1451.
Maqueda M.A.M., Martinez S.A., Narváez D., Rodriguez M.G., Aguilar-López R., Herrero V. M. (2006) Dynamical modeling of an activated sludge system of a petrochemical plant operating at high temperatures. Water Science and Technology 53, (11), 135-142.
Martínez S., Rodríguez M., Morales M., Aguilar R. (2005) Effect of the temperature in the performance of a biological system for the treatment of wastewater in a petrochemical industry. Ingeniería Hidráulica en México November - December.
Ministry of the Environment, Natural Resources and Fisheries SEMARNAP (1997). NOM001-ECOL-1996. México D.F., México.
Nijmeijer H., Fossen T.I. (1999). New directions in nonlinear observer design. Springer.
Raghavan S., Hendrick J.K. (1994) Observer design for a class of nonlinear systems. International Journal of Control. 59, 515-528.
Ramalho, R. (1999) Wastewater Treatment. Ed. Reverté. Spain. Thau F.E. (1973). Observing state of nonlinear dynamic systems. International Journal of Control 17, 471-479.
Zwieterig, M.H., De Koos, J.T., Hasenack, B.E., De Wit, J.C. and Van ’T riet, K. (1991). Modeling of bacterial growth as a function of temperature. Applied Environmental Microbiology 57, 1094-1101.
By publishing your paper in our journal you are also granting it the copyright of the information that it contains.