Pablo A. López Pérez¹, Ricardo Aguilar–López²*

^1,2 Departamento de Biotecnología y Bioingeniería, Centro de Investigación y de Estudios Avanzados del I.P.N., CINVESTAV–IPN Av. Instituto Politécnico Nacional No. 2508, San Pedro Zacatenco, México, D.F. 07360. *raguilar@cinvestav.mx

ABSTRACT

The main objective of this work is to present an alternative methodology for the design of a class of integral high order sliding–mode controller applied to a class of continuous chemical reactor with complex behavior for temperature tracking purposes. The proposed design is based on the differential geometry framework, where the named reaching trajectory contains a high order sliding mode term in order to diminish chattering. Considering that the proposed technique is model based, an observer–based uncertainty estimator is coupled, which provides robustness against model uncertainties and noisy measurements. Numerical simulations are performed in order to show the capacities of the proposed controller, which is compared with other nonlinear methodologies.

Keywords: Chemical Reactor, Temperature tracking, observer based high order sliding mode controller, robust performance.

RESUMEN

El principal objetivo de este trabajo es presentar una metodología alternativa para el diseño de una clase de controlador integral de tipo modo deslizante de alto orden, que es aplicado a un reactor químico continuo con comportamiento complejo con fines de seguimiento de temperatura. El diseño propuesto se realiza bajo el marco de la geometría diferencial, donde la denominada trayectoria guía contiene un termino de tipo deslizante de alto orden con el fin de disminuir los problemas de oscilaciones. Considerando que la metodología propuesta está basada en el modelo de la planta, se acopla un estimador de incertidumbres basado en un observador, el cual provee condiciones de robustez contra errores de modelado y ruido en las mediciones. Simulaciones numéricas son realizadas para mostrar las capacidades del controlador propuesto, el cual es comparado con otras metodologías no lineales.

Palabras clave: Reactor químico, seguimiento de temperatura, controlador de modo deslizante de alto orden basado en observador, desempeño robusto.

DESCARGAR ARTÍCULO EN FORMATO PDF

References

[1] Aris, R. and Admundson, N. An analysis of chemical reactor stability and control. Chem. Engng Sci. Vol. 7, 1958, pp. 121–155.         [ Links ]

[2] Ricardo Aguilar, R. Martínez–Guerra and Rafael Maya–Yescas. State Estimation for Partially Unknown Nonlinear Systems: A Class of Integral High Gain Observers. IEE Proceedings Control Theory and Applications. Vol. 150, No.3, 2003, pp. 240–244.         [ Links ]

[3] Ricardo Aguilar–López and Rafael Martínez–Guerra. Control of chaotic oscillators via a class of model free active controller: suppression and synchronization. Chaos, Solitons and Fractals.Vol. 38, , 2008, pp. 531–540.         [ Links ]

[4] Ricardo Aguilar, Jesús González, José Alvarez and Miguel Angel Barrón. Temperature regulation of a class of continuous chemical reactor based on a nonlinear Luenberger–like observer. Journal of Chemical Technology and Biotechnology. Vol. 70, No. 3, 1997, pp. 209–216.         [ Links ]

[5] Samuel Bowong, FM Moukam, Kakmeni and Clement Tchawoua. Controlled synchronization of chaotic systems with uncertainties via a sliding mode control design. Physical Review E. Vol. 70, No. 066217, 2004, pp. 1–8,         [ Links ]

[6] Oscar Camacho and Carlos A. Smith. Sliding mode control: an approach to regulate nonlinear chemical processes. ISA Transactions. Vol. 39, No. 2, April 2000, pp. 205–218.         [ Links ]

[7] C.Edwards and S.Spurgeon, Sliding Mode Control. Taylor and Francis, 1998.         [ Links ]

[8] Girin, A.; Plestan, F.; Brim, X.; Glumineau, A. "A 3rd order sliding mode controller based on integral sliding mode for an electropneumatic system," 2006 45th IEEE Conference on Decision and Control, Vol. 45, No. 4, 1315 Dec. 2006, pp. 1617 – 1622        [ Links ]

[9] J. González, R. Aguilar, J. Alvarez–Ramirez and M. A. Barrón. Linearizing control of a binary distillation column based on a neuro–estimator. Artificial Intelligence in Engineering. 1999. Vol. 13, pp. 405–412.         [ Links ]

[10] Isidori, A. Nonlinear Control Theory. 3d Edition. Springer–Verlag, 1995).         [ Links ]

[11] Jorgensen, D.V. & Aris, R. On the dynamics of a stirred tank with consecutive reactions. Chemical Engineering Science. Vol. 38, 1983, pp. 45–53.         [ Links ]

[12] Kolavennu, S. Palanki, S. and Cockburn, J. Robust control of I/O linealizable systems via multi–model H₂/H∞ Synthesis. Chem. Eng. Sci. Vol. 55, 2000, pp. 1583–1589.

[13] Salah Laghrouche, Franck Plestan, Alain Glumineau, Higher order sliding mode control based on integral sliding mode, Automatica, Vol. 43, No. 3, March 2007, pp. 531–537.         [ Links ]

[14] Levant, A. Universal single–input–single–output (SISO) sliding–mode controllers with finite–time convergence. IEEE Transactions on Automatic Control. Vol. 46, No. 9, 2001, pp. 1447–1451.         [ Links ]

[15] Levant, A. Sliding order and sliding accuracy in sliding mode control. Int. J. of Control. Vol. 58, 1993, pp. 1247–1263.         [ Links ]

[16] R. Maya–Yescas and R. Aguilar. Controllability assessment approach for chemical reactors: non–linear control affine systems. Chemical Engineering Journal.. Vol. 92, No. 1, 2003, pp. 69–79.         [ Links ]

[17] Janos Madar, Janos Abonyi and Ferenc Szeifert. Feedback linearizing control using hybrid neural networks identified by sensitivity approach. Engineering Applications of Artificial Intelligence. Vol. 18, No. 3, April 2005, pp. 343–351.         [ Links ]

[18] Mohamed Azlan Hussain. Review of the applications of neural networks in chemical process control — simulation and online implementation. Artificial Intelligence in Engineering. Vol. 13, No. 1, January 1999, pp. 55–68.         [ Links ]

[19] M.I. Neria.González and R. Aguilar–López. Tracking Trajectories in a Continuous Anaerobic Bioreactor employing a Nonlinear Proportional Controller. Int. Journal of Chemical Reactor Engineering. Vol. 5, A73, 2007.         [ Links ]

[20] M.I. Neria.González, R. Martínez–Guerra and R. Aguilar–López. Feedback regulation of an industrial aerobic wastewater plant. Chemical Engineering Journal. Vol. 139, 2008, pp. 475–481.         [ Links ]

[21] Ogunnaike, B.A. and Ray, W.H. Process, Dynamics, Modeling and Control. Oxford University Press. New York, 1994.         [ Links ]

[22] F.G. Shinskey. Feedback Controllers for the Process Industries. Mc Graw Hill. 1994        [ Links ]

[23] V.Utkin, J.Guldner, and J.Shi. Sliding Modes in Electromechanical Systems. Taylor and Francis, 1999.         [ Links ]