Identification of a PWA Model of a Batch Reactor for Model Predictive Control
The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328830Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1799
References:Batch reactor, fuzzy clustering, hybrid systems, identification, nonlinear systems, PWA systems.
 R. Babu╦çska. Fuzzy Modelling for Control. KAP, 1998.
 R. Babu╦çska and H. B. Verbruggen. An overview of fuzzy modelling for control. Control Engineering Practice, 4(11):1593-1606, 1996.
 A. Bemporad. Efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form. IEEE Trans. Automatic Control, 49(5):832-838, 2004.
 A. Bemporad and M. Morari. Control of systems integrating logic, dynamics and constraints. Automatica, 35(3):407-427, 1999.
 D. Girimonte and R. Babu╦çska. Structure for nonlinear models with mixed discrete and continuous inputs: a comparative study. In Proc. of IEEE International Conf. on system, Man and Cybernetics, pages 2392-2397, 2004.
 W. P. M. H. Heemels, B. De Schutter, and A. Bemporad. Equivalence of hybrid dynamical models. Automatica, 37(7):1085-1091, 2001.
 G. Karer. Prediktivno vodenje hibridnih sistemov. PhD thesis, Fakulteta za elektrotehniko, Univerza v Ljubljani, 2009.
 G. Karer, G. Mu╦çsi╦çc, I. ╦ç Skrjanc, and B. Zupan╦çci╦çc. Hybrid fuzzy modelbased predictive control of temperature in a batch reactor. Computers and Chemical Engineering, 31:1552-1564, 2007.
 E. C. Kerrigan and D. Q. Mayne. Optimal control of constrained, piecewise affine systems with bounded disturbances. In Proc. 41st IEEE Conference on Decision and Control, Las Vegas, 2002.
 D. Q. Mayne and S. Rakovi'c. Model predictive control of constrained piecewise affine discrete-time systems. International Journal of Robust and Nonlinear Control, 13(3):261-279, 2003.
 R. Palm and D. Driankov. Fuzzy switched hybrid systems - modelling and identification. In Proc. of the 1998 IEEE/ISCI/CIRA/SAS Joint Conf., Gaithersburg MD, pages 130-135, 1998.
 B. Poto╦çcnik, G. Mu╦çsi╦çc, and B. Zupan╦çci╦çc. A new technique for translating discrete hybrid automata into piecewise affine systems. Math. comput. model. dyn. syst., 10(1):41-57, 2004.
 B. Poto╦çcnik, G. Mu╦çsi╦çc, and B. Zupan╦çci╦çc. Model predictive control of discrete time hybrid systems with discrete inputs. ISA Transactions, 44(2):199-211, 2005.
 Y. Qin and L.-M. Jia. Fuzzy hybrid control and its application in complex combustion processes. In 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS-02), page 78. IEEE, 2002.
 D. S'aez, C. E. Cort'es, and A. N'u╦£nez. Hybrid adaptive predictive control for the multi-vehicle dynamic pick-up and delivery problem based on genetic algorithms and fuzzy clustering. Computers and Operations Research, 35(11):3412 - 3438, 2008.
 I. ╦ç Skrjanc and D. Matko. Fuzzy predictive functional control in the state space domain. Journal of Intelligent and Robotic Systems, 31:283-297, 2001.
 E. Sontag. Nonlinear regulation: The piecewise linear approach. IEEE Transactions on Automatic control, 26(2):346-358, 1981.
 M. Sugeno and K. Tanaka. Successive identification of a fuzzy model and its application to prediction of a complex system. Fuzzy Sets and Systems, 42:315-334, 1991.
 T. Takagi and M. Sugeno. Fuzzy identification of systems and its application to modelling and control. IEEE Trans. System Man Cybernet., 15:116-132, 1985.
 A. Van der Schaft and H. Schumacher. An introduction to hybrid dynamical systems. Lecture Notes in Control and Information Sciences, 251:v-vii, 1999.
 H. S. Witsenhausen. A class of hybrid-state continuous time dynamic systems. IEEE Trans. on Automatic Control, 11(2):161-167, 1966.