Abstract
This chapter presents neurofuzzy networks for nonlinear process modeling and control. The neurofuzzy network uses local linear models to model a nonlinear process and the local linear models are combined using center of gravity (COG) defuzzification. In order to be able to provide accurate long-range predictions, a recurrent neurofuzzy network structure is developed. An advantage of neurofuzzy network models is that they are easy to interpret. Insight about the process characteristics at different operating regions can be easily obtained from the neurofuzzy network parameters. Based on the neurofuzzy network model, nonlinear model predictive controllers can be developed as a nonlinear combination of several local linear model predictive controllers that have analytical solutions. Applications to the modeling and control of a neutralization process and a fed-batch process demonstrate that the proposed recurrent neurofuzzy network is very effective in the modeling and control of nonlinear processes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automatic Control 19:716–723
Astrom KJ, Wittenmark B (1989) Adaptive control, 2nd edn. Addison-Wesley, Reading, MA
Barron AR (1984) Predicted squared error: a criterion for automatic model selection. In: Farlow SJ (ed) Self organising methods. Marcel Dekker, New York, pp 87–103
Bhat NV, McAvoy TJ (1990) Use of neural nets for dynamical modelling and control of chemical process systems. Comput Chem Eng 14:573–583
Billings SA, Voon WSF (1986) Correlation based model validity tests for non-linear models. Int J Control 44:235–244
Blanco A, Delgado M, Pegalajar MC (2001a) A real-coded genetic algorithm for training recurrent neural networks. Neural Netw 14:93–105
Blanco A, Delgado M, Pegalajar MC (2001b) Fuzzy automaton induction using neural networks. Int J Approx Reasoning 27:1–26
Brown M, Harris CJ (1994) Neurofuzzy adaptive modelling and control. Prentice Hall, Hemel Hempstead
Bulsari AB (ed) (1995) Computer-aided chemical engineering. Neural networks for chemical engineers, vol 6. Elsevier, Amsterdam
Clarke DW, Mohtadi C, Tuffs PS (1987) Generalised predictive control, Parts 1 and 2. Automatica 23:859–875
Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signal Syst 2:303–314
Eaton JW, Rawlings JB (1990) Feedback control of chemical processes using on-line optimization techniques. Comput Chem Eng 14:469–479
Elman JL (1990) Finding structures in time. Cogn Sci 14:179–211
Frasconi P, Gori M, Soda G (1992) Local feedback multilayered networks. Neural Comput 4:120–130
Geladi P, Kowalski BR (1986) Partial least-squares regression: a tutorial. Anal Chim Acta 185:1–17
Gembicki FW (1974) Vector optimisation for control with performance and parameter sensitivity indices, Ph.D. Thesis, Case Western Reserve University
Girosi F, Poggio T (1990) Networks and the best approximation property. Biol Cybern 63:169–179
Harris CJ, Brown M, Bossley KM, Mills DJ, Ming F (1996) Advances in neurofuzzy algorithms for real-time modelling and control. Eng Appl Artif Intell 9:1–16
Hernandez E, Arkun Y (1993) Control of nonlinear systems using polynomial ARMA models. AIChE J 39:446–460
Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12:55–67
Horikawa S, Furuhashi T, Uchikawa Y (1992) On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm. IEEE Trans Neural Netw 3:801–806
Jang JSR (1992) Self-learning fuzzy controllers based on temporal back propagation. IEEE Trans Neural Netw 3:714–723
Jang JSR, Sun CT (1995) Neuro-fuzzy modeling and control. Proc IEEE 83:378–406
Jang JSR, Sun CT, Mizutani E (1997) Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Prentice Hall, Englewood Cliffs, NJ
Johansen TA, Foss BA (1993) Constructing NARMAX models using ARMAX models. Int J Control 58:1125–1153
Kuipers B, Astrom K (1994) The composition and validation of heterogeneous control laws. Automatica 30:233–249
Leonard JA, Kramer MA (1990) Improvement of the back-propagation algorithm for training neural networks. Comput Chem Eng 14:337–341
Leontaris IJ, Billings SA (1987) Model selection and validation methods for nonlinear systems. Int J Control 45:311–341
Li WC, Biegler LT (1989) Multistep, Newton-type control strategies for constrained, nonlinear processes. Chem Eng Res Des 67:562–577
Mak MW, Ku KW, Lu YL (1999) On the improvement of the real time recurrent learning algorithm for recurrent neural networks. Neurocomputing 24:13–36
Maner BR, Doyle FJ III (1997) Polymerization reactor control using autoregressive-plus Volterra-based MPC. AIChE J 43:1763–1784
Marquardt D (1963) An algorithm for least squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441
McAvoy TJ, Hsu E, Lowenthal S (1972) Dynamics of pH in controlled stirred tank reactor. Ind Eng Chem Process Des Dev 11:68–70
Morris AJ, Montague GA, Willis MJ (1994) Artificial neural networks: studies in process modelling and control. Chem Eng Res Des 72:3–19
Nie J, Linkens DA (1993) Learning control using fuzzified self-organising radial basis function networks. IEEE Trans Fuzzy Syst 1:280–287
Omlin CW, Thornber KK, Giles CL (1998) Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks. IEEE Trans Fuzzy Syst 6:76–89
Park J, Sandberg IW (1991) Universal approximation using radial basis function networks. Neural Comput 3:246–257
Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by error propagation. In: Rumelhart DE, McClelland JL (eds) Parallel distributed processing. MIT Press, Cambridge, MA
Saint-Donat J, Bhat N, McAvoy TJ (1991) Neural net based model predictive control. Int J Control 54:1452–1468
Scott GM, Ray WH (1993) Creating efficient nonlinear network process models that allow model interpretation. J Process Control 3:163–178
Sistu PB, Gopinath RS, Bequette BW (1993) Computational issues in nonlinear predictive control. Comput Chem Eng 17:361–366
Sjoberg J, Zhang Q, Ljung L, Benveniste A, Delyon B, Glorennec P, Hjalmarsson H, Juditsky A (1995) Nonlinear black-box modelling in system identification: a unified overview. Automatica 31:1691–1724
Su HT, McAvoy TJ, Werbos P (1992) Long term prediction of chemical processes using recurrent neural networks: a parallel training approach. Ind Eng Chem Res 31:1338–1352
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modelling and control. IEEE Trans Syst Man Cybern 15:116–132
Terwiesch P, Ravemark D, Schenker B, Rippin DWT (1998) Semi-batch process optimization under uncertainty: theory and experiments. Comput Chem Eng 22:201–213
Tian Y, Zhang J, Morris AJ (2002) Optimal control of a batch emulsion copolymerisation reactor based on recurrent neural network models. Chem Eng Process 41:531–538
Tsoi AC, Back AD (1994) Locally recurrent globally feedforward networks: a critical review of architectures. IEEE Trans Neural Netw 5:229–239
Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice Hall, Englewood Cliffs, NJ
Werbos PJ (1990) Backpropagation through time: what it does and how to do it. Proc IEEE 78:1550–1560
Yager RR, Filev DP (1994) Essentials of fuzzy modelling and control. Wiley, New York
Zhang J (2004) A reliable neural network model based optimal control strategy for a batch polymerisation reactor. Ind Eng Chem Res 43:1030–1038
Zhang J (2005) Modelling and optimal control of batch processes using recurrent neuro-fuzzy networks. IEEE Trans Fuzzy Syst 13:417–427
Zhang J (2006) Modelling and multi-objective optimal control of batch processes using recurrent neuro-fuzzy networks. Int J Automation Comput 3:1–7
Zhang J, Morris AJ (1994) On-line process fault diagnosis using fuzzy neural networks. Intell Syst Eng 3:37–47
Zhang J, Morris AJ (1995) Fuzzy neural networks for nonlinear systems modelling. IEE Proc, Control Theory Appl 142:551–561
Zhang J, Morris AJ (1999) Recurrent neuro-fuzzy networks for nonlinear process modelling. IEEE Trans Neural Netw 10:313–326
Zhang J, Morris AJ, Martin EB (1998) Long term prediction models based on mixed order locally recurrent neural networks. Comput Chem Eng 22:1051–1063
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this entry
Cite this entry
Zhang, J. (2012). Nonlinear Process Modelling and Control Using Neurofuzzy Networks. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-92910-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92909-3
Online ISBN: 978-3-540-92910-9
eBook Packages: Computer ScienceReference Module Computer Science and Engineering