A nonlinear predictive control strategy based on radial basis function models

A predictive control strategy for nonlinear processes based on radial basis function models is proposed. First, a radial basis function model of the process is developed using stepwise regression and least squares estimation. This model is then used to train a nonlinear predictive controller, which is also implemented as a radial basis function network. Since no optimization problems have to be solved on-line, this control strategy can be implemented easily. The proposed strategy is applied to an experimental pH neutralization process; it provides both excellent setpoint tracking and disturbance rejection when compared to conventional PI control.

[1]  Thomas J. McAvoy,et al.  Optimizing Neural Net based Predictive Control , 1990 .

[2]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[3]  A. Sideris,et al.  A multilayered neural network controller , 1988, IEEE Control Systems Magazine.

[4]  B. Bequette.  Nonlinear control of chemical processes: a review , 1991 .

[5]  Daniel Sbarbaro,et al.  Neural Networks for Nonlinear Internal Model Control , 1991 .

[6]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[7]  R. E. Carlson,et al.  The parameter R2 in multiquadric interpolation , 1991 .

[8]  Richard Franke,et al.  Recent Advances in the Approximation of surfaces from scattered Data , 1987, Topics in Multivariate Approximation.

[9]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[10]  Thomas E Marlin,et al.  Process Control , 1995 .

[11]  Sheng Chen,et al.  Recursive hybrid algorithm for non-linear system identification using radial basis function networks , 1992 .

[12]  Richard S. Sutton,et al.  Neuronlike adaptive elements that can solve difficult learning control problems , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  C.W. Anderson,et al.  Learning to control an inverted pendulum using neural networks , 1989, IEEE Control Systems Magazine.

[14]  Phillip D. Schnelle,et al.  Model predictive control of an industrial packed bed reactor using neural networks , 1995 .

[15]  Larry L. Schumaker,et al.  Topics in Multivariate Approximation , 1987 .

[16]  Dale E. Seborg,et al.  Adaptive nonlinear control of a pH neutralization process , 1994, IEEE Trans. Control. Syst. Technol..

[17]  Dale E. Seborg,et al.  Nonlinear Process Control , 1996 .

[18]  Rice,et al.  Method of false nearest neighbors: A cautionary note. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[20]  W. T. Miller,et al.  CMAC: an associative neural network alternative to backpropagation , 1990, Proc. IEEE.

[21]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[22]  James S. Albus,et al.  New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC)1 , 1975 .

[23]  Yaman Arkun,et al.  Control of nonlinear systems using polynomial ARMA models , 1993 .

[24]  Dale E. Seborg,et al.  Modelling and Self-Tuning Control of a Multivariable pH Neutralization Process Part I: Modelling and Multiloop Control , 1989, 1989 American Control Conference.

[25]  B. Bequette.  NONLINEAR PREDICTIVE CONTROL USING MULTI-RATE SAMPLING , 1991 .

[26]  Derrick H. Nguyen,et al.  Neural networks for self-learning control systems , 1990 .

[27]  Sheng Chen,et al.  Practical identification of NARMAX models using radial basis functions , 1990 .

[28]  Enis Ersü,et al.  Learning control with interpolating memories―general ideas, design lay-out, theoretical approaches and practical applications , 1992 .

[29]  J. Rawlings,et al.  Feedback control of chemical processes using on-line optimization techniques , 1990 .

[30]  J. A. Leonard,et al.  Radial basis function networks for classifying process faults , 1991, IEEE Control Systems.

[31]  L.G. Kraft,et al.  A comparison between CMAC neural network control and two traditional adaptive control systems , 1990, IEEE Control Systems Magazine.

[32]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[33]  John W. Eaton,et al.  Stability of neural net based model predictive control , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[34]  Norman R. Draper,et al.  Applied regression analysis (2. ed.) , 1981, Wiley series in probability and mathematical statistics.

[35]  Yaman Arkun,et al.  Neural Network Modeling and an Extended DMC Algorithm to Control Nonlinear Systems , 1990, 1990 American Control Conference.

[36]  Filson H. Glanz,et al.  Application of a General Learning Algorithm to the Control of Robotic Manipulators , 1987 .

[37]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[38]  Martin Pottman,et al.  Identification of non-linear processes using reciprocal multiquadric functions , 1992 .

[39]  Henk B. Verbruggen,et al.  Design and real time testing of a neural model predictive controller for a nonlinear system , 1995 .

[40]  Dale E. Seborg,et al.  Theoretical analysis of unconstrained nonlinear model predictive control , 1993 .

[41]  Peter J. Gawthrop,et al.  Neural networks for control systems - A survey , 1992, Autom..

[42]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[43]  Tore K. Gustafsson.  An experimental study of a class of algorithms for adaptive pH control , 1985 .

[44]  T Poggio,et al.  Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks , 1990, Science.