Non-Linear Model Based Predictive Control Through Dynamic Non-Linear Partial Least Squares

The extension of model predictive control (MPC) to non-linear systems is proposed through dynamic non-linear Partial Least Squares (PLS) models. PLS has been shown to be an appropriate multivariate regression methodology for modelling noisy, correlated and/or collinear data. It has been applied extensively, within a ‘static’ framework, for the modelling and analysis of industrial process data. The contribution of this paper is the development of a non-linear dynamic PLS framework for applications in MPC. The non-linear dynamic PLS models make use of an error based non-linear partial least squares algorithm where the non-linear inner models are built within an AutoRegressive with eXogeneous inputs (ARX) framework. In particular, quadratic and feedforward neural network inner models are considered. The application of a dynamic PLS model within a MPC framework opens up the potential of using multivariate statistical projection based methods not only for process modelling, inferential estimation and performance monitoring, but also for model predictive control. A benchmark simulation of a pH neutralization system is used to demonstrate the application of a non-linear dynamic PLS framework for model predictive control.

[1]  H. Wold.  Nonlinear Iterative Partial Least Squares (NIPALS) Modelling: Some Current Developments , 1973 .

[2]  S. Wold.  Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models , 1978 .

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

[4]  E. Martin,et al.  Non-linear projection to latent structures revisited: the quadratic PLS algorithm , 1999 .

[5]  A. J. Morris,et al.  Estimation of impurity and fouling in batch polymerisation reactors through the application of neural networks , 1999 .

[6]  N. L. Ricker.  The use of biased least-squares estimators for parameters in discrete-time pulse-response models , 1988 .

[7]  W. Harmon Ray,et al.  Dynamic PLS modelling for process control , 1993 .

[8]  S. Wold,et al.  Nonlinear PLS modeling , 1989 .

[9]  S. Qin,et al.  Partial least squares regression for recursive system identification , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[10]  Barry M. Wise,et al.  A non-linear dynamic model identification challenge problem , 1995 .

[11]  S. Wold.  Exponentially weighted moving principal components analysis and projections to latent structures , 1994 .

[12]  Dale E. Seborg,et al.  A nonlinear predictive control strategy based on radial basis function models , 1997 .

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

[14]  Sirish L. Shah,et al.  Modeling and control of multivariable processes: Dynamic PLS approach , 1997 .

[15]  Thomas J. McAvoy,et al.  Neural net based model predictive control , 1991 .

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

[17]  A. J. Morris,et al.  Non-linear projection to latent structures revisited (the neural network PLS algorithm) , 1999 .

[18]  Jay H. Lee,et al.  Model predictive control: past, present and future , 1999 .

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

[20]  Ronald K. Pearson,et al.  Nonlinear model predictive control of a simulated multivariable polymerization reactor using second-order Volterra models , 1996, Autom..

[21]  Michael A. Henson,et al.  Nonlinear model predictive control: current status and future directions , 1998 .

[22]  B. Kowalski,et al.  Partial least-squares regression: a tutorial , 1986 .

[23]  George W. Irwin,et al.  Nonlinear PLS modelling using radial basis functions , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[24]  Bryon R. Maner,et al.  Polymerization reactor control using autoregressive‐plus Volterra‐based MPC , 1997 .

[25]  L. Ljung,et al.  Issues in system identification , 1991, IEEE Control Systems.

[26]  Thomas J. McAvoy,et al.  Nonlinear PLS Modeling Using Neural Networks , 1992 .

[27]  A. J. Morris,et al.  Non-linear dynamic projection to latent structures modelling , 2000 .

[28]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..