Unscented Kalman filter based nonlinear model predictive control of a LDPE autoclave reactor

Abstract This paper presents a multivariable nonlinear model predictive control (NMPC) scheme for the regulation of a low-density polyethylene (LDPE) autoclave reactor. A detailed mechanistic process model developed previously was used to describe the dynamics of the LDPE reactor and the properties of the polymer product. Closed-loop simulations are used to demonstrate the disturbance rejection and tracking performance of the NMPC algorithm for control of reactor temperature and weight-averaged molecular weight (WAMW). In addition, the effect of parametric uncertainty in the kinetic rate constants of the LDPE reactor model on closed-loop performance is discussed. The unscented Kalman filtering (UKF) algorithm is employed to estimate plant states and disturbances. All control simulations were performed under conditions of noisy process measurements and structural plant–model mismatch. Where appropriate, the performance of the NMPC algorithm is contrasted with that of linear model predictive control (LMPC). It is shown that for this application the closed-loop performance of the UKF based NMPC scheme is very good and is superior to that of the linear predictive controller.

[1]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[2]  Paulo Afonso,et al.  Unscented Kalman Filtering of a Simulated pH System , 2004 .

[3]  Kenneth R. Muske,et al.  Disturbance modeling for offset-free linear model predictive control , 2002 .

[4]  Stephen J. Wright,et al.  Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming , 2004, Comput. Optim. Appl..

[5]  Hyun-Ku Rhee,et al.  Modeling and control of an LDPE autoclave reactor , 1996 .

[6]  Andrei Romanenko,et al.  The unscented filter as an alternative to the EKF for nonlinear state estimation: a simulation case study , 2004, Comput. Chem. Eng..

[7]  C. V. Rao,et al.  Steady states and constraints in model predictive control , 1999 .

[8]  S. Joe Qin,et al.  An Overview of Nonlinear Model Predictive Control Applications , 2000 .

[9]  Francis J. Doyle,et al.  Polymer grade transition control using advanced real-time optimization software , 2004 .

[10]  Ramdhane Dhib,et al.  Modeling of ethylene polymerization with difunctional initiators in tubular reactors , 2008 .

[11]  J. E. Cuthrell,et al.  On the optimization of differential-algebraic process systems , 1987 .

[12]  Kil Sang Chang,et al.  Analysis of an LDPE compact autoclave reactor by two‐cell model with backflow , 1999 .

[13]  Gabriele Pannocchia,et al.  Disturbance models for offset‐free model‐predictive control , 2003 .

[14]  Stephen J. Wright,et al.  Closed‐loop behavior of nonlinear model predictive control , 2004 .

[15]  G. Luft,et al.  Prediction of molar mass distribution, number and weight average degree of polymerization and branching of low density polyethylene , 1985 .

[16]  James B. Rawlings,et al.  Model Predictive Control , 2012 .

[17]  Bjarne A. Foss,et al.  Constrained nonlinear state estimation based on the UKF approach , 2009, Comput. Chem. Eng..

[18]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

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

[20]  E. Kreund,et al.  The structure of decoupled non-linear systems , 1975 .

[21]  C. Georgakis,et al.  Nonlinear model predictive control of end-use properties in batch reactors , 2002 .

[22]  A. Shenoy,et al.  Melt flow index: More than just a quality control rheological parameter. Part I , 1986 .

[23]  W. Harmon Ray,et al.  Nonlinear dynamics found in polymerization processes — a review , 2000 .

[24]  Ramdhane Dhib,et al.  Modelling of free radical polymerisation of ethylene using difunctional initiators , 2002 .

[25]  Biao Huang,et al.  Estimation and control of solid oxide fuel cell system , 2010, Comput. Chem. Eng..

[26]  W. Harmon Ray,et al.  Effects of imperfect mixing on low‐density polyethylene reactor dynamics , 1998 .

[27]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[28]  Peter Singstad,et al.  Multivariable Non-linear Control of Industrial LDPE Autoclave Reactors , 1992, 1992 American Control Conference.

[29]  Luigi Marini,et al.  Low‐density polyethylene vessel reactors: Part I: Steady state and dynamic modelling , 1984 .

[30]  Ridvan Berber,et al.  Dynamic simulation and quadratic dynamic matrix control of an industrial low density polyethylene reactor , 1996 .

[31]  J. Villadsen,et al.  Solution of differential equation models by polynomial approximation , 1978 .

[32]  L. Grüne,et al.  Nonlinear Model Predictive Control : Theory and Algorithms. 2nd Edition , 2011 .

[33]  Sirish L. Shah,et al.  State estimation and nonlinear predictive control of autonomous hybrid system using derivative free state estimators , 2010 .

[34]  J. Balchen,et al.  Internal Decoupling in Nonlinear Process Control , 1988 .

[35]  W. Harmon Ray,et al.  Runaway phenomena in low‐density polyethylene autoclave reactors , 1996 .

[36]  Luigi Marini,et al.  Low‐density polyethylene vessel reactors: Part II: A novel controller , 1984 .

[37]  Dilhan M. Kalyon,et al.  High pressure polymerization of ethylene and rheological behavior of polyethylene product , 1994 .

[38]  B. Finlayson The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[39]  B. Foss,et al.  A new optimization algorithm with application to nonlinear MPC , 2004 .