REAL-TIME DYNAMIC OPTIMIZATION OF NON-LINEAR BATCH SYSTEMS

In this paper, a methodology for designing and implementing a real time optimizing controller for non-linear batch processes is discussed. The controller is used to optimize the system input and state trajectories according to a cost function. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov-based extremum seeking approach is used to compute the trajectory parameters. Smooth trajectories were generated with reduced computing time compared to many optimizations in literature. In this paper, the theory is applied to general non-flat non-linear systems in a true on-line optimization. Dans cet article, on etudie une methodologie pour la conception et l'implantation d'un controleur d'optimisation en temps reel de procedes discontinus non lineaires. Le controleur sert a optimiser l'entree du systeme et les trajectoires d'etat d'apres une fonction de couts. Pour calculer par ordinateur les parametres de trajectoire, on recourt a une methode a points interieurs avec une fonction de penalites pour incorporer des contraintes dans une methode de recherche des extremes lyapunovienne et une fonctionnelle de cout modifiee. Des trajectoires lisses ont ete produites avec un temps de calcul reduit comparativement a de nombreuses optimisations de la litterature scientifique. Dans cet article, la theorie est appliquee a des systemes non lineaires non plats generaux dans une veritable optimisation en ligne.

[1]  Y BensonHande,et al.  Interior-point methods for nonconvex nonlinear programming , 2008 .

[2]  Martin Guay,et al.  A NEW REAL-TIME APPROACH FOR NONLINEAR MODEL PREDICTIVE CONTROL , 2005 .

[3]  M. A. Latifi,et al.  Methodology of dynamic optimization and optimal control of batch electrochemical reactors , 1999 .

[4]  Costas Kravaris,et al.  SYNTHESIS OF STATE FEEDBACK LAWS FOR END-POINT OPTIMIZATION IN BATCH PROCESSES , 1993 .

[5]  Z. Nagy,et al.  Robust nonlinear model predictive control of batch processes , 2003 .

[6]  Riccardo Scattolini,et al.  Model predictive control of continuous-time nonlinear systems with piecewise constant control , 2004, IEEE Transactions on Automatic Control.

[7]  F. Fontes.  A General Framework to Design Stabilizing Nonlinear Model Predictive Controllers , 2001 .

[8]  Masaru Noda,et al.  On-line optimization system of pilot scale multi-effect batch distillation system , 2000 .

[9]  J. Rudolph,et al.  Control of flat systems by quasi-static feedback of generalized states , 1998 .

[10]  Francis J. Doyle,et al.  A Flatness Based Approach to Optimization in Fed-Batch Bioreactors , 2000 .

[11]  Wolfgang Marquardt,et al.  Model predictive control for online optimization of semi-batch reactors , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[12]  Evanghelos Zafiriou,et al.  A methodology for on-line setpoint modification for batch reactor control in the presence of modeling error , 1999 .

[13]  B. Srinivasan,et al.  Economic Performance Analysis in the Design of On-line Batch Optimization Systems , 1999 .

[14]  Wolfgang Marquardt,et al.  Flatness and higher order differential model representations in dynamic optimization , 2002 .

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

[16]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[17]  Hande Y. Benson,et al.  INTERIOR-POINT METHODS FOR NONCONVEX NONLINEAR PROGRAMMING: COMPLEMENTARITY CONSTRAINTS , 2002 .

[18]  R. Bellman.  Dynamic programming. , 1957, Science.

[19]  Martin Guay,et al.  Trajectory optimization for flat dynamic systems , 2001 .

[20]  Martin Guay,et al.  A Real-Time Framework for Model-Predictive Control of Continuous-Time Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[21]  R. Murray,et al.  Trajectory Planning of Differentially Flat Systems with Dynamics and Inequalities , 2000 .

[22]  Francis J. Doyle,et al.  Differential flatness based nonlinear predictive control of fed-batch bioreactors , 2001 .

[23]  Wen-Teng Wu,et al.  Semi-realtime optimization and control of a fed-batch fermentation system , 2000 .

[24]  Srinivas Palanki,et al.  On-line optimization of batch processes with nonlinear manipulated input , 1996 .

[25]  Robert J. Vanderbei,et al.  Interior-Point Methods for Nonconvex Nonlinear Programming: Filter Methods and Merit Functions , 2002, Comput. Optim. Appl..

[26]  Tao Zhang,et al.  Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties , 2003, Autom..

[27]  M. Hestenes.  Calculus of variations and optimal control theory , 1966 .

[28]  R. Murray,et al.  Real‐time trajectory generation for differentially flat systems , 1998 .

[29]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[30]  Mark A. Kramer,et al.  Algorithm 658: ODESSA–an ordinary differential equation solver with explicit simultaneous sensitivity analysis , 1988, TOMS.

[31]  Srinivas Palanki,et al.  State feedback synthesis for on-line optimization of batch reactors with multiple manipulated inputs , 1998 .

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

[33]  Sohrab Rohani,et al.  On-line optimal control of a seeded batch cooling crystallizer , 2003 .

[34]  S. Palanki,et al.  State feedback synthesis for on-line optimization of batch reactors with a non-affine manipulated input and free terminal time , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[35]  Iqbal M. Mujtaba,et al.  On-line dynamic optimization and control strategy for improving the performance of batch reactors , 2005 .

[36]  Jie Yu,et al.  Unconstrained receding-horizon control of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[37]  S. Palanki,et al.  A feedback-based implementation scheme for batch process optimization , 2000 .