An Input/Output Approach to the Optimal Transition Control of a Class of Distributed Chemical Reactors

An input/output approach to the optimal concentration transition control problem of a certain type of distributed chemical reactors is proposed based on the concept of residence time distribution, which can be determined in practice by using data from experimental measurements or computer simulations. The main assumptions for the proposed control method to apply are that the thermal and fluid flow fields in the reactor are at pseudo-steady-state during transition and that the component whose concentration is to-be-controlled participates only in first-order reactions. Using the concept of cumulative residence time distribution, the output variable is expressed as the weighted sum of discretized inputs or input gradients in order to construct an input/output model, on the basis of which a constrained optimal control problem, penalizing a quadratic control energy functional in the presence of input constraints, is formulated and solved as a standard least squares problem with inequality constraints. The effectiveness of the proposed optimal control scheme is demonstrated through a continuous-stirred- tank-reactor (CSTR) network and a tubular reactor with axial dispersion and a first-order reaction. It is demonstrated through computer simulations that the proposed control method is advantageous over linear quadratic regulator (LQR) and proportional-integral (PI) control in terms of control cost minimization and input constraint satisfaction.

[1]  S. Dubljevic,et al.  Predictive control of parabolic PDEs with state and control constraints , 2006, Proceedings of the 2004 American Control Conference.

[2]  Achim Kienle,et al.  Development and experimental investigation of an extended Kalman filter for a molten carbonate fuel cell system , 2006 .

[3]  C. K. Harris,et al.  Computational Fluid Dynamics for Chemical Reactor Engineering , 1996 .

[4]  J. Banga,et al.  Reduced-Order Models for Nonlinear Distributed Process Systems and Their Application in Dynamic Optimization , 2004 .

[5]  L. Petzold,et al.  Computational Algorithm for Dynamic Optimization of Chemical Vapor Deposition Processes in Stagnation Flow Reactors , 2000 .

[6]  Panagiotis D. Christofides,et al.  Predictive control of transport-reaction processes , 2005, Comput. Chem. Eng..

[7]  Computational fluid dynamic modeling of tin oxide deposition in an impinging chemical vapor deposition reactor , 2006 .

[8]  Wr Graham,et al.  OPTIMAL CONTROL OF VORTEX SHEDDING USING LOW-ORDER MODELS. PART I-OPEN-LOOP MODEL DEVELOPMENT , 1999 .

[9]  Freek Kapteijn,et al.  Liquid residence time distribution in the film flow monolith reactor , 2005 .

[10]  H. S. Fogler,et al.  Elements of Chemical Reaction Engineering (4th Edition) (Prentice Hall International Series in the Physical and Chemical Engineering Sciences) (Hardcover) , 2005 .

[11]  J. Banga,et al.  Dynamic optimization of complex distributed process systems , 2005 .

[12]  P. Daoutidis,et al.  Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds , 1997 .

[13]  Panagiotis D. Christofides,et al.  Optimization of transport-reaction processes using nonlinear model reduction , 2000 .

[14]  Jyeshtharaj B. Joshi,et al.  Axial mixing in laminar pipe flows , 2004 .

[15]  Freek Kapteijn,et al.  Gas and liquid phase distribution and their effect on reactor performance in the monolith film flow reactor , 2001 .

[16]  Stelios Rigopoulos,et al.  A hybrid CFD: reaction engineering framework for multiphase reactor modelling: basic concept and application to bubble column reactors , 2003 .

[17]  Ioannis G. Kevrekidis,et al.  Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis , 1996 .

[18]  P. Christofides,et al.  Dynamic optimization of dissipative PDE systems using nonlinear order reduction , 2002 .

[19]  P. Christofides,et al.  Nonlinear Control of Incompressible Fluid Flow: Application to Burgers' Equation and 2D Channel Flow☆ , 2000 .

[20]  W. Ray,et al.  Dynamic modeling of polyethylene grade transitions in fluidized bed reactors employing nickel-diimine catalysts , 2006 .

[21]  P. Christofides,et al.  Finite-dimensional approximation and control of non-linear parabolic PDE systems , 2000 .

[22]  P. V. Danckwerts Continuous flow systems. Distribution of residence times , 1995 .

[23]  Panagiotis D. Christofides,et al.  Multi-scale modeling and analysis of an industrial HVOF thermal spray process , 2005 .

[24]  Panagiotis D. Christofides,et al.  Optimal control of diffusion-convection-reaction processes using reduced-order models , 2008, Comput. Chem. Eng..

[25]  Panagiotis D. Christofides,et al.  Predictive control of parabolic PDEs with boundary control actuation , 2006 .

[26]  P. Christofides,et al.  Computational study of particle in-flight behavior in the HVOF thermal spray process , 2006 .

[27]  Antonios Armaou,et al.  Optimal operation of GaN thin film epitaxy employing control vector parametrization , 2006 .

[28]  Vivek V. Ranade,et al.  Liquid Distribution and RTD in Trickle Bed Reactors: Experiments and CFD Simulations , 2008 .

[29]  P. Christofides,et al.  Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes , 2002 .

[30]  J. Macgregor,et al.  Optimal Grade Transitions in a Gas Phase Polyethylene Reactor , 1992 .

[31]  H. S. Fogler,et al.  Elements of Chemical Reaction Engineering , 1986 .

[32]  Control of Navier-Stokes equations by means of mode reduction , 2000 .

[33]  Antonios Armaou,et al.  Nonlinear feedback control of parabolic PDE systems with time-dependent spatial domains , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[34]  L. Biegler,et al.  Large-scale dynamic optimization for grade transitions in a low density polyethylene plant , 2002 .

[35]  P. Christofides,et al.  Wave suppression by nonlinear finite-dimensional control , 2000 .

[36]  P. V. Danckwerts Continuous flow systems , 1953 .