Model predictive control of an industrial pyrolysis gasoline hydrogenation reactor Amornchai Arpornwichanop a, * , Paisan Kittisupakorn a , Yaneeporn Patcharavorachot a , Iqbal M. Mujtaba b a Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand b School of Engineering, Design & Technology, University of Bradford, Bradford, West Yorkshire BD7 1DP, UK Received 11 January 2007; accepted 29 September 2007 Abstract This study focuses on the implementation of a nonlinear model predictive control (MPC) algorithm for controlling an industrial fixed-bed reactor where hydrogenations of raw pyrolysis gasoline occur. An orthogonal collocation method is employed to approximate the original reactor model consisting of a set of partial differential equations. The approximate model obtained is used in the synthesis of a MPC controller to control the temperature rising across a catalyst bed within the reactor. In the MPC algorithm, a sequential optimization approach is used to solve an open- loop optimal control problem. Feedback information is incorporated in the MPC to compensate for modeling error and unmeasured disturbances. The control studies are demonstrated in cases of set point tracking and disturbance rejection. # 2007 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. Keywords: Model predictive control; Fixed-bed reactor; Distributed parameter system; Reactor control; Simulation 1. Introduction The presence of the complexity in chemical processes due to higher product quality requirement and tighter environmental regulations posts challenging control problems that are difficult to handle with linear control techniques. With the limitation of linear controllers in achieving a satisfactory control perfor- mance, many advanced nonlinear control strategies have been devised over the past years. Among nonlinear control methodologies, a model predictive control (MPC) emerges as a powerful practical control technique. A key feature contributing to the success of MPC is its ability to cope with a multivariable system with constraints [1]. MPC has been widely applied in a wide range of applications, especially in the processes that their dynamic behavior is described by relatively simple models consisting of ordinary differential and/or algebraic equations. However, the implementation of MPC in complex systems like a distributed parameter system (DPS) which is naturally modeled by a set of nonlinear partial differential equations (PDEs) has been rarely addressed [2,3] and therefore, control studies on this type of the systems are still the subject of interest. Controlling a DPS, i.e., a fixed-bed reactor and a tubular reactor has been accepted to be a difficult task. A control design may be considerably complicated due to inherent difficulties such as high nonlinearity and the presence of spatial variations [4]. Such difficulties prompt the need for an effective control algorithm. In general, the approaches to control a DPS are mainly based on various lumping techniques which can be classified into two different strategies: late lumping and early lumping methods. The late lumping method applies a distributed parameter control theory to full PDE models for designing a control system. After the controller design has been completed, the resulting control algorithms are then solved by lumping approximate techniques. Various approaches have been considered to directly use PDE models in controller designs. Examples include the control algorithm proposed by Dochain et al. [5], Renou et al. [6] and Christofides and Daoutidis [7]. However, this approach requires the greater knowledge of a distributed system control theory. The alternative early lumping approach, on the other hand, is a straightforward method and widely used in chemical engineering. The idea behind the approach is that a DPS is first converted into an approximate www.elsevier.com/locate/jiec Available online at www.sciencedirect.com Journal of Industrial and Engineering Chemistry 14 (2008) 175–181 * Corresponding author. Tel.: +66 2 218 6878; fax: +66 2 218 6877. E-mail address: Amornchai.A@chula.ac.th (A. Arpornwichanop). 1226-086X/$ – see front matter # 2007 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2007.09.009