Journal of Process Control 24 (2014) 1671–1690 Contents lists available at ScienceDirect Journal of Process Control j ourna l ho me pa ge: www.elsevier.com/locate/jprocont Model predictive control of axial dispersion chemical reactor Liu Liu, Biao Huang, Stevan Dubljevic ∗ Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2V4 a r t i c l e i n f o Article history: Received 29 January 2014 Received in revised form 22 July 2014 Accepted 25 August 2014 Available online 26 September 2014 Keywords: Distributed-parameter systems Axial dispersion chemical reactor Model predictive control Input/state constraints a b s t r a c t This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describ- ing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dom- inant dynamics of the PDEs system is derived for controller design through Galerkin’s method and modal decomposition technique. Tustin’s discretization and Cayley transform are used to obtain infinite- dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is con- structed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints. © 2014 Elsevier Ltd. All rights reserved. 1. Introduction Transport-reaction process is a typical example of a distributed-parameter system as it usually possesses the characteristic of con- siderable spatial variations caused by the potential presence of convection and diffusion phenomena. First-principle modeling of the transport-reaction process within finite spatial domain usually leads to the system of parabolic PDEs. The major characteristic of parabolic PDEs systems is that their spatial differential operators are featured by a spectrum that can be partitioned into a slow part which includes a finite number of eigenvalues that are close to the imaginary axis and a fast complement which consists of an infinite set of eigenvalues that are located far-left in the complex plane [1]. The traditional approach for control of parabolic PDEs systems utilizes spatial discretization techniques to obtain systems of ordinary differential equations (ODEs), which are subsequently utilized as the foundation of the finite- dimensional controllers design; see [2,3]. This approach has a significant drawback that the number of states which must be preserved to obtain a system of ODEs in order to yield the required order of approximation, might be quite large, which leads to a high dimensional controller realization and complex controller design. In the past, considerable work has concentrated on the construction of a general framework of reduced-order control synthesis for parabolic PDEs systems and other PDEs systems arising from the modeling of distributed-parameter systems on the basis of low-order ODEs models which are derived by the combination of the concept of inertial manifolds [4] and spectral method. A number of researchers have explored many problems related to control of a system described by PDE, such as dynamic optimization, output feedback controller design, nonlinear and robust control of the PDE system [5–7]. Besides the above results which are concerned with the order reduction, stabilization, and tracking problem of a parabolic PDE system, notable research has been carried out on the development of methodologies on optimal control for the distributed-parameter systems [8,1]. Apart from the issue of optimal controller design for distributed-parameter systems with fixed sensors or actuators [9], significant research has been devoted to the optimal location of sensors and actuators [10] and how to switch among actuators under an optimal control policy [11,12]. Furthermore, control practitioners will often face the scenarios in which actuators and sensors have their limits due to physical properties or practical characteristics associated with actuators/sensors implementation, or the system state is required not to be in excess of specified limit values (for example, requiring the concentration of a certain product to be maintained above some desired purity condition). Motivated by this consideration, the issue of development ∗ Corresponding author. Tel.: +1 780 248 1596; fax: +1 780 492 2881. E-mail address: Stevan.Dubljevic@ualberta.ca (S. Dubljevic). http://dx.doi.org/10.1016/j.jprocont.2014.08.010 0959-1524/© 2014 Elsevier Ltd. All rights reserved.