Observer-based MPC Design of an Axial Dispersion Tubular Reactor: Addressing Recycle Delays through Transport PDEs

The model predictive control of an axial dispersion tubular reactor equipped with a recycle stream is presented. The intrinsic time delay imposed by the recycle stream, an often overlooked aspect in chemical engineering process control studies, is modeled as a transport PDE, leading to a boundary-controlled system of coupled parabolic and hyperbolic PDEs under Danckwerts boundary conditions, suitable for this reactor type. Considering the digital nature of modern controllers, a discrete-time linear model predictive controller is designed to stabilize the system, coupled with a Luenberger state estimator to address the controller’s limited access to the system’s full state. The need for model reduction through spatial approximation is eliminated by following a late lumping approach, while utilizing Cayley-Tustin time discretization method to preserve the continuous-time system’s characteristics. The controller’s effectiveness is demonstrated through numerical simulations, showcasing its capability to stabilize an unstable system while adhering to input constraints, having access merely to output measurements.