Linear Model Predictive Control for a Coupled CSTR and Axial Dispersion Tubular Reactor with Recycle

Abstract

This manuscript addresses a novel output model predictive controller design for a representative model of continuous stirred-tank reactor (CSTR) and axial dispersion reactor with recycle. The underlying model takes the form of ODE-PDE in series and it is operated at an unstable point. The model predictive controller (MPC) design is explored to achieve optimal closed-loop system stabilization and to account for naturally present input and state constraints. The discrete representation of the system is obtained by application of the structure properties (stability, controllability and observability) preserving Cayley-Tustin discretization to the coupled system. The design of a discrete Luenberger observer is also considered to accomplish the output feedback MPC realization. Finally, the simulations demonstrate the performance of the controller, indicating proper stabilization and constraints satisfaction in the closed loop.

BIBO stability for funnel control: semilinear internal dynamics with unbounded input and output operators

“…x I (1, t) x F (t) Fig. 2: Coupled CSTR-tubular reactor system Consider the system depicted in Figure 2 comprised of a continuous stirred-tank reactor (CSTR) and a tubular reactor with axial dispersion (TRAD) that is similar to the one discussed in [15], dropping the terms describing disturbances for simplicity. Furthermore, in order for the system being able to serve as an example for the type of systems discussed in this contribution, two changes have been made.…”

“…Second, the Dirichlet boundary control has been supplanted with a Neumann boundary control ensuring that the original linear distributed system will be BIBO stable. Using the same notation as [15] this input-output system is then described by the coupled PDE-ODE system…”

A thermodynamic approach to the stabilization of tubular reactors

“…We do not prove existence of solution nor pre-compactness of trajectories. At first we look for the expression of the jacket heat flow q(t, x) to shape the derivative of the availability function (24) such that it fulfils the Lyapunov stability conditions for the closed loop system. With the use of the constitutive expression of the heat flow q(t, x) we deduce the expression of the jacket temperature T j (t, x).…”

“…From this set of possible equilibria, the unstable steady state is usually of industrial interest as it corresponds to a high reaction efficiency with admissible temperature. Thus, many studies have been dedicated to the control of tubular reactors described by partial differential equations models around the unstable steady state profile [1,6,8,13,12,22,24,28,32].…”