Optimal control of an advection-dominated catalytic fixed-bed reactor with catalyst deactivation

• Description of catalytic fixed-bed reactor by time-varying PDE model.
• Dynamical properties of the linearized model are analyzed via the concept of evolution systems.
• An optimal LQ-feedback is computed via the solution of a matrix Riccati PDE.
• Numerical simulations are performed to evaluate the closed loop performance of the designed controller.

The paper focuses on the linear-quadratic control problem for a time-varying partial differential equation model of a catalytic fixed-bed reactor. The classical Riccati equation approach, for time-varying infinite-dimensional systems, is extended to cover the two-time scale property of the fixed-bed reactor. Dynamical properties of the linearized model are analyzed using the concept of evolution systems. An optimal LQ-feedback is computed via the solution of a matrix Riccati partial differential equation. Numerical simulations are performed to evaluate the closed loop performance of the designed controller on the fixed-bed reactor. The performance of the proposed controller is compared to performance of an infinite dimensional controller formulated by ignoring the catalyst deactivation. Simulation results show that the performance of the proposed controller is better compared to the controller ignoring the catalyst deactivation when the deactivation time is close to the resident time of the reactor.