Anti-Windup Design for a Reaction-Diffusion Equation

This letter focuses on the anti-windup design for saturated 1-D linear reaction-diffusion equation which admits a finite number of unstable poles. We consider a scenario in which the system is controlled via a dynamic, finite-dimensional output feedback controller ensuring closed-loop exponential stability. A method is proposed to design a dynamic anti-windup compensator to maximize the region of attraction and minimize the effect of external perturbations. More precisely, the sufficient conditions for the local exponential stability of the closed-loop system are derived and expressed in terms of a set of matrix inequalities. Using generalized sector conditions and proper change of variables, the conditions are then recast as an optimization problem solving linear matrix inequalities. A numerical example is provided to showcase the proposed method and highlight its effectiveness.