State LQ-feedback control for a class of hyperbolic PDE's system: Application to a fixed-bed reactor

A general linear controller design method for a class of hyperbolic partial differential equations (PDE's) systems is presented, which uses infinite-dimensional Hilbert state-space description. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem where one elementary reaction takes place. An optimal controller is designed for the linearized fixed-bed reactor model, it is applied to the nonlinear original model and the resulting closed-loop stability is analyzed.