Optimal control and duality-based observer design for a hyperbolic PDEs system with application to fixed-bed reactor

Abstract

This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combined with a linear-quadratic state feedback controller for a system of hyperbolic PDEs. The design is based on the duality fact between the control design and the observer design. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to a fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the temperature and the reactant concentration in a fixed-bed reactor is investigated by using the developed algorithm, which lead to express the jacket temperature (manipulated variable) as a feedback of the estimated temperature and concentration in the reactor.