Infinite-dimensional LQ optimal control of a dimethyl ether (DME) catalytic distillation column

Abstract

This contribution addresses the development of a linear quadratic (LQ) regulator in order to control the concentration profiles along a catalytic distillation column, which is modelled by a set of coupled hyperbolic partial differential and algebraic equations (PDAEs). The proposed method is based on an infinite-dimensional state-space representation of the PDAE system which is generated by a transport operator. The presence of the algebraic equations, makes the velocity matrix in the transport operator, spatially varying, non-diagonal, and not necessarily negative through of the domain. The optimal control problem is treated using operator Riccati equation (ORE) approach. The existence and uniqueness of the non-negative solution to the ORE are shown and the ORE is converted into a matrix Riccati differential equation which allows the use of a numerical scheme to solve the control problem. The result is then extended to design an optimal proportional plus integral controller which can reject the effect of load losses. The performance of the designed control policy is assessed through a numerical study.