Optimal LQ-Control of a PDAE Model of a Catalytic Distillation Process

Abstract

In this contribution a linear quadratic (LQ) control design for a partial differential and algebraic equation (PDAE) system which represents a catalytic distillation process, is presented. The model involves a set of coupled partial differential equations (PDEs), ordinary differential equations (ODEs), and algebraic equations (AEs). The design is based on an infinite-dimensional state-space representation of the system in a Hilbert space and the well-known operator Riccati equation (ORE) method. The underlying PDE-ODE-AE system is converted to one containing coupled PDEs-ODEs, in which the PDE part involves a hyperbolic operator with a space-varying and non-symmetric velocity matrix whose eigenvalues are not necessarily negative through of the domain. Moreover, in the resulting PDE-ODE system, the control variable acts through the ODE part on the boundaries of the PDE section. Using the boundary control transformation method, the PDE-ODE system is represented in an infinite-dimensional state-space with a homogeneous boundary condition. The stabilizability and the detectability properties of the resulting system are explored, which provide guarantees of the existence and uniqueness of the solution to the resulting ORE. The ORE is solved by converting it to a set of equivalent matrix Riccati equations. The designed LQ controller is implemented on the process and its performance is evaluated.