DISTRIBUTED PARAMETER PREDICTIVE CONTROL OF BLEACHING TOWERS

摘要

In bleaching towers the process variables, such as lignin and chemical concentrations, vary spatially within the reactor. Processes in which the variables of interest vary spatially are termed distributed parameter systems (DPS) and represent a substantial challenge for developing high performance control systems. This control challenge in DPS stems from the requirement that process dynamics must be represented in terms of partial differential equations (PDE) and/or integral equations; whereas, almost all of control theory assumes that the process dynamics can be represented by ordinary differential equations (ODE). In this paper, we present the key ideas in the development of a distributed parameter approach to model predictive control (MPC) of chemical bleaching towers. The proposed control approach is based on the method of characteristics and uses finite difference approximations of the second-order (diffusion) terms in bleaching tower models. This approach allows the underlying PDE model to be converted to a set of ODEs, which are amenable to the rich array of advanced control techniques currently available. The efficacy of the proposed method is illustrated using a chlorine dioxide bleaching case study. It should be noted that although the method is illustrated with a ClO_2 simulation study, our technique applies to any convection-diffusion-reaction system at high Peclet numbers. The performance of our approach is compared to a more standard, finite-difference MPC approach with respect to control accuracy, robustness to plant-model mismatch and computational expense.