Design of hybrid batch-to-batch and within-batch self-optimizing control structures for batch processes

Abstract

In this paper, we present a novel framework for hybrid batch-to-batch and within-batch self-optimizing control (SOC) of batch processes. In this framework, batch-to-batch and within-batch controlled variables (CVs) are selected respectively corresponding to the point-wise and profile necessary conditions of optimality of batch processes. For the within-batch SOC, the extended combination matrix is introduced, which is structurally constrained to deal with the causality issue, as well as practical ways for within-batch implementations. The setpoint strategy for a within-batch SOC scheme is also discussed. For the batch-to-batch SOC, which has no causality requirement, the structure of the combination matrix is allowed to be full. The overall combination matrix contains two types of self-optimizing CVs, which will be solved simultaneously in a unified framework. In addition, the active-set change problem is handled using a conservative approach. The hybrid SOC problem is finally characterized as a constrained nonlinear programming (NLP) problem, where the overall combination matrix has particular structural constraints. The design approach is applied to two batch examples, where various benefits and properties of the hybrid SOC methodology are illustrated. The importance of using a simple within-batch SOC scheme is also highlighted, in which case the overall combination matrix is sparse.