Two concurrent β-variable adaptive model-free controls of a seeded batch crystallizer

Abstract

The design of an efficient controller for a process of batch crystallization is still an important area of ongoing research. In this paper, a [Formula: see text]-variable adaptive model-free control ([Formula: see text]-AMFC) has been proposed to control a seeded batch adipic acid crystallization process to get a final unimodal crystal size distribution (CSD) within the required mean weight size. The [Formula: see text]-AMFC is developed based on [Formula: see text] online adaptive estimation algorithm to enhance the classic model-free control’s (MFC) performance. It copes with unknown as well as partially known dynamics and the inherent complex behavior of this nonlinear process. The concept consists of using an updated local approximation model. Two structures of [Formula: see text]-AMFC are considered. The first is a [Formula: see text]-AMFC based on intelligent Proportional-Integral ([Formula: see text]-iPI) control and the second is based on intelligent Proportional-Integral control combined with Sliding Mode Control ([Formula: see text]-iPISMC). To obtain the controller parameters of the two [Formula: see text]-AMFC structures, the particle swarm optimization (PSO) method was employed. The comparison of alternative approaches is performed by means of simulations including different scenarios. It is found that the [Formula: see text]-iPISMC has a superior performance: it allows the output convergence 50 minutes earlier than the [Formula: see text]-iPI and it is more robust against any sudden disturbances.