Stochastic Nonlinear Observers for Industrial Seeded Batch Crystallization Processes

A substantial amount of materials in the pharmaceutical, food, and fine chemical industry is produced in crystalline form. Batch crystallization is a key separation and purification unit in such industries, with a significant impact on the efficiency and profitability of the overall process. Advanced model-based control of crystallization processes offers many possibilities to achieve the stringent requirements of the final product quality, such as crystal size, purity and morphology, and also enhance the process efficiency. The control of batch crystallization processes is traditionally done by tracking predetermined batch recipes using PID controllers. As the recipes are largely based on operator's experience, they often lack the ability to systematically push the process to its most optimal operating trajectory while various operational and quality limitations are met. In the recent years, the development of computationally powerful modeling and optimization tools has considerably facilitated the use of first principle models in devising optimal batch recipes. Application of the off-line optimization approach is however insufficient as plant-model mismatch, process disturbances and uncertain initial conditions often deteriorate the effectiveness of the off-line optimized operating policies. A remedy for the latter deficiency is real-time optimal control of the batch process in a receding horizon framework [1][2]. The closed-loop optimal control approach continuously optimizes the system in the presence of plant-model mismatch and unmeasured disturbances and, therefore, drives the process to its most optimal operation at any time during the batch. The effectiveness of this model-based control strategy is due to the feedback of measurements that are used by an observer to estimate the system states. The observer essentially facilitates implementation of the receding horizon framework that makes the control strategy less sensitive to process disturbances and variations. Furthermore, the observer enables the estimation, i.e. soft sensing, of process variables, for which actual measurements may not be available due to various technological and economical limitations. Observers enable estimation of the state variables based on a process model, as well as in-situ measurements. The design of observers for batch crystallization processes is a challenging task due to a variety of reasons. These processes are distributed systems typically represented by a set of differential algebraic equations; derived from the population balance equation using discretization schemes. The complexity of the process model arisen from the large number of differential equations, which are often highly nonlinear due to the complex kinetic expressions, necessitates efficient observation techniques to render real-time implementation of …