Optimal Operation of Industrial Batch Crystallizers: A Nonlinear Model-based Control Approach

Batch crystallization is extensively employed in the chemical, pharmaceutical, and food industries to separate and purify high value-added chemical substances. Despite their widespread application, optimal operation of batch crystallizers is particularly challenging. The difficulties primarily result from the complexity of process models, uncertainties in crystallization kinetics, sensor limitations for reliable measurement of process variables, and the inherent process uncertainties that may impair the effectiveness of advanced control strategies. In addition, the optimal operation of batch crystallizers is often hampered by lack of process actuators. Nonetheless, advanced control of batch crystallizers offers ample opportunities to effectively respond to the dynamic market demands of crystalline products. This is to realize the stringent product specifications of the consumer-driven market as enhancing the process productivity. In this thesis, a nonlinear model-based control approach is developed to address the inherent challenges of real-time control of existing industrial batch crystallizers. The primary requirement on the control approach is its applicability to a wide range of industrial batch crystallizers. This calls for a generic modeling framework, which allows us to describe the dynamics of diverse crystallization kinetics of any complexity and to incorporate the effect of different actuating mechanisms. The generic framework of the process model necessitates the use of computationally efficient model solution techniques and optimization strategies to ensure the real-time feasibility of the control approach. In addition, model imperfections, along with process disturbances, make the online adaptation of model predictions a prerequisite for successful application of the control approach. In pursuit of the research objective, the contributions of this thesis are structured in three major directions: 1. Population balance modeling: A full population balance modeling framework is developed as the cornerstone of the control approach. The inference of model parameters from experimental data is discussed. In addition, various population balance solution methods are investigated in terms of the performance requirements essential for online control applications. 2. Nonlinear state estimation: The effectiveness of several nonlinear state estimation techniques for output feedback control of industrial batch crystallizers is evaluated. The ability of the state estimators in coping with model imperfections and process uncertainties is examined. 3. Real-time dynamic optimization: The feasibility of real-time dynamic optimization of population balance models is explored using different direct optimization strategies. The research program leads to the design of an output feedback nonlinear model-based control approach. The distinct contribution of this thesis lies in using a full population balance modeling framework, which is essential for the applicability of the control approach to a wide range of industrial batch crystallizers. It is shown that the numerical difficulties of solving the population balance equation can be alleviated by using high order finite volume methods combined with a flux limiting function. These numerical techniques facilitate efficient model solution, which is a prerequisite for real-time control. In addition, it is shown that the multiple shooting strategy is well-suited for online dynamic optimization of population balance models. Successful application of the control approach is demonstrated by several simulation case studies, viz a single-input single-output semi-industrial crystallizer and a multi-input multi-output industrial crystallizer. It is illustrated that model imperfections and process uncertainties are largely detrimental to the performance of the nonlinear model-based controller. The performance inadequacy can be effectively compensated for by using an extended Kalman filter or an unscented Kalman filter with time-varying process noise covariance matrix. The real-time performance of the control approach is demonstrated experimentally by several implementations on a semi-industrial crystallizer. It is shown that lack of actuation may obstruct the optimal operation of industrial crystallizers throughout the entire batch run.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin