Nonlinear model-based control of particulate processes

Particulate processes are characterized by the co-presence of a continuous phase and a dispersed (particulate) phase, and are widely used in industry for the manufacturing of many high-value products. Examples include the crystallization of proteins for pharmaceutical applications, the emulsion polymerization reactors for the production of latex and the titania powder aerosol reactors used in the production of white pigments. It is now well understood that the physico-chemical and mechanical properties of materials made with particulates depend heavily on the characteristics of the corresponding particle size distribution (PSD).; Population balances have provided a natural framework for mathematical modeling of PSDs and typically lead to systems of nonlinear partial integro-differential equations that describe the rate of change of the PSD. The complex nature of population balance models has motivated extensive research efforts on the development of efficient numerical methods for the computation of their solutions. However, research on population balance model-based control of particulate processes has been very limited. The need to control the shape of PSDs in industrial applications, together with recent advancements in technology for real-time PSD measurements, motivates the synthesis and implementation of high performance model-based feedback control systems on particulate processes.; This thesis presents a general and practical framework for the synthesis of nonlinear practically-implementable feedback controllers for particulate processes using population balances. A model reduction procedure based on combination of the method of weighted residuals and the concept of approximate inertial manifold is proposed for the construction of low-order ODE systems that accurately reproduce the dominant dynamics of the particulate process. These ODE systems are subsequently used for the synthesis of nonlinear low-order output feedback controllers that enforce exponential stability in the closed-loop system and achieve a particle size distribution with desired characteristics. The important practical issues of robust controller design using uncertain population balances and nonlinear controller design in the presence of control actuator constraints are also studied. The proposed control algorithms are successfully applied to continuous and batch crystallization systems and are shown to outperform conventional control schemes.