Reduced-order methodologies for feedback control of particle size distribution in semi-batch emulsion copolymerization

Within-batch feedback control strategies are developed for the regulation of the particle size distribution (PSD) in a semibatch vinyl acetate (VAc)/butyl acrylate (BuA) emulsion copolymerization system. These strategies are also applicable for regulation of distributions in other particulate systems governed by population balances. In the first strategy, PID controllers are employed for regulating nucleation and growth events through tracking the nominal trajectories of total number of particles and the solids content by manipulating the feed-rates of the more reactive monomer, BuA, and the surfactant. The second control strategy is based on tracking nominal trajectories of the moments of the distribution with a quadratic dynamic matrix controller (QDMC). To determine the appropriate number of moments to describe the PSD during various stages of a nominal batch, a maximum-entropy approach is utilized. In the final and most complex approach, a nonlinear model predictive controller is designed utilizing the detailed population balance model of the system. The ill-conditioning resulting from the high-dimensionality of the resulting dynamical system is removed by principal component analysis (PCA)-based model order reduction and a multi-rate estimator is designed to compensate for the measurement delay associated with the PSD measurements.