Nonlinear control of particulate processes



A general methodology is proposed for the synthesis of practically-implementable nonlinear output feedback controllers for spatially-homogeneous particulate processes modeled by population balance equations. Initially, a nonlinear model reduction procedure based on a combination of the method of weighted residuals and the concept of approximate inertial manifold is presented for the construction of low-order ordinary differential equation (ODE) systems that accurately reproduce the dominant dynamics of the particulate process. These ODE systems are then used for the synthesis of nonlinear low-order output feedback controllers that enforce exponential stability in the closed-loop system and achieve particle-size distributions with desired characteristics. Precise closed-loop stability conditions are given and controller implementation issues are discussed. The proposed nonlinear control method is successfully applied to a continuous crystallizer, and is shown to outperform a proportional-integral controller and cope effectively with model uncertainty and measurement delays.