Nonlinear control of particulate processes

Abstract

Abstract 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.