Analysis and control of particulate processes with input constraints

A general methodology is proposed for the analysis and control of spatially-homogeneous particulate processes with input constraints modeled by population balance equations. A nonlinear model reduction procedure based on the method of weighted residuals is used for the construction of finite-dimensional ordinary differential equation (ODE) systems that accurately reproduce the dominant dynamics of the particulate process. These ODE systems are used to analyze the limitations imposed by input constraints on the ability to modify the dynamics of the particulate process, leading to an explicit characterization of the set of admissible set points that can be achieved in the presence of constraints. This information, together with the derived ODE systems, is then used as the basis for the synthesis of practically-implementable nonlinear bounded output feedback controllers with well-characterized constraint-handling capabilities. The designed controllers enforce exponential stability in the closed-loop system and achieve particle-size distributions with desired characteristics in the presence of active input constraints. Precise closed-loop stability conditions are given and controller implementation issues are addressed. This method is successfully used to regulate a continuous crystallizer with constrained control action at an open-loop, unstable equilibrium point.