Model predictive control of MSMPR crystallizers

Abstract

A multi-input–multi-output (MIMO) control problem of isothermal continuous crystallizers is addressed in order to create an adequate model-based control system. The moment equation model of mixed suspension, mixed product removal (MSMPR) crystallizers that forms a dynamical system is used, the state of which is represented by the vector of six variables: the first four leading moments of the crystal size, solute concentration and solvent concentration. Hence, the time evolution of the system occurs in a bounded region of the six-dimensional phase space. The controlled variables are the mean size of the grain; the crystal size-distribution and the manipulated variables are the input concentration of the solute and the flow rate. The controllability and observability as well as the coupling between the inputs and the outputs was analyzed by simulation using the linearized model. It is shown that the crystallizer is a nonlinear MIMO system with strong coupling between the state variables. Considering the possibilities of the model reduction, a third-order model was found quite adequate for the model estimation in model predictive control (MPC). The mean crystal size and the variance of the size distribution can be nearly separately controlled by the residence time and the inlet solute concentration, respectively. By seeding, the controllability of the crystallizer increases significantly, and the overshoots and the oscillations become smaller. The results of the controlling study have shown that the linear MPC is an adaptable and feasible controller of continuous crystallizers.