Reachability analysis and control of crystal size distribution in batch crystallization processes

This paper deals with the control problem of crystallization processes, whose dynamics are governed by hyperbolic partial differential equations. Given a desired crystal size distribution, we study its reachability using the temperature control from the initial condition without seeding. If the desired crystal size distribution is reachable, we are able to construct an admissible control to steer the states to the desired distribution. Moreover, our construction is developed both for the discretized model and for the original model described by partial differential equations. To ensure that the final desired distribution is attained, we design an output feedback control law to correct the errors resulted from uncertain model parameters.