Inventory control of particulate processes

In this work we address the problem of designing model-based controllers for particulate processes described by population balance (PB) models. We focus on PB models that are solved by numerical discretization, for which many standard control methodologies are not suitable due to the high order of these models. We interpret discretized PB models as chemical reaction networks and suggest to combine inventory control with techniques of stability of chemical reaction networks to design the controller. Inventory control is based on the idea of manipulating process flows so that certain extensive variables defining the system, called inventories, follow their setpoints. The whole system is stabilized by controlling the dominant inventories. The discretized PB is exploited in all aspects of controller design, from determining the controlled inventories to the final implementation of the control law. The methodology is illustrated with an industrial leaching reactor, the Silgrain®process. We show that the discretized PB model takes the form of a Feinberg–Horn–Jackson zero-deficiency network, allowing us to prove stabilization of the whole system. The performance of standard inventory control and robust inventory control are investigated by simulation, with satisfactory results even in the presence of modeling errors.