Model predictive control of a granulation system using soft output constraints and prioritized control objectives

A granulation system presented by Pottman et al. [J. Powder Technol., 108 (2) (2000) 192] is used to demonstrate two Model Predictive Control (MPC) control methods. The first method penalizes process output constraint violations using soft constraints in the objective function. It is found that the soft constraints must be much tighter than the actual constraints for effective control of the granulation system. The soft constraint formulation is presented as a variation of the asymmetric objective function formulation described by Parker et al. [Proc. American Control Conf. Chicago, IL (2000)]. The second control method is based on the prioritized objective formulation originally proposed by Tyler and Morari [Automatica 35 (1999) 565]. The prioritized objective method uses optimization constraints involving binary variables to explicitly represent and prioritize control objectives. The formulation presented in this article demonstrates a multi-level objective function which first maximizes the number of objectives satisfied in order of priority, then maximizes the number of total objectives, and finally minimizes the traditional MPC error tracking and move suppression terms. This prioritized objective formulation also allows for delayed implementation of output objective constraints, allowing for relaxation of control objectives.