460885 Integration of Scheduling and Control Under Process Uncertainties
An effective framework for the scheduling and control problem involves two control loops, where the inner loop is a nominal model predictive control and the outer loop is an integrated schedule and control problem, which generates both the production scheduling and the state reference for control problem, and it is solved every time the system suffers a disturbance that cannot be handle by the inner control (Zhuge and Ierapetritou 2015). However, this is a reactive approach, which can become computationally expensive if the uncertainties occur frequently.
In this work, a preventive strategy for the integration of scheduling and control problems under uncertainty in process operations is proposed. First, the design of robustly stabilizing model predictive control (RMPC) of nonlinear systems is presented. Process uncertainties are treated as variables and the original process dynamics is approximated using a piece-wise affine model (PWA). The uncertain parameters are confined by upper and lower bounds, and the model is formulated aiming to optimize the worst case performance. For uncertainty descriptions that are linearly related to the state variables, the minmax optimization can be recasted as a quadratic program. Second, the PWA approximation is integrated with the scheduling level and an integrated problem is formed. Solving the integrated problem results in the scheduling and state references to be used by the robust MPC. Several case studies are presented to illustrate the proposed approach and provide comparisons with the deterministic case.
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