(158b) Integration of Scheduling and Control Under Process Uncertainties

Scheduling and control problems are closely related and, when addressed simultaneously, can lead to an improved objective function and avoid suboptimal solutions (Flores-Tlacuahuac and Grossmann 2006). Meanwhile, the integration of this problems often results in MIDO problems, and the discretized MINLP requires excessive computation effort to get solved (Flores-Tlacuahuac and Biegler 2005). Furthermore, dynamical models of the systems used in the integration problems are usually considered to adequately describe the system behavior, and it is known that this assumption is not valid for physical system (Campo and Morari 1987), which are subject to uncertainties in process operations and models.

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.

Campo, P. J. and M. Morari (1987). "Robust Model Predictive Control." Proc. American Contr. Conf.. 2: 6.Flores-Tlacuahuac, A. and L. Biegler (2005). "A robust and efficient mixed integer non-linear dynamic optimization approach for simultaneous design and control." Computer Aided Chemical Engineering 20: 5.Flores-Tlacuahuac, A. and I. E. Grossmann (2006). "Simultaneous cyclic scheduling and control of a multiproduct CSTR." Industrial Engineerign Chemistry Research 45(20): 15.Zhuge, J. and M. G. Ierapetritou (2015). "An Integrated Framework for Scheduling and Control Using Fast Model Predictive Control." Aiche Journal 61(10): 16.