(697e) Simultaneous Scheduling and Control Using Fast MPC

In chemical process operations simultaneous consideration of scheduling and control helps to enhance the overall process profitability but meanwhile increases the complexity of modeling and thus the computational efficiency of the solution approaches (Terrazas-Moreno, et al., 2008) (Engell and Harjunkoski, 2012). Online integration of scheduling and control requires updating operation solutions for both scheduling and control levels at real time in the presence of disturbance, thus the online integration requires a repetitive solution of the integrated problem at each time interval (Zhuge and Ierapetritou, 2012).

Model Predictive Control (MPC) is an online optimization technique that involves repetitively solving optimization problems over a future time horizon. To reduce the computation burden of conventional MPC, multi-parametric Model Predictive Control (mp-MPC) was proposed to solve for the explicit control law offline and thus the online optimization is reduced to simple function evaluations (Pistikopoulos, 2009). However, as the problem size increases in terms of state dimension and prediction horizon, the number of polyhedral regions in the state partition increases exponentially and this limits the applicability of mp-MPC to small and medium-sized control problems (Richter, et al., 2012).

Fast MPC on the other hand is capable in handling large scale problems, and therefore can be used to facilitate the efficient integration of scheduling and control of large-scale processes. Fast MPC transforms the MPC problem into a convex quadratic programming for which efficient nonlinear programming methods and computational tools can be used to speed up the computation by exploring the problem structure. Among the existing work in the literatures three solution approaches can be identified: active set method (Ferreau, et al., 2008), interior point method (Rao, et al., 1998) (Wang and Boyd, 2010) and Fast gradient method (Richter, et al., 2009) (Richter, Jones and Morari, 2012).

In this study we propose a cascade control strategy that involves two control loops for the online integration of scheduling and control. In the outer loop we approximate the original process dynamics using a piece-wise affine (PWA) model and incorporate it with the scheduling level. This leads to an integrated problem that is subject to linear constraints. The primary MPC at the outer loop solves the integrated problem and  generates both the production scheduling and the control solution. However, only the scheduling solution is transferred to the inner loop where the secondary MPC (a fast MPC) treats the scheduling solution as parameters and computes the exact control solution online. Note that these two loops correspond to different models. The outer loop uses the integrated model while the inner loop uses the process dynamic model. Following this approach the primary MPC is able to achieve an overall optimalility for both scheduling and control levels efficiently and the secondary MPC is able to respond quickly to the local disturbance. Results of case studies show the feasibility and efficiency of the proposed approach.

References:

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(2) Engell, S.; Harjunkoski, I. Optimal operation: Scheduling, advanced control and their integration. Computers & Chemical Engineering 2012,47, 121-133.

(3) Zhuge, J.; Ierapetritou, M. G. Integration of Scheduling and Control with Closed Loop Implementation. Industrial & Engineering Chemistry Research 2012,51, (25), 8550-8565.

(4) Pistikopoulos, E. N. Perspectives in multiparametric programming and explicit model predictive control. AIChE Journal 2009,55, (8), 1918-1925.

(5) Richter, S.; Jones, C. N.; Morari, M. Computational Complexity Certification for Real-Time MPC With Input Constraints Based on the Fast Gradient Method. Automatic Control, IEEE Transactions on 2012,57, (6), 1391-1403.

(6) Ferreau, H. J.; Bock, H. G.; Diehl, M. An online active set strategy to overcome the limitations of explicit MPC. International Journal of Robust and Nonlinear Control 2008,18, (8), 816-830.

(7) Rao, C. V.; Wright, S. J.; Rawlings, J. B. Application of Interior-Point Methods to Model Predictive Control. Journal of Optimization Theory and Applications 1998,99, (3), 723-757.

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(9) Richter, S.; Jones, C. N.; Morari, M. Real-time input-constrained MPC using fast gradient methods. Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference., 2009, pp 7387-7393.