(696c) On-Line Integration of Scheduling and Control Using Mp-MPC

Simultaneous scheduling and control generates an integrated optimization problem that addresses the optimal operations at both scheduling and control level. Compared to individual modeling of scheduling or control stages, the simultaneous approach is preferable because an integrated decision making realizes information sharing between levels and thus promotes the improvement of the overall process performance. Using the simultaneous approach a Mixed Integer Dynamic Optimization (MIDO) problem is formed and then is discretized into Mixed Integer Nonlinear Programming (MINLP) through collocation point method(Flores-Tlacuahuac and Grossmann, 2006). Solving the resulting MINLP generates the optimal production time, product sequence and transition profiles between different products. In our previous work we developed a closed loop implementation strategy in order to be able to deal with realistic cases where disturbances are present (Zhuge and Ierapetritou, 2012). However, this approach requires a repetitive solution of the integrated problem at each time interval. Moreover the large problem size of the resulting MINLP and thus large computation requirements, limit the scale of problems it can be considered in online applications.

Model Predictive Control (MPC) is an online optimization technique based on a receding horizon mode. At each sample point the current state and output are measured and a constrained optimization problem is solved over a future time horizon to generate the optimal future control strategy. After the first control strategy is implemented to the process, the procedure is repeated in the following time point with the horizon moving forward. Multi-Parametric Model Predictive Control (mp-MPC) generates the control law as a set of explicit functions of state variables, via multi-parametric programming (Bemporad, et al., 2000) (Pistikopoulos, 2009). The explicit control law can then be obtained offline and the online optimization is reduced to simple function evaluations. Therefore mp-MPC results in faster application of MPC in larger scale problems. However, in this area most of the previous study addresses application at control level, bringing the possibility of integrating it with other levels in plant operations.

In this study we propose to use mp-MPC in the integration of scheduling and control, since it is capable in generating the control solution fast in the presence of disturbance by evaluating the function of pre-determined explicit solution. In order to enable this implementation we first linearize the non-linear dynamics around the steady state points and obtain the piece wise approximation (PWA) model. Then we apply Multi-Parametric Toolbox (MPT) (Kvasnica, et al., 2004) and obtain the control solution, transition duration and transition cost as functions of state variables. We can then incorporate these explicit functions into the constraints of scheduling and obtain the integrated problem. Since the integrated problem is a Mixed Integer Linear Programming (MILP) model, we can solve the problem on-line. When disturbance occurs, the values of the required variables including state and the partial transition that is fulfilled are recorded and the updated solution for the integrated problem is produced. Results of a number of different case studies demonstrate the feasibility and efficiency of the proposed approach.

References:

(1) Flores-Tlacuahuac, A.; Grossmann, I. E. Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR. Industrial & Engineering Chemistry Research 2006, 45, (20), 6698-6712.

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

(3) Bemporad, A.; Bozinis, N. A.; Dua, V.; Morari, M.; Pistikopoulos, E. N.; Sauro, P., Model predictive control: A multi-parametric programming approach. In Computer Aided Chemical Engineering, Elsevier: 2000; Vol. Volume 8, pp 301-306.

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

(5) Kvasnica, M.; Grieder, P.; Baoti, M. Multi-Parametric Toolbox (MPT). http://control.ee.ethz.ch/~mpt/ 2004.