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381814 Effects of Closed-Loop Dynamics in Dynamic Real-Time Optimization

In the multilayer plant decision-making hierarchy, real-time optimization (RTO) optimizes plant economics in response to low frequency disturbances affecting profit. RTO interacts with the lower level process automation activities in a cascade fashion by providing economically optimal set-points for the underlying regulatory control system - typically MPC as an advanced, multivariable-constrained control strategy. Most industrial applications use a high fidelity, fundamental steady-state process model in the RTO formulation (Marlin and Hrymak, 1997; Darby et al., 2011). However, for systems that undergo relatively frequent transitions, the use of a dynamic model at the RTO level would be more appropriate, hence transforming the steady-state RTO to dynamic RTO (D-RTO) (Tosukhowong et al., 2004; Würth et al., 2011). An alternative to the two-layer architecture is a single-layer economic MPC based on a dynamic fundamental model (Amrit et al., 2013), which in some cases considers a hybrid objective of plant economics and control tracking (Zanin et al., 2002).

D-RTO in the two-layer framework typically uses an open-loop model prediction, which does not recognize the presence of the plant control system. In this study, the effects of the closed-loop behaviour of the MPC control system are considered at the upper level D-RTO calculations. We consider an industrial type, input-constrained MPC controller based on a state-space formulation at the lower level. Both the D-RTO and controller levels are implemented based on a moving horizon approach, with a time-scale separation. We compare the performance of open-loop and closed-loop D-RTO formulations. The open-loop D-RTO formulation optimizes process input moves to minimize operating cost or maximize production profit based on the dynamic process model and operational constraints. In this case, set-points to the lower level MPC controller are essentially the open-loop input/output trajectories. On the other hand, the closed-loop D-RTO problem considers a rigorous inclusion of the MPC closed-loop dynamics in its formulation, thus optimizing the controller set-point trajectories directly. The overall closed-loop D-RTO problem structure is in the form of a multilevel programming problem as it considers a sequence of MPC controller optimization problems over the D-RTO optimization horizon. A simultaneous solution approach is employed in which the convex MPC-QP subproblems are reformulated using their equivalent Karush-Kuhn-Tucker (KKT) optimality conditions, initially derived in Baker and Swartz (2008). This permits the original problem to be transformed to a single-level mathematical program with complementarity constraints (MPCC) that can be handled using an exact penalty formulation or an interior point approach.

The formulations are applied to multi-input, single-output (MISO) and multi-input, multi-output (MIMO) systems for steady-state transition problems with an objective to minimize the transition cost. Re-optimization at the D-RTO level is executed periodically based on a predefined sample time, which is larger than that of MPC. To gauge the benefit of using the closed-loop formulation over the open-loop formulation, a cost performance measure is introduced to compute a cumulative plant profitability during the transient period. Compared to the open-loop formulation, the closed-loop formulation is shown to give better transition economics. It also helps aid feasibility through set-point trajectories that are appropriately backed-off from output constraints, hence minimizing the degree of output constraint violation during control execution. The problem formulations are presented, challenges discussed, and avenues for future work identified.

**References**

Amrit, R., Rawlings, J. B., and Biegler, L. T. (2013). Optimizing process economics online using model predictive control. Computers & Chemical Engineering, 58(0), 334 – 343.

Baker, R. and Swartz, C. L. E. (2008). Interior point solution of multilevel quadratic programming problems in constrained model predictive control applications. Industrial & Engineering Chemistry Research, 47(1), 81–91.

Darby, M. L., Nikolaou, M., Jones, J., and Nicholson, D. (2011). RTO: An overview and assessment of current practice. Journal of Process Control, 21(6), 874 – 884.

Marlin, T. E. and Hrymak, A. N. (1997). Real-time operations optimization of continuous processes. In Kantor, J., Garcia, C., and Carnahan, B. (Eds.), AIChE Symposium Series: Proceedings of the 5th International Conference on Chemical Process Control, Vol. 93, pp. 156 164. AIChE and CACHE.

Tosukhowong, T., Lee, J. M., Lee, J. H., and Lu, J. (2004). An introduction to a dynamic plant-wide optimization strategy for an integrated plant. Computers & Chemical Engineering, 29(1), 199 – 208.

Würth, L., Hannemann, R., and Marquardt, W. (2011). A two-layer architecture for economically optimal process control and operation. Journal of Process Control, 21(3), 311 – 321.

Zanin, A., de Gouva, M. T., and Odloak, D. (2002). Integrating real-time optimization into the model predictive controller of the FCC system. Control Engineering Practice, 10(8), 819 – 831.

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