(745a) Dynamic Real Time Optimization Under Uncertainty with Embedded Closed-Loop Prediction

Large chemical plants commonly utilize a hierarchical automation configuration, where longer term decisions are made at the higher level and short-term decisions at the lower levels. These control hierarchies typically include PID control at the lowest level, followed by Model Predictive Control (MPC), and thereafter some form of Real Time Optimization (RTO). RTO systems are traditionally based on steady-state models, and thus require the plant to be approximately at steady state before each RTO execution (Marlin, 1997). Modern-day operating environments are highly dynamic in nature, for which steady-state RTO paradigms become suboptimal. This has led to the development of dynamic RTO (DRTO) and economic MPC paradigms, where plant dynamics are considered in the determination of economic operating conditions (Ellis et al., 2014; Jamaludin and Swartz, 2017). In this paper, we focus on the two-layer DRTO-MPC architecture due to the industrial prevalence of the hierarchical decision-making paradigm.

Tosukhowong et. al. (2004) propose a DRTO strategy with reduced order linear dynamics employed in a hierarchical control architecture with MPC being used for shorter period target tracking. Similarly, Kadam et. al. (2002) employ a two-level control architecture, but with the DRTO layer being triggered by a disturbance analysis, rather than being performed at regular intervals. Wurth et. al. (2011) add a neighbouring-extremal strategy to the MPC layer to provide faster updates to the optimal reference trajectory. Jamaludin and Swartz (2017) propose the use of closed-loop dynamics at the DRTO level, where the DRTO decisions are based on the predicted dynamics of the plant under the action of constrained MPC. The resulting multilevel optimization problem is transformed into a single-level problem by replacing the inner MPC optimization subproblems by algebraic constraints corresponding to their first-order optimality conditions. The strategy is applied in Li and Swartz (2018) to the dynamic coordination of distributed MPC systems. The present work extends the DRTO approach with closed-loop prediction to a robust formulation for explicit handling of uncertain dynamic systems.

Our robust DRTO method follows a multi-scenario approach. Within the robust MPC literature, there is a growing body of work on multistage multi-scenario approaches, in which future control inputs are treated as recourse decisions, hence capturing the effects of future feedback action. Lucia et al. (2013) present such a scheme in which the evolution of uncertainty in time is represented as a scenario tree. Decomposition approaches are proposed for reducing the computation time due to exponential growth of the number of scenarios with increasing number of stages and parameters. Lucia et. al. (2014) extend the multi-scenario approach to economic MPC, and apply it to a batch polymerization system. Mastragostino et al. (2014) develop a scenario-based two-stage stochastic formulation for robust MPC of supply chain systems that include discrete decisions arising from production scheduling.

In this work, a multi-scenario stochastic approach is applied within the DRTO formulation of Jamaludin and Swartz (2017) to account for plant uncertainty. Uncertain parameter realizations result in a set of DTRO plant models that are utilized in the generation of predicted closed-loop scenarios under the action of constrained MPC. An expected economic objective is optimized over the DRTO prediction horizon, subject to constraints on the closed-loop trajectories. The DRTO problem formulation and solution strategy will be presented, and the performance of the method evaluated through application to case studies. Remaining challenges will be discussed, and future research avenues identified.

References

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