(42g) Dynamic Real-Time Optimization of Distributed MPC Systems

Real-time optimization (RTO) is a supervisory control algorithm that provides set-points to an underlying regulatory control system based on optimizing the plant economics. Industrial RTO systems typically utilize a steady-state model of the process, and are executed every few hours in order to track the economic optimum, as parameters affecting the plant conditions and process economics change (Marlin and Hrymak, 1997; Darby et al., 2011). The limited execution frequency of steady-state RTO systems poses a drawback for applications to processes that exhibit frequent transitions or slowly varying dynamics, which has prompted the development of dynamic RTO strategies. Two key control architectures for addressing plant economics within a dynamic setting are (i) a hierarchical structure, similar to way that current industrial RTO systems are implemented, but with a dynamic model used instead of a steady-state model, and (ii) a single-level control structure in which the economic objective is incorporated within the MPC controller formulation (Engell, 2007; Rawlings and Amrit, 2009; Ellis et al., 2014). The present work follows the former approach due to its compatibility with existing industrial control systems, and builds on recent advances that have considered DRTO in conjunction with a single MPC system.

Previously proposed DRTO strategies that follow a two-layer architecture typically perform economic optimization in an open-loop fashion without taking into account the presence of the plant control system. In this open-loop DRTO approach, the set-points prescribed to the underlying control system are based on the optimal open-loop trajectories under an expectation that the closed-loop response dynamics at the plant level will follow the economically optimal trajectories obtained at the DRTO level. In Tosukhowong et al. (2004), the DRTO framework is designed based on a linear(ized) process model, while Würth et al. (2011) utilize a nonlinear dynamic model. In an earlier study, we proposed the use of a dynamic model at the DRTO level that predicts the effects of the underlying MPC system on the plant dynamics (Jamaludin and Swartz, 2014). Neglecting the effect of the control system in the DRTO optimization tacitly assumes perfect control, which is not achievable in practice and leads to suboptimal economic performance. However, this new formulation results in a more complex problem, since each MPC control calculation over the future prediction horizon is itself defined by an optimization problem. This is handled by replacing the MPC optimization subproblems by their equivalent first-order optimality conditions, and including the resulting algebraic equations as equality constraints in the DRTO economic optimization problem. In Jamaludin and Swartz (2015), the closed-loop prediction problem was approximated as a bi-level rather than a multi-level problem, resulting in significantly reduced computation times with modest loss in economic performance.

An overall optimal process operation can be achieved via utilization of a centralized model predictive control (MPC) system in which all control inputs are computed simultaneously from a single optimization problem. However, large scale systems, such as refineries, manufacturing plants and power generation networks, typically have a collection of MPC controllers, with each controlling a subset of process units (Qin and Badgwell, 2003). Key considerations in the selection of distributed MPC systems are process scale and complexity, computational tractability, and geographic footprint. Distributed MPC architectures are designed to meet performance specifications that are relatively equivalent to the centralized MPC system, but retaining the modularity, reliability and maintainability of each controller (Pannochia, 2014). A variety of approaches to coordination of distributed MPC systems has been proposed in the literature. Camponogara et al. (2002) and Stewart et al. (2010) present cooperative control strategies in which the MPC modules compute control actions taking into account the actions of the other MPC controllers. Cheng et al. (2008) apply Dantzig-Wolfe decomposition to the calculation of steady-state targets for the MPC controllers based on a linear objective function. In Chen et al. (2012), steady-state optimization is performed, with distributed Lyapunov-based MPC controllers executed sequentially to drive the system to the steady-state optimum.

In this study, the closed-loop DRTO formulation is extended to economic coordination of a distributed MPC system. The DRTO formulation determines optimal set-point trajectories for all MPC controllers simultaneously, based on plant economics. The DRTO plant model represents the overall process dynamics whereas the MPC models represent the local unit dynamics. The plant model used within the DRTO module is consistent with the dynamic models used in the MPC controllers, but with the interactions between the process subsystems captured through appropriate linking relationships, such as material flows. The response of the plant under the action of the MPC subsystems is computed by taking into account the actions of all the controllers, as well as the process interactions between the subsystems. Interaction between local controllers is addressed via output feedback from the DRTO plant model to the MPC model predictions. The MPC optimization subproblems to be used in the DRTO closed-loop response prediction are again be replaced by their first-order optimality conditions to yield a single-level economic optimization problem. The performance of the proposed approach is assessed via case study simulations.

References

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Chen, X., Heidarinejad, M., Liu, J., and Christofides, P.D. (2012). Distributed economic MPC: Application to a nonlinear chemical process network. J. Proc. Contr., 22, 689-699.

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