Coordination of distributed MPC systems through dynamic real-time optimization with closed-loop prediction
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abstract
A dynamic real-time optimization (DRTO) formulation with closed-loop prediction is used to coordinate distributed model predictive controllers (MPCs) by rigorously predicting the interaction between the distributed MPCs and full plant response in the DRTO formulation. This results a multi-level optimization problem and that is solved by replacing the MPC quadratic programming subproblems by their equivalent Karush-Kuhn-Tucker (KKT) first-order optimality conditions to yield a single-level mathematical program with complementarity constraints (MPCC). The proposed formulation is able to perform both target tracking and economic optimization with significant performance improvement over decentralized control, and similar performance to centralized MPC. A linear dynamic case study illustrates the performance of the proposed strategy for coordination of distributed MPCs for different levels of plant interaction,. The method is thereafter applied to a nonlinear integrated plant with recycle, where its performance in both set-point target tracking and economic optimization is demonstrated.
Subsequently, this study presents two techniques for approximation of the closed-loop prediction within the DRTO formulation - a hybrid closed-loop formulation and an input clipping formulation. The hybrid formulation generates closed-loop predictions for a limited number of time intervals along the DRTO prediction horizon, followed by an open-loop optimal control formulation extended to rest of the horizon. The input clipping formulation utilizes an unconstrained MPC optimization formulation for each distributed MPC, coupled with the application of an input saturation mechanism. The performance of the approximation techniques is evaluated through application to case studies based on linear and nonlinear dynamic plant models respectively. The approximation techniques are demonstrated to be more computationally efficient than than the rigorous counterpart without significant loss in performance.
The performance of the proposed DRTO formulation can be further improved by the introduction of nonlinearity. The nonlinear dynamic plant model is firstly introduced in the DRTO formulation while maintaining the linear formulation for the distributed MPCs. The performance of resulting formulation is demonstrated and compared against the linear counterpart. The nonlinear MPC formulation is then included in both lower-level control implementation and DRTO formulation. By reformulating the Lagrangian of the nonlinear MPC optimization subproblems, the nonlinear MPC formulation is successfully implemented in the DRTO formulation. The performance of such DRTO formulation is further improved and shown using a nonlinear case study.
The conclusion of this study is summarized and the potential directions of this research such as large-scale applications, variation of MPC implementations, and robust model-based control are outlined and explained in the end.
