(40f) Coordination of Distributed MPC Systems with Closed-Loop Prediction Approximation in Dynamic Real-Time Optimization (DRTO)

Industrial process control systems typically follow a hierarchical structure. Within this structure, dynamic real-time optimization (DRTO) can be used a supervisory layer to compute set-point trajectories for an underlying regulatory control system based on economic optimization and a dynamic process model. It addresses the shortcomings of traditional steady-state RTO systems since it does not require the plant to be at steady state prior to execution. Tosukhowong et al. presented a DRTO formulation that handles slow dynamics of a system based on a linear dynamic model [1], while a DRTO formulation proposed by Kadam and Marquardt uses a sensitivity technique and estimation of uncertain parameters [2]. Open-loop models of the process are generally adopted by the DRTO formulation discussed above without considering the dynamic effects of the underlying regulatory controller. However, DRTO formulations based on the closed-loop prediction of the plant under constrained MPC have recently been developed [3, 4].

Using a single, monolithic MPC system is imprudent for large-scale industrial process systems, which instead favor a distributed MPC architecture that takes the modularity of a large process into consideration and provide additional flexibility [5]. Thorough reviews on the architecture and formulations of distributed MPCs have been conducted in [6, 7, 8]. The coordination scheme proposed by Camponogara et al. allows communication among MPC subsystems either once or multiple times before implementation of the control actions [9]. The distributed Lyapunov-based MPC schemes developed by Liu et al. [10] adopt a sequential one-directional and iterative bi-directional approach respectively, assuming state feedback for all controllers. The cooperative scheme proposed by Stewart et al. [11] for distributed MPCs ensures the closed-loop stability of the system upon termination of iterations for all subsystems.

In previous work, a closed-loop DRTO formulation was developed for the coordination of distributed MPC systems by assigning computed set-point trajectories based on the prediction of future interactions between the plant dynamics and distributed MPCs [12]. This closed-loop formulation naturally results in a multilevel optimization problem whose primary optimization problem computes the reference trajectories for each MPC subsystem based on a full plant dynamic model under an economic objective, and whose MPC optimization sub-problems compute optimal control actions to be applied to the full plant dynamic model based on partial models each of which contains model equations relevant to its associated subsystem. Such a multilevel optimization problem can be transformed into a single-level optimization problem by applying the Karush-Kuhn-Tucker (KKT) optimality conditions to transform the MPC optimization sub-problems into sets of algebraic constraints embedded in the primary optimization problem, resulting in a single mathematical program with complementarity constraints (MPCC). No direct exchange of information is needed between local controllers, and communication is achieved through set-point trajectories generated by the DRTO formulation for the lower level MPCs.

This work extends the use of the DRTO formulation for dynamic coordination of distributed MPC systems [12], but addresses the issue of computational complexity for systems with a long MPC control horizon or DRTO prediction horizon which can lead to large DRTO optimization problems, which is further exacerbated with increasing plant scale and complexity. Two techniques are applied for approximating the predicted closed-loop response of the plant, developed originally for closed-loop prediction under centralized MPC [3]. Relevant linear and nonlinear case studies are conducted to demonstrate the capability of target tracking and economic optimization by the DRTO formulation. Results show that the closed-loop DRTO formulation is able to coordinate distributed MPCs to achieve an optimal economic transition or the desired target value rapidly in a computationally efficient manner and without significant performance loss when compared to the counterpart with rigorous closed-loop prediction.

References

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