(295d) Distributed Estimation and Model Predictive Control of Integrated Nonlinear Process Systems Using an Adaptive Community Detection Approach

Model predictive control (MPC) is a common approach for implementing optimal decision-making and control strategies in the chemical process manufacturing and energy systems industries because it is flexible, inherently robust, and can efficiently handle complex multivariable systems with operational and safety constraints [1]. In MPC, the control problem is formulated as a constrained dynamic optimization problem that must be solved repeatedly at each process sampling time to get the current values of the manipulated inputs [2, 3]. Hence, the applicability of MPC relies on the real-time solvability of the underlying dynamic optimization problem subject to the process model and constraints. This limits the use of MPC in a centralized setting for large-scale integrated process networks. Distributed model predictive control (DMPC) is an alternative to centralized MPC, which could accelerate computations while maintaining control performance at a certain level. For DMPC, the structure of the control system is decomposed into smaller local controller agents that can cooperate and communicate with each other in different ways.

System decomposition is the first step toward developing a distributed control framework. This means determining the number of required subsystems and how manipulated inputs and controlled outputs are allocated to different subsystems. High-quality decompositions minimize the necessary communication between subsystems, decreasing computational effort. From a network theory standpoint, the decomposition problem can be interpreted as identifying subsystems with weak connections whose variables are tightly correlated [4]. Clustering based on input/output connectivity has been proposed to build hierarchies of system decompositions [5]. Community detection has also been used to find dense subsystems for a distributed control architecture [6]. In particular, community detection on a graph representation of process systems is formulated by achieving the highest value of a modularity index for the system, quantifying an excess percentage of edges that belong to a community relative to a random graph [7, 8]. It has also been expanded to include initial response intensities and finite-time interactions [9]. Case studies on a benchmark reactor-separator process network, the process of benzene alkylation with ethylene, and an amine gas sweetening plant using different optimization platforms, different communication patterns between the local controllers, and taking model uncertainty into account have shown that decompositions based on community detection allow for faster computations without significant performance degradation compared to centralized implementations [10-13].

This work focuses on exploring the impact of variable interactions among manipulated inputs, state variables, and controlled outputs at different operational conditions on community detection-based distributed state estimation and control of integrated process networks. Furthermore, a framework for adaptive spectral community detection is developed to improve the modularity and computational efficiency of the decomposition for real-time applications. The distributed state estimation and control architecture design is then recast as a spectral community detection problem for the weighted graph representation of the process system. Unlike commonly used hierarchical community detection methods that use recursive divisions of subsystems until reaching maximum modularity, spectral community detection partitions the system into the desired number of subsystems (that can be optimized) in one setting [14]. In this approach, the eigenvalues and eigenvectors of the system are used to assign a starting vector to each subsystem as well as a vertex vector to each node of the graph representation of the system. Each node will then be allocated to the closest subsystem based on measuring the distance between its vertex vector and the subsystem vector. The new subsystems' vectors are the summations of the nodes' vertex vectors that belong to the subsystems. This procedure is repeated until convergence.

Finally, an iterative integrated distributed moving horizon estimation (DMHE) and DMPC is synthesized to address the setpoint-tracking problem based on the proposed spectral community detection-based adaptive distributed architecture for a general class of highly integrated nonlinear process networks. The proposed adaptive distributed estimation and control method is implemented in the process of benzene alkylation with ethylene. The closed-loop performance and computation time are evaluated under varying operating conditions. The resulting spectral community detection-based decompositions of the weighted graph representations of the process system show improvements in distributed estimation and control compared to the commonly used unweighted hierarchical community-based decompositions for all operating regions.

References:

[1] Rawlings, J. B.; Mayne, D. Q.; Diehl, M. M. Model Predictive Control: Theory, Computation, and Design 2nd Edition; 2019.

[2] Mayne, D. Q. Model Predictive Control: Recent Developments and Future Promise. Automatica, 2014, 50 (12), 2967–2986.

[3] Qin, S. J.; Badgwell, T. A. A Survey of Industrial Model Predictive Control Technology. Control Eng. Pract. 2003, 11 (7), 733–764.

[4] Girvan, M.; Newman, M. E. J. Community Structure in Social and Biological Networks. Proc. Natl. Acad. Sci. U.S.A. 2002, 99 (12), 7821–7826.

[5] Heo, S.; Daoutidis, P. Control-Relevant Decomposition of Process Networks via Optimization-Based Hierarchical Clustering. AIChE J. 2016, 62 (9), 3177–3188.

[6] Jogwar, S. S.; Daoutidis, P. Community-Based Synthesis of Distributed Control Architectures for Integrated Process Networks. Chem. Eng. Sci. 2017, 172, 434–443.

[7] Leicht, E. A.; Newman, M. E. J. Community Structure in Directed Networks. Phys. Rev. Lett. 2008, 100 (11), 118703.

[8] Pourkargar, D. B.; Almansoori, A.; Daoutidis, P. Impact of Decomposition on Distributed Model Predictive Control: A Process Network Case Study. Ind. Eng. Chem. Res. 2017, 56 (34), 9606–9616.

[9] Tang, W.; Pourkargar, D. B.; Daoutidis, P. Relative Time-Averaged Gain Array (RTAGA) for Distributed Control-Oriented Network Decomposition. AIChE J. 2018, 64 (5), 1682–1690.

[10] Pourkargar, D. B.; Almansoori, A.; Daoutidis, P. Comprehensive Study of Decomposition Effects on Distributed Output Tracking of an Integrated Process over a Wide Operating Range. Chem. Eng. Res. Des. 2018, 134, 553–563.

[11] Moharir, M.; Pourkargar, D. B.; Almansoori, A.; Daoutidis, P. Distributed Model Predictive Control of an Amine Gas Sweetening Plant. Ind. Eng. Chem. Res. 2018, 57 (39), 13103–13115.

[12] Pourkargar, D. B.; Moharir, M.; Almansoori, A.; Daoutidis, P. Distributed Estimation and Nonlinear Model Predictive Control Using Community Detection. Ind. Eng. Chem. Res. 2019, 58 (30), 13495–13507.

[13] Moharir, M.; Pourkargar, D. B.; Almansoori, A.; Daoutidis, P. Graph Representation and Distributed Control of Diffusion-Convection-Reaction System Networks. Chem. Eng. Sci. 2019, 204, 128–139.

[14] X. Zhang and M. E. J. Newman, “Multiway spectral community detection in networks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2015, 92, 5.