# (190b) Control Configuration Selection Using Agglomerative Hierarchical Clustering: Graph-Theoretic Approach

- Conference: AIChE Annual Meeting
- Year: 2016
- Proceeding: 2016 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Monday, November 14, 2016 - 3:45pm-5:45pm

Lixia Kang^{1}, Wentao Tang^{2}, Yongzhong Liu^{1} and Prodromos Daoutidis^{2}

^{1}*Department of Chemical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049,China*

^{2}*Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA*

* *

Control configuration synthesis, is a classic problem in control, which has been extensively studied in modern systems and control theory [1]. The goal is to identify single-input single-output control pairs (decentralized control configurations) or multi-input multi-output ones (block decentralized configurations) with favorable interaction characteristics. This problem becomes particularly challenging for large, integrated networks due to the inherent computational complexity, robustness and reliability problems, as well as communication bandwidth limitations [2]. To this end, distributed control approaches have been proposed for the control of such networks, a key part of which is the identification of block decentralized control configurations [3]. A promising way to address this problem is to use relative degrees as a measure of interaction among inputs and outputs. In reference [4], a notion of a relative degree matrix was postulated and used to quantify the structural interactions associated with a particular input/output assignment. Relative degree was also used to assess the dynamic effect of different manipulated inputs on economic cost functions in the context of economic model predictive control [5]. The generation of optimal decentralized control configurations such that a global relative degree index capturing structural coupling is maximized was proposed in [6]. A hierarchical agglomerative clustering procedure for generating block decentralized configuration candidates was also proposed in this work. An integer optimization framework was adopted for both of the above tasks. Such optimization methods however can be computationally expensive as the dimension of the system increases. Further, while [6] described the generation of an entire hierarchy of control configurations, the selection of the optimal control configuration was not addressed. In this work, a graph-theoretic formulation of the control configuration synthesis problem is developed. Relative degrees are used as a measure of distance between inputs and outputs as well as between input/output pairs. The method initinally identifies individual input/output pairs (decentralized control configuration) that are optimal in the sense of maximizing a structural decoupling criterion, through the solution of a bipartite matching problem. These optimal input/output pairs are then clustered hierarchically by generating a minimum spanning tree on the corresponding graph. The resulting hierarchy of clusters is further evaluated via a suitable notion of modularity to identify the optimal one (or obtain a ranked list). The proposed method can be implemented efficiently using well-established powerful graph theoretic algorithms. The application of the proposed method is illustrated through an energy integrated solid oxide fuel cell system and a heat exchanger network. In both case studies, the resulting configurations make physical sense, capturing important structural process characteristics.

References

[1]Â van de Wal, M. and de Jager, B. "A review of methods for input/output selection,"Â AutomaticaÂ 37.4 (2001): 487-510.

[2]Â Scattolini, R. "Architectures for distributed and hierarchical Model Predictive Control â?? A review,"Â Journal of Process ControlÂ 19.5 (2009): 723-731.

[3]Â Yin, X., Arulmaran, K., Liu, J. and Zeng, J.Â "Subsystem decomposition and configuration for distributed state estimation,"Â AIChE JournalÂ (2016) doi:10.1002/aic.15170.

[4]Â Daoutidis, P. and Kravaris, C. "Structural evaluation of control configurations for multivariable nonlinear processes," Chemical Engineering Science 47.4 (1992): 1091-1107.

[5] Ellis, M. and Christofides, P. D. "Selection of control configurations for economic model predictive control systems," AIChE Journal 60 (2014): 3230-3242.

[6] Heo, S., Marvin, W. A. and Daoutidis, P."Automated synthesis of control configurations for process networks based on structural coupling," Chemical Engineering Science 136 (2015): 76-87.

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