(497c) Graph-Theoretic Approach for the Synthesis of Distributed Control Architecture

Designs with multiple material recycle and energy integration loops are quite common in modern chemical plants. Such designs promise favourable economics, however, their operation and control is quite challenging due to strong interactions between process units. For such networks, traditional decentralized controllers have limited effectiveness due severe control loop interactions. On the other hand, the design and implementation of a fully centralized controller is impractical due to large system size. To this end, distributed control has been exploited as an efficient control framework [1]. Most of the work in this area has addressed issues like feasibility, stability and optimality of the control solution for a heuristically selected architecture.

In this talk, we present a systematic framework for the synthesis of distributed control architecture using principles of graph theory. To this end, the control problem of an integrated network is abstracted as an equation graph with the various input, output and state variables as nodes and their (static or dynamic) interdependence as edges. In this setting, the distributed architecture synthesis problem is equivalent to decomposing the equation graph into ‘communities’ with strong connectivity between nodes belonging to each community and weak inter-community edges. Initially, it is considered that all the edges are equally important. The distributed structure obtained in this case thus results in minimum inter-controller interactions. Subsequently, strength of interaction between a variable pair is used as an edge weight. The distributed architecture obtained in this case results in optimal input-output pairing.

The direct decomposition of the equation graph allows for deriving state-space descriptions for the individual sub-controllers. The framework uses minimum system information and is highly scalable due to advances in community detection algorithms. The effectiveness of the proposed framework is illustrated with the help of a case study on an integrated network.

References:

[1] Liu, J., Munoz de la Pena, D., Christofides, P. D. Distributed model predictive control of nonlinear process systems. AIChE J. 55 (5), 1171-1184.