(497g) Relative Time Averaged Gain Array for Distributed Control Architecture Design

Modern chemical and energy plants are large-scale, complex networks. Distributed control strategies, especially distributed model predictive control (DMPC) [1], which are based on a decomposition of the network into separate subsystems and coordination between the corresponding controllers, play a central role in controlling such systems. A major problem in the implementation of DMPC is the network decomposition itself, i.e. the assignment of input and output variables into subsystems. This requires an analysis of input-output interactions with an appropriate characterization of the effect of inputs on the outputs.

The classical concept of relative gain array (RGA) for input-output interaction analysis has been a mainstream for traditional decentralized control design. The applicability of RGA was well established through theoretical analysis and many variants has been proposed for a better characterization of interactions [2]. Since RGA and its variants characterize input-output interactions based on long-time response, the network topology is not taken into consideration when used in the context of large-scale networks. Recently, input-output partitioning methods based on network connectivity (relative degrees) and response sensitivities have been proposed. Specifically, in [3], an input-output interaction measure combining connectivity and response sensitivities was defined, and the input-output subsystems were generated through a community detection approach based on modularity maximization. In [4], the inputs and outputs are first grouped based on the corresponding relative degree values, and then paired within each group using response sensitivities in the form of a relative sensitivity array (RSA). However, connectivity and sensitivities used in the above methods capture only infinitesimally short time response characteristics.

In this work, we first propose a time-averaged gain, defined as the integration of output responses over step inputs weighted by an exponential distribution, equivalent to a real-axis evaluation of the system transfer function, to capture the effect of the inputs on the outputs during any given time scale of interest. A relative time-averaged gain array (RTAGA), defined in the same manner as RGA, is then proposed as the input-output interaction measure. We show that the classical RGA and RSA are in fact limiting cases of RTAGA as the time scale parameter becomes infinitely long and infinitesimally short, respectively. To generate multiple-input-multiple-output subsystems efficiently, we employ the network-theoretic tool of community detection in the input-output bipartite network, where the input-output edges are weighted by the RTAGA elements. The communities thus detected correspond to the control subsystems with favorable interaction properties over any desired time scale. We also provide systematic guidelines for the proper choice of time scale in the context of distributed model predictive control.

The proposed method is applied to a reactor-separator process containing 9 inputs and 9 outputs, and the decomposition result is tested with a distributed MPC scheme. Compared to other decompositions, the proposed method results in a finer decomposition and a significant reduction of computational time, while the control performance remains close to that under centralized control.

References:

[1] Christofides, P. D., Scattolini, R., Muñoz de la Peña, D., & Liu, J. (2013). Distributed model predictive control: A tutorial review and future research. Computers & Chemical Engineering, 51, 21-41.

[2] McAvoy, T. J. (1983). Interaction analysis: Principles and applications. ISA.

[3] Tang, W. & Daoutidis, P. (2017). Community detection in input-output bipartite graph based on short-time response. IEEE Transactions on Automatic Control, submitted.

[4] Yin, X. & Liu, J. (2017). Input-output pairing accounting for both structure and strength in coupling. AIChE Journal, 63(4): 1226-1235.