Input–output pairing accounting for both structure and strength in coupling

Abstract

Input–output pairing is an important problem in control system design and is often performed using the relative gain array (RGA) based approaches. While RGA‐based approaches have been very successful in many applications, they have some well‐known limitations. For example, they may give results which are not consistent with the physical topology since only the strength of interaction between inputs and outputs is taken into account in the RGA. In this work, we propose a new measure for input–output pairing that explores both strength and structural information in input–output coupling. Specifically, we take advantage of the tool of relative degree to measure the physical closeness of input–output pairs and to explore the strength of interaction progressively with respect to the relative degree. We call the proposed measure relative sensitivity array (RSA) between inputs and outputs. Detailed analysis is performed to reveal the relationship between the gain matrix used in the RGA and the sensitivity matrix in the RSA from a mathematical point of view. Since the RSA is an analog of the RGA, many existing pairing guidelines developed for the RGA can be used in the proposed RSA‐based pairing. The proposed RSA‐based approach is applied to two examples. The results show that pairs formed by the proposed approach are consistent with the physical topologies of the processes. Also, the results show that the proposed approach can handle larger systems that cannot be effectively handled by RGA‐based approaches. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1226–1235, 2017