(390f) Input-Output Paring Accounting for Both Structure and Strength in Coupling

Within process control, the decentralized and distributed control frameworks have attracted great attention due to the merits in terms of structural flexibility and fault tolerance. Input-output pairing is one fundamental step in both decentralized and distributed control system designs in order to achieve desired control performance. Input-output pairing has been an active research topic for a few decades and different approaches have been proposed. The relative grain array (RGA) analysis that was used to measure the strength of interaction between inputs and outputs is a widely-used tool [1]. However, RGA may give pairing results that are not consistent with the process physical topology, which is not favorable for control system designs. The relative degree analysis adopted in the evaluation of control configurations is another promising input-output pairing approach [2]. It provides valuable information on how directly a manipulated input can affect an output variable from a structural point of view. While the relative degree analysis provides a measure of physical closeness of inputs and outputs, it neglects entirely the strength of interaction. Consequently, it may also fail to work in different situations.

Motivated by above observations, in this work, we aim at developing an input-output pairing approach that takes into account both structural and strength information in coupling. Specifically, the relative degree analysis is taken advantage of to measure the physical closeness of input-output pairs and relative sensitivity is used to explore the strength of interaction progressively with respect to the relative degree. The proposed measure is the so-called relative sensitivity array (RSA) between inputs and outputs. Detailed analysis reveals the relationship between the gain matrix in the RGA analysis and the sensitivity matrix defined in the RSA, which implies that the RSA can be interpreted as truncated RGA with respect to a specific relative degree. To account for more general input-output paring problems, an iterative algorithm for the RSA-based method as the implementation guideline is proposed. Since the RSA is essentially an analog of the RGA, many existing pairing rules that were originally developed for RGA can be adopted in the RSA-based approach as the pairing rules.

The proposed RSA-based method is compared with RGA- and relative degree-based approaches in the input-output pairing of several chemical process examples. From the results, it can be seen that (a) the pairs formed by the proposed RSA-based approach are more consistent with the physical topologies of the studied processes; (b) results obtained by only considering the coupling strength as in RGA could be different at different operating points which is not desirable from a practice point of view; (c) results obtained by RGA-based methods may not consistent with the physical topologies of the processes which may increase the information coupling of the entire control system; (d) the relative degree analysis may even fail to give a complete pairing recommendation since coupling strength is ignored. Furthermore, it is demonstrated that the proposed approach is able to handle input-output pairing tasks for systems with larger scales.

[1] Bristol, E. On a New Measure of Interaction for Multivariable Process Control. IEEE Transactions on Automatic Control, 11:133-134, 1966.

[2] Kravaris, C. and Soroush, M. Synthesis of Multivariable Nonlinear Controllers by Input/output Linearization. AIChE Journal, 36:249-264, 1990.