(202d) A New Measure of Process Interaction in Time Domain Dynamics

The process with multiple-input, multiple-output (MIMO) is quite common in process industries. Due to the presence of interactions in such systems, their analysis needs very different approach in comparison to the conventional single-input, single-output (SISO) systems. The relative gain array (RGA), as proposed by Bristol in 1966 [1] was the first formal tool in the analysis of MIMO processes with loop interaction. The RGA was originally defined, assuming a linearized,  time-invariant,  multivariable  process. Thus it seeks minimal information about the process in particular the steady state gains. The analysis of closed loop interaction and pairing of manipulated inputs to the appropriate controlled outputs, considering only the steady state gains may lead to the selection of inferior control configuration. The open loop step response of the process transfer functions was then adopted to incorporate the effect of process dynamics on the selection of control configuration [2, 3]. Both the methods depends only on the open loop step responses and does not give a clear depiction about the closed loop interaction.   

In this paper a new measure (Relative response array, RRA) for analyzing the effect of process dynamics on the selection of the control configuration with minimal interaction is presented. The proposed measure is based on the ratio of integral of open loop response to that of closed loop response. For any practically realizable process the assumption of "Perfect control" inherent in the definition of relative gain array never holds. Thus, in our approach, the closed loop responses are calculated based on internal model control (IMC) principle. Our approach is an improvement over relative dynamic array method [2], which was solely based on the integral of open-loop step responses. A preliminary condition for the screening of worst pairing has also been developed. The paper is organized as follows. The first part gives the underlying concepts of steady state and dynamic RGA with a brief review. Our approach and a preliminary screening condition will be presented next. To show the usefulness of the proposed measure various simulation examples have been considered, where the static RGA fails to suggest correct input-output pairing whereas RRA successfully identifies the best pairing available. The results obtained are then compared with the process response of conventional multi-loop feedback control scheme using PI controllers. All the simulations were carried out in Matlab 7.6/Simulink.