ROmA loop pairing criteria for multivariable processes

An important aspect in the control of multivariable (MIMO) systems is the pairing of the input and output variables for decentralized control. The relative gain array (RGA) introduced in 1966 by Bristol gives a quantitative measure of static interaction and is a simple technique widely applied by process engineers. Many improved approaches, RGA-like, have been proposed for defining different measures of dynamic loop interactions. However, none of these techniques is generally accepted as a globally satisfactory solution by process engineers. In this paper an alternative approach is presented: a global index, called Relative Omega Array (ROmA), is proposed. In single-input single-output systems the critical frequency remains unchanged in the passage from open loop to closed loop. This property holds also for multi-input multi-output systems, whenever perfect decoupling occurs. The key concept in ROmA index is to capture information from critical frequencies variation in the passage from open loop to closed loop, for measuring interactions in multi-input multi-output systems. This method retains the characteristics of simplicity of RGA but include additional information about dynamic interactions. Examples are given in order to show the effectiveness of the ROmA index in critical cases, where incorrect loop pairings is suggested by RGA. It is also shown how to combine RGA and ROmA in a relative performance array, similar to the effective RGA (ERGA) recently introduced.