Interaction measure for decentralized control of multivariable processes

Norms of differences in the sensitivity function matrices and the complementary sensitivity function matrices (closed-loop transfer function matrices) are used to determine better models in the context of iterative identification and model reduction. Some insights on the relative error matrix between the process transfer function matrix and its diagonal matrix, which has been used in analyzing dynamic interactions by several authors, are also obtained. Proposed interaction measures can be interpreted as the amounts of differences of the complementary sensitivity function matrices when loops are closed, extending the concept of gain changes in the relative gain array. To employ the interaction measures, control systems are designed in advance using internal model control. By changing the closed-loop time constant, proper pairings based on closed-loop response speeds can be obtained.