Analysis of Interactions using Structured Singular Values

Multivariable controllers are often avoided in the chemical process industries in favor of simpler, diagonal or block-diagonal controllers. Such "decentralized" controllers are desirable because they result in control systems with fewer tuning parameters. However, the ensuing simplicity in controller design must be weighted against the interactions which result from "ignoring" the off-diagonal system blocks and which can lead to performance deterioration and even instability. The purpose of an Interaction Measure (IM) should be to indicate under what conditions the stability of the diagonal loops/blocks will guarantee that of the complete system. Using the notion of Structured Singular Value, we have derived a new dynamic IM for systems under feedback with diagonal or block-diagonal controllers. In addition to predicting the stability of decentralized control systems, this measure, the ¿ IM, will measure the performance loss caused by these control structures. In particular, its steady-state value provides a sufficient condition for achieving offset-free performance with the control system.