Unitary Interactor Matrices and Minimum Variance Control

Abstract

There are many limitations to achievable control loop performance, for example, time delays, the existence of poorly damped or non-invertible zeros, constraints on control action, desired robustness characteristics, etc. Amongst all these constraints, the time delay is the most fundamental constraint that has attracted much interest in the development of process control. Wolovich and Falb (1976) have shown that the analog of the time-delay term for a SISO system, which is feedback control-invariant, is the inter actor matrix for a MIMO system, which is also feedback control-invariant. Subsequently, Wolovich and Elliott (1983) and Goodwin and Sin (1984) extended the concept of the in-teractor matrix to discrete systems. The interactor matrix characterizes the most fundamental performance limitation of a linear multivariable system.