Non‐diagonal controllers in MIMO quantitative feedback design

Abstract

SUMMARYThis paper discusses multivariable quantitative feedback design through the use of controllers with offdiagonal elements. Controller design for multivariable plants with significant uncertainty is simpler and potentially less conservative if some sort of dominance is achieved (by reducing the interaction effect of offdiagonal plant elements) before a diagonal (decentralized) controller design is attempted. Traditional approaches for achieving dominance are not applicable when plant uncertainty must be considered. This paper discusses parallel and series implementations and for the latter, a pseudo-Gauss elimination approach to the design has been developed. The interaction is measured using the Perron-Frobenius root of an interaction matrix. In some applications, it is possible to trade off individual plant cases against each other in order to reduce to the worst-case interaction over the entire plant set.

An improved non‐sequential multi‐input multi‐output quantitative feedback theory design methodology

“…The developed theory employs non-negative matrix theory and the multivariable Nyquist stability theorem. Existing results from the theory of non-negative matrices and their application to dominance theory can be found in Reference [18], and specifically applied to MIMO QFT designs in References [9,11,16,19].…”

“…Despite these limitations, the NS MIMO QFT design methodology presents a straightforward design method and a feasible methodology for design initialization. Furthermore, the design methodology can be combined with other control techniques to provide a less conservative design solution [10][11][12]. Herein the NS MIMO QFT design methodology is considered and an improved design methodology developed.…”

Non‐sequential MIMO QFT control of the X‐29 aircraft using a generalized formulation

“…Subsequently, the sequential MIMO QFT design methodology is less conservative, and has therefore become the standard MIMO QFT design methodology. Alternate MIMO QFT design methodologies were presented in [26,27] that employed dominance measures to guarantee acceptable closedloop stability and performance properties. These approaches give fully populated controllers.…”

“…Due to the conservatisms the methodology generally performs best for low dimension, diagonally dominant plant TFMs. However, the design methodology can be combined with other control techniques to provide a less conservative design solution [27,31,47], as demonstrated herein.…”

“…is achieved, a necessary and sufficient condition for closed-loop stability of the true system is [50,51] (see also [14,42,27] for similar dominance based stability theory)…”