Control of two-input two-output systems exploiting alignment

This paper considers the problem of controlling the difficult class of uncertain multivariable systems that are strongly interacting (ill-conditioned) and potentially unstable and/or non-minimum phase. A classically formulated decentralized design procedure is presented within a proposed generalized formulation that permits the exploitation of directional information in a design. Limiting the presentation to two-input two-output systems, the plant/controller alignment theory for single-input two-output systems is extended and employed, along with the freedom to condition the poles and zeros of the single-input single-output plants considered in the designs, which is related to a proposed concept of pole-zero alignment. The developed theory and design method is motivated by, and employed to control, an uncertain linear model of the X-29 aircraft. The results provide insights into the general issues of decentralized control and performance limitations.