A New Non-Full Rank Algorithm for the IMC-Derived d-Step MIMO Structures in the Pole-Free State Space

Abstract

In this paper, the powerful issue of a non-full rank inverse model control investigation is provided. It is broadly known, that the inverse-based methodology is associated with the full-rank control systems only. However, following the recently obtained authors' results in this matter, it should be concluded, that for single-delayed non-full rank state-space plants, the inverse model control-related perfect control expression can also be established. It is shown here, that for all right- and left-oriented multivariable LTI non-full rank systems, including the square ones, governed by the discrete-time state-space domain arranging the zero-reference value, the maximum-speed pole-free instance of such inverse model control strategy can be achieved. Thus, the new non-full rank algorithm does not coincide with the z-transfer-function scenario, which additionally sounds the intriguing peculiarity. The innovative content of the manuscript, that has never been seen before, is strongly supported by the numerical examples. Henceforth, the presented methodology covers the entire set of LTI MIMO state-space-oriented plants in the discrete-time domain, which is also a consequence of conducted research investigation in the past.

Keywords

• Non-full rank
• perfect control procedure
• Moore–Penrose inverse
• generalized inverses
• skeleton factorization
• pole-free delayed plants