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.
Highlights
The inverse model control (IMC) has widely been investigated over the past decades due to its application in many scientific and engineering fields [1]–[4], [5]–[8], [9]–[12], [13], [14], [15]–[18], [19]–[22], [23]–[25]
The widely known IMC-based perfect control law, which constitutes the deterministic instance of the minimum variance control (MVC), has been associated with the full-rank square MIMO systems, including SISO ones [1]
Since in the non-full rank scenario the pseudoinverse formula supported by the so-called skeleton factorization mechanism has to be engaged in the inverse model control design, the perfect control law requirements cannot structurally be fulfilled [8]
Summary
The inverse model control (IMC) has widely been investigated over the past decades due to its application in many scientific and engineering fields [1]–[4], [5]–[8], [9]–[12], [13], [14], [15]–[18], [19]–[22], [23]–[25]. The multivariable nonsquare rightinvertible plants, i.e. systems with greater number of input than output variables, can be subjected by such noisefree control law [3] In such a case, through the application of nonunique parameter/polynomial right inverses, we can redefine the special properties of the closed-loop state-feedback. Since in the non-full rank scenario the pseudoinverse formula supported by the so-called skeleton factorization mechanism has to be engaged in the inverse model control design, the perfect control law requirements cannot structurally be fulfilled [8]. Following the recent authors’ results it is certain, that for some single-delayed state-space plant being under zero-setpoint, the non-full rank perfect control structure can be successfully obtained [12].
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