Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation

Abstract

Abstract A new perfect control algorithm dedicated to fractional-order right-invertible systems, i.e. plants with a greater number of input than output variables, is presented in this paper. It is shown that such a control strategy can be particularly applied with regard to practical tasks. Henceforth, the Grünwald-Letnikov difference operator Δ α of an assumed order α can be truncated without loss of generality. For that reason, the so-called pole-free perfect control formula can be used to minimize the essential drawback of the Grünwald-Letnikov approach engaged, so as to define the intriguing issue regarding the robust perfect control for non-integer-order right-invertible LTI discrete-time state-space systems. Simulation examples show that the presented method can compete with a classical stable-pole one, for which the actual systems described by a fractional-order model often correspond with an inconvenient asymptotic perfect control solution given by the unlimited original operator Δ α . In the end, the possibility of employing of author’s nonunique right inverses dedicated to nonsquare MIMO system matrices is demonstrated, thus giving rise to the introduction of a new powerful tool for robustification of non-integer-order closed-loop perfect control plants as well.