Robust Tracking Design for Uncertain MIMO Systems Using Proportional-Integral Controller of Order v

This paper provides a systematic method to design robust tracking controllers of reference signals with bounded derivatives of order v for uncertain multi-input multi-output (MIMO) systems with bounded parametric uncertainties, in particular, of rational multi-affine type, and/or in presence of disturbances with bounded derivatives of order ν. The proposed controllers have state-feedback structures combined with proportional-integral regulators of order v (PIv). Theoretical tools and systematic methodologies are provided to effectively design robust controllers for the considered systems, also in case of additional bounded nonlinearities and/or not directly measurable states. Applicability and efficiency of the proposed methods are validated through three examples: the first one is theoretical and useful to validate the proposed methodology, the second case study presents a metal-cutting problem for an industrial robot, and the third example deals with a composite robot, such as a milling machine.