Robust tracking design for uncertain MIMO systems using proportional–integral controller of order <i>v</i>

Abstract

Abstract This paper provides a systematic method to design robust tracking controllers of reference signals with bounded derivatives of order ν 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 ν ( PI ν ). 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.