Majorant-Based Control Methodology for Mechatronic and Transportation Processes

This paper provides a unified approach via majorant systems, which allows one to easily design a family of robust, smooth and effective control laws of proportional -
$h$
order integral -
$k$
order derivative
$(PI_{h} D_{k})$
-type for broad classes of uncertain nonlinear multi-input multi-output (MIMO) systems, including mechatronic and transportation processes with ideal or real actuators, subject to bounded disturbances and measurement errors. The proposed control laws are simple to design and implement and are used, acting on a single design parameter, to track a sufficiently smooth but generic reference signal, yielding a tracking error norm less than a prescribed value, with a good transient phase and feasible control signals, despite the presence of disturbances, parametric and structural uncertainties, measurement errors, and in case of real actuators and amplifiers. Moreover, some guidelines to easily design the proposed controllers are given. Finally, the stated unified methodology and various performance comparisons are illustrated and validated in two case studies.