Design of a pseudo-PD or PI robust controller to track C2 trajectories for a class of uncertain nonlinear MIMO systems

In this paper, some theorems are stated, which allow to design robust control laws without chattering, of type PD or PI, for uncertain nonlinear MIMO systems having a quite general structure, to track sufficiently regular trajectories with preassigned maximum error. The proposed control laws are easy to design and implement, above all for the robotic systems, because these laws can also be decentralized and they are based on two design parameters: the first related to the maximum eigenvalue of the inertia matrix from which the practical stability depends on, and the second related to the practical region of asymptotic stability (RAS), to the precision of the tracking error and to the convergence velocity of the tracking error to the desired neighborhood. If the trajectories to track are not sufficiently regular, suitable filtering laws are proposed for these trajectories, so as to facilitate the implementation of the controller and reduce the control action especially during the transient phase. Three significant examples of application in the terrestrial, sea transportation and robotic areas, well showing the simplicity of design and implementation of the controllers and their effectiveness, are reported