Pseudo-PID Robust Tracking Design Method for a Significant Class of Uncertain MIMO Systems

Abstract

In this paper, for a significant class of uncertain MIMO systems, in particular for robots, new fundamental results are stated. These allow to design robust control laws without chattering, of pseudo-PID type, in order to track sufficiently regular trajectories with a preassigned maximum error. The proposed pseudo-PID controllers are easy to design and implement because these laws can also be decentralized and they are based on two design parameters. The first parameter is related to the minimum eigenvalue of a suitable matrix, depending on the inertia matrix in the case of a mechanical system, from which the practical stability depends on, and the second parameter is related to the practical region of asymptotic stability, to the precision of the tracking error and to the time constant of an appropriate linearized majorant system of the closed-loop control system. The utility and the efficiency of the main results proposed in this paper are illustrated with a significant example.