Cascade Synthesis of Observers of Mixed Variables for Flexible Joint Manipulators Tracking Systems under Parametric and External Disturbances

Abstract

This paper considers a tracking system developed for a full-actuated manipulator with flexible joints under the following assumptions: torques are control actions, and current loop dynamics are not considered; the mass-inertial characteristics of the manipulator and other parameters are not exactly known; the external matched and unmatched disturbances act on the system, and matched disturbances are not smooth; the derivatives of the reference actions are achievable but are unknown functions of time; the set of sensors is not complete. Based on the representation of the control plant model in a block form of input–output with respect to mixed variables (functions of state variables, external influences and their derivatives), we have developed a combined control law for the case where the control matrix contains additive uncertain elements. In addition, we have designed the mixed variable observers of the smallest possible dimension with piecewise linear corrective actions for two cases: (i) only the generalized coordinates of the manipulator are measured; (ii) only the angular positions and velocities of the motors are measured. It is shown that in a closed-loop system with dynamic feedback, a given tracking error stabilization accuracy is provided in the conditions of incomplete information. We presented the results of numerical simulation of these algorithms for a single-link manipulator.