ON THE CONSTRUCTION OF CONTROL ENSURING GLOBAL STABILIZATION OF THE SINGLE-LINK MANIPULATOR WITH A NONLINEAR ELASTIC JOINT IN THE VICINITY OF A TIME-DEPENDENT TRAJECTORY

Abstract

This study presents a control law for the electric motor’s rotation, globally stabilizing the motion of a single-link manipulator model with a nonlinear elastic joint near a specified time-dependent trajectory. The joint’s elasticity is modeled by a torsion spring, with the elastic force assumed to be nonlinearly dependent on the displacement. This nonlinearity complicates the control construction task, precluding the use of conventional approaches assuming linear elastic force. However, employing the Dynamic Surface Control (DSC) technique yields the desired control law. A specific selection of control parameters and filter constants prevents an increase in the order of the auxiliary system and avoids the “explosion of complexity” phenomenon. The reduction of the system’s order and simplification enable the derivation of an auxiliary Lyapunov function, demonstrating that the proposed control law effectively addresses the control problem.