Inverse Dynamics Nonsingular Terminal Sliding Mode Control of Two-Link Flexible Manipulators

Abstract

The nonminimum phase characteristics of flexible manipulators hinder their asymptotic tracking of a desired tip trajectory with a bounded control input. To address this problem, the authors propose an inverse dynamics nonsingular terminal sliding mode control strategy for a two-link flexible manipulator. First, the output of the two-link flexible manipulator system is redefined as a function of joint angles, modes, and parameters that affect the zero dynamics of the system. The input-output subsystem is derived from the redefined output and the original system. An inverse dynamics nonsingular terminal sliding mode controller is designed to make the input-output subsystem converge to its equilibrium point in finite time. The characteristics of the zero dynamics of the system are analyzed and calculated. The relationship between the eigenvalues of the zero dynamics and the parameters of the redefined output is obtained, which can be used to design the controller to guarantee the zero dynamics to be asymptotically stable at equilibrium point. Thus, the whole original flexible manipulator system is guaranteed to be asymptotically stable. Simulation results are presented to validate the design.