Composite position control of two-link flexible manipulator employing nonlinear decoupling method

Abstract

In high performance flexible machines such as robotic manipulators, vibration control of flexible machines becomes important as the demand for faster and lighter machines increases. Also, these energy efficient manipulators are of special interest for space applications in which the gravitational forces are negligible. When a light and flexible machine moves quickly, the inertia of the machines can produce deformation of the machine, and results in long lasting vibration in case of light damping. Generally the operation of high performance positioning systems such as robots, space structures and etc. is limited by this unnecessary vibration, therefore some effective techniques to reduce this vibration are needed. In this paper, based on nonlinear decoupling method (NLD), variable structure control (VSC) is extended to the problem of optimal control for tracking joint angles and stabilizing flexible vibrations of a two-link flexible manipulator simultaneously. VSC law is designed which accomplishes asymptotic decoupled joint angle trajectory tracking. In VSC, the trajectories are attracted toward a chosen hypersurface in the state space and then sliding it along. VSC law based on NLD is derived which decouples the joint-angle motion from the flexible motion. Although, the joint angles are controlled using VSC law, the zero dynamics (i.e., the flexible modes of the links) remains unstable. In order to suppress the flexible vibration actively, it is necessary to sacrifice the joint angle tracking performance somewhat by introducing a composite position control scheme in the vicinity of a desired trajectory. Exploiting the asymptotic linear behavior of the closed-loop system, a composite position controller is designed for regulating the flexible vibration simultaneously in the vicinity of a desired trajectory. Simulation results show that the two contradictory requirements, the robust joint angle tracking performance and the vibration stabilization, can be met ev...