Application of the integral manifold concept for the end-effector trajectory tracking of a flexible link manipulator

Abstract

A new strategy for the end- effector trajectory tracking (EETT) of a single flexible link manipulator (SFLM) is introduced. The linear dynamic model of the SFLM is expressed in the singularly perturbed form. To reduce the EETT error, a corrective torque is added to the computed torque control command of the rigid link counterpart of the SFLM. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. It is proven that the EETT error is a function of the fundamental natural frequency of the SFLM. That is, the order of the EETT error, after employing 3 2 this new method, is greater than epsiv3 and smaller than epsiv2 , where epsiv = 1(2pif) and f is the fundamental natural frequency of the SFLM. The implementation of the introduced technique does not require the full state measurements, since by designing an observer; the rate of the change of the flexible variables with respect to time is estimated. Thus only the measurements of the joint rotation, joint velocity, and flexible variables are required. The proof of the stability, based on the Lyapunov criteria, is given. The results of the simulation and experimental studies are also included. Making the error of the EETT smaller and reducing the number of state measurements are the main contributions of this work.