End-effector trajectory tracking of a flexible link manipulator using integral manifold concept

A new controller for the end-effector trajectory tracking of a single flexible link manipulator is introduced. The linear dynamic model of the single flexible link manipulator is expressed in the singularly perturbed form. To reduce the end-effector trajectory tracking error, a corrective torque is added to the computed torque command of the rigid link counterpart of the single flexible link manipulator. The corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. This corrective torque is of order ε2 where , and f is the fundamental natural frequency of the single flexible link manipulator. The implementation of the introduced technique does not require the full-state measurements since by designing an observer, the time derivative of the link's lateral deflection is estimated. The stability proof of the new controller, which is based on the Lyapunov criterion, is presented. The results of the simulation and experimental studies are also included to, respectively, show the effectiveness and feasibility of the new controller.