End-Effector Trajectory Tracking of a Class of Flexible Link Manipulators

A new controller for the end-effector trajectory tracking (EETT) of a class of flexible link manipulators which composed of a chain of rigid links with an end-link flexible (CREF) is introduced. The dynamic model of the CREF is expressed into the standard singularly perturbed form; that is, the dynamic model is decomposed into slow and fast subsystems. The states of the slow subsystem are the joints’ rotations and their time derivatives, while the states of the fast subsystem are flexible variables, which model the lateral deflection of the end-link, and their time derivatives. For the slow subsystem, corrective torque is added to the computed torque control commands of the rigid link counterpart of the CREF to reduce the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. It was shown that this corrective term is of order ε² where ε = 1/(2πf) and f is the smallest non-zero natural frequency of the CREF. To stabilize the fast subsystem, an observer-based controller is designed by the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time derivative of the flexible variables, which their measurements are hardly practical. To facilitate the derivation and implementation of introduced controller here, several properties of the mass matrix of the CREF are introduced and used. The effectiveness and feasibility of the new controller are shown through the simulation and experimental studies.