Trajectory Tracking for the End-effector of a Class of Flexible Link Manipulators

Anewcontroller for the end-effector trajectory tracking (EETT)of a class of flexible linkmanipulatorswhich consists of a chain of rigid links with a flexible end-link (CRFE) is introduced. To design this new controller, a dynamic model of the CRFE is expressed in the singularly perturbed form; that is, decomposed into slow and fast subsystems. The states of the slow sub-system are the joints ’ rotations and their time derivative, while the states of the fast subsystem are the flexible variables, which model the lateral deflection of the end-link, and their timederivative. For the slow subsystem, the new controller requires only ‘‘one’ ’ corrective torque in addition to the computed torque command of the rigid link counterpart of theCRFE for the reduc-tion of the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly per-turbed differential equations. The need for only one corrective torque and its derivation are among the contributions of the new controller. To stabilize the fast subsystem, an observer-based controller is designed according to the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time deri-vative of the flexible link’s lateral deflection, in which its measurement is difficult if not impossible in practice. This feature of thenewcontroller is an advantage for it. To facilitate the derivation and implementationof this controller, several properties of thematrices in the dynamicmodel of theCRFE are introduced and usedwhich are other contributions of this research. The effectiveness and feasibility of the new controller are shown by simulation and experimental studies