A direct approach for tip regulation of a single-link flexible manipulator

The aim of this study is to investigate the direct approach for tip regulation. Since the tip transfer function contains unstable zeros and the first few dominant flexible modes (complex poles), a reference model of the same order is selected which does not have any finite zeros but all negative real poles. In order to force the system to follow the reference model in the presence of the unstructured uncertainties, a variable structure controller is adopted in which the switching surface is derived from the reference model. When in sliding mode, the system performs as the reference model. Hence, there will be no vibration and the tip position regulation can be achieved when the system approaches a steady state. To further improve the system responses, an adaptation law with dead zone scheme is combined with the variable structure controller. Simulation results show that link vibrations have been eliminated and the control profile is fairly smooth