Active vibration control of a single-link flexible manipulator by pole-placement approach

The tip regulation task of flexible manipulators is usually solved indirectly by direct control of joint angle and suppression of the flexible link vibration. 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 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 and tip vibration can be eliminated. To further improve the system responses, an adaptation law with dead zone scheme is combined with the variable structure controller. Simulation results confirm the effectiveness of the proposed method.