Dynamic modeling and adaptive VSC of two-link flexible manipulators using a hybrid sliding surface

To suppress the resonance modes of flexible manipulator and to expedite the convergence, a hybrid sliding mode consisting of frequency shaped optimal sliding mode (FSOSM) and terminal sliding mode (TSM) is proposed and applied to two-link flexible manipulator, which is an extension of the authors' previous work (2000). An adaptive variable structure control (AVSC) is designed to estimate the upper bounds on the norm of uncertainties. The adaptation law generates a relatively small gain in the initial stage to reduce the impact to the system and a higher gain at the equilibrium to lower steady state error. Dead zone scheme is introduced to further improve system robustness. Attractiveness of the dead zone for the proposed AVSC is proven. Simulation results demonstrate the effectiveness of the proposed method.