Sliding Mode Boundary Control for a Planar Two-link Rigid-flexible Manipulator with Input Disturbances

This paper investigates the robust control problem for a planar two-link rigid-flexible coupling manipulator, whose input torques are influenced by bounded disturbances. A nonlinear partial differential equation (PDE) model which only contains measurable states in the boundary conditions is developed and based on this model, and a sliding mode control (SMC) scheme is proposed to realize joint angles reaching desired value, flexible vibration suppression and anti-interference. To overcome the difficulties brought by the inherent nonlinearity of the PDE and controller, the existence and uniqueness of the solution for the closed-loop system are proven by the Galerkin approximation sequences. The numerical simulations demonstrate the validity and effectiveness of our control design.