Modeling and control of a slewing nonlinear flexible arm with tip body

This paper deals with the nonlinear dynamic modeling and control of a slewing flexible arm with eccentric tip body. Both bending and torsion motion of the arm is allowed and the modeling preserves the kinematic nonlinearities of the maneuvering arm. Control is accomplished by a motor equipped at the base of the manipulator. The Lagrangian formulation is treated in deriving mathematical model which reveals to be nonlinear and to consist of one ordinary differential equation and two partial differential ones. Using the Lie theoretic approach and the boundary homogenization technique, the nonlinear system is partially linearized with its inhomogeneous boundary conditions transformed to homogeneous ones. By introducing an idea of equivalent linearization, positioning control incorporating both rigid motion control and vibration suppression is obtained in a feedback form. Finally, several numerical simulation results are presented to demonstrate the effectiveness of the proposed theory.