Dynamic modeling and vibration control for a nonlinear 3-dimensional flexible manipulator

In this paper, the control design and stability analysis are presented for a 3-dimensional flexible manipulator system with input disturbances. To provide an accurate and concise representation of the manipulator's dynamic behavior, the flexible manipulator is described by a distributed parameter system with a set of partial differential equations and ordinary differential equations. Boundary control laws with disturbance observers are proposed to regulate orientation and suppress elastic vibrations simultaneously. The closed-loop stability is achieved through rigorous analysis without any simplification of the dynamics based on the Lyapunov direct method. Numerical simulations demonstrate the effectiveness of the proposed scheme.