Abstract: Based on the assumed mode method and the Lagrange equation, the dynamic model is developed for the flexible single-link robot manipulator with piezoelectric materials as collocated actuators and sensors bonded to its surface. The non-minimum phase inherent in the end-effector tracking control of the flexible manipulator may result in the instability of the system, so a combined PD feedback control law is designed by using the Lyapunov function, which takes the angle displacement of the rigid hub as the control output and suppresses the end-effector vibration of the flexible manipulator using piezoelectric patches. Simulation results show that the vibration of the end-effector is suppressed by applying a command voltage to the piezoelectric actuator patch while the trajectory is tracked by driving the rigid hub, and the control law is less complex in computation and can be practically implemented.

Key words: flexible manipulators, piezoelectric materials, trajectory tracking, vibration control