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This paper investigates a tip angular position controller for a single-link flexible robot arm that considers the passivity of the flexible robot arm on the basis of a distributed parameter system. A Lyapunov function related to the total energy of the distributed parameter system is considered to derive a direct output feedback control law for the flexible robot arm. To achieve tip angular position control, the Lyapunov function is modified by potential energy shaping and dynamics extension. Computational simulations of control of the flexible robot arm confirm the feasibility of the derived controller.