Sliding Mode Control and Elastic Mode Stabilization of a Robotic Arm With Flexible Links

This paper treats the question of control of an elastic robotic arm of two links based on variable structure system (VSS) theory and pole assignment technique for stabilization. A discontinuous joint angle control law, based on VSS theory, is designed which accomplishes asymptotic decoupled joint angle trajectory tracking. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. Although, joint angles are controlled using variable structure control (VSC) law, the flexible modes of the links are excited. Using center manifold theory, it is shown that the closed-loop system, including the sliding mode controller, is stable. Based on a linearized model about the terminal state, a stabilizer is designed using pole assignment technique to control the elastic oscillations of the links. A control logic is included which switches the stabilizer at the instant when the joint angle trajectory enters a specified neighborhood of the terminal state. Simulation results are presented to show that in the closed-loop system, accurate joint angle trajectory tracking, and elastic mode stabilization are accomplished in the presence of payload uncertainty.