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

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Thispaper treats the question of control of an elastic roboticarm of two links based on variable structure system (VSS)theory and pole assignment technique for stabilization. A discontinuous jointangle control law, based on VSS theory, is designed whichaccomplishes asymptotic decoupled joint angle trajectory tracking. In the closed-loopsystem, the trajectories are attracted toward a chosen hypersurface inthe state space and then slide along it. Although, jointangles are controlled using variable structure control (VSC) law, theflexible modes of the links are excited. Using center manifoldtheory, it is shown that the closed-loop system, including thesliding mode controller, is stable. Based on a linearized modelabout the terminal state, a stabilizer is designed using poleassignment technique to control the elastic oscillations of the links.A control logic is included which switches the stabilizer atthe instant when the joint angle trajectory enters a specifiedneighborhood of the terminal state. Simulation results are presented toshow that in the closed-loop system, accurate joint angle trajectorytracking, and elastic mode stabilization are accomplished in the presenceof payload uncertainty.


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