In this paper we describe a new tracking control law for multijoint flexible-link manipulators. The scheme is a synthesis of the inverse dynamics solution for flexible manipulators developed by Bayo at UCSB and tracking control theory for rigid-link manipulators put forth by Bayard, Wen and others. We show that passive joint controllers, together with the feedforward of nominal joint torques corresponding to a desired end-effector trajectory, results in exponentially stable tracking control. Stability is proved (local to the desired trajectory) for a large class of passive controllers which include proportional and derivative controllers, and lead compensators. The proof is based on a simple Lyapunov analysis and the Positive-Real lemma.
Exponentially Stable Tracking Control for Multijoint Flexible-Link Manipulators
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Paden, B., Chen, D., Ledesma, R., and Bayo, E. (March 1, 1993). "Exponentially Stable Tracking Control for Multijoint Flexible-Link Manipulators." ASME. J. Dyn. Sys., Meas., Control. March 1993; 115(1): 53–59. https://doi.org/10.1115/1.2897407
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