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Abstract
In this paper the control of flexible joint manipulators is studied in detail. The model of N-axis flexible joint manipulators is derived and reformulated in the form of singular perturbation theory and an integral manifold is used to separate fast dynamics from slow dynamics. A composite control algorithm is proposed for the flexible joint robots, which consists of two main parts. Fast control, u f, guarantees that the fast dynamics remains asymptotically stable and the corresponding integral manifold remains invariant. Slow control, u s, consists of a robust PID designed based on the rigid model and a corrective term designed based on the reduced flexible model. The stability of the fast dynamics and robust stability of the PID scheme are analyzed separately, and finally, the closed-loop system is proved to be uniformly ultimately bounded (UUB) stable by Lyapunov stability analysis. Finally, the effectiveness of the proposed control law is verified through simulations. The simulation results of single- and two-link flexible joint manipulators are compared with the literature. It is shown that the proposed control law ensures robust stability and performance despite the modeling uncertainties.