Stability analysis and robust composite controller synthesis for flexible joint robots

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 perturbations, and the 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, which guarantees that the fast dynamics remains asymptotically stable, and the corresponding integral manifold remains invariant. Slow control, u_s, itself consists of a robust PID design based on the rigid model, and a corrective term designed based on the reduced flexible model. The stability of the overall closed loop system is proved to be UUB stable, by Lyapunov stability analysis. Finally, the effectiveness of the proposed control law is verified through simulations. It is shown that the proposed control law ensures robust stability and performance, despite the modeling uncertainties.