Nonlinear PD plus sliding mode control with application to a parallel delta robot

In this paper, a hybrid nonlinear proportional-derivative-sliding mode controller (NPD-SMC) is developed for the trajectory tracking of robot manipulators. The proposed controller combines the advantage of the easy implementation of NPD control and the robustness of SMC. The gains of PD control are tuned on-line in order to increase the convergence rate, whereas the SMC term is introduced to reject the external disturbances without requiring to know the system dynamics. The stability of the NPD-SMC is proved using Lyaponuv theorem, and it is demonstrated that the tracking error and the tracking error rate converge asymptotically to zero. Experiments are carried out on the parallel Delta robot to illustrate the effectiveness and robustness of the proposed approach. It is also shown the superiority of the NPD-SMC control over the NPD control and PD-SMC control.