H∞H∞ tracking adaptive fuzzy integral sliding mode control for parallel manipulators

Highly nonlinear coupling phenomenon is an inherently inevitable in parallel manipulators in which limbs/links undergo rotating and sliding with/without fixed base. In this paper, an H∞H∞ tracking adaptive fuzzy integral sliding mode control scheme is proposed for controlling parallel manipulators with nonlinear unmodeled dynamics, external disturbances, and limb-to-limb couples in which each coupled uncertainty is assumed to be bounded by an unknown gain. The dynamics of the parallel manipulator is formulated as an error dynamics according to a specified reference model; then, a fuzzy model is used to approximate the uncertainties. Two on-line estimation schemes are developed to overcome the uncertainties and identify the gains of the unknown coupled uncertainty bounds from limb-to-limb couples, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear uncertain functions with an on-line update law. By the concept of parallel distributed compensation (PDC), the adaptive fuzzy scheme uses an integral sliding mode control scheme to resolve the system uncertainties, unknown limb-to-limb coupled uncertainties, and the external disturbances such that H∞H∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB) and the effect on the tracking error can be attenuated to any prescribed level to achieve H∞H∞ tracking performance. Finally, a numerical example of a planar 2-dof parallel robot system is given to verify the effectiveness of the proposed control scheme.