Integral Sliding Modes with Nonlinear H∞ -Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances

Abstract

This paper presents a methodology for controlling nonlinear time-varying minimum-phase underactuated systems affected by matched and unmatched perturbations. The proposed control structure consists of an integral sliding mode control coupled together with a global nonlinear H∞-control for rejecting vanishing and nonvanishing matched perturbations and for attenuating the unmatched ones, respectively. It is theoretically proven that, using the proposed controller, the origin of the free-disturbance nonlinear system is asymptotically stabilized, while the matched disturbances are rejected whereas the L2-gain of the corresponding nonlinear system with unmatched perturbation is less than a given disturbance attenuation level γ with respect to a given performance output. The capability of the designed controller is verified through a flexible joint robot manipulator typically affected by both classes of external perturbations. In order to assess the performance of the proposed controller, an existing sliding modes controller based on a nonlinear integral-type sliding surface is also implemented. Both controllers are then compared for trajectory tracking tasks. Numerical simulations show that the proposed approach exhibits better performance.