Integral Sliding Modes with Nonlinear H∞-Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances. (17th January 2017)

• Record Type: Journal Article
• Authors: Miranda-Colorado, Roger; Chavez, Carlos; Aguilar, Luis T.
• Other Names: Veluvolu Kalyana C. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2017(2017)
• Publication Date: 2017-01-17
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2017/4876019
• Languages: English
• ISSNs: 1024-123X

Abstract

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 L 2 -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.