Global sliding mode with fractional operators and application to control robot manipulators

ABSTRACT

In this paper, a novel fractional-order global sliding-mode control scheme is presented. It is first used to stabilise a coupled second-order nonlinear system, and then it is generalised to control a class of multi-input and multi-output nonlinear systems with the model uncertainties and external disturbances. The proposed sliding manifold, which will converge to the origin in finite time by utilising a classical quadratic Lyapunov function, ensures global stabilisation of the system and the reduction of the chattering phenomenon during the control processes. Based on input-to-state stability and Lyapunov's stability theorem, the closed-loop system can be globally uniformly asymptotically stabilised to the origin in the future time. Some results about the control and stabilisation of integer-order nonlinear systems, when the fractional-order sliding-mode controller is used, are illustrated in this paper. Finally, an application to two-degree of freedom polar robot manipulator is provided to show the validity and feasibility of the proposed method.

KEYWORDS:

• Fractional calculus
• integer-order dynamical systems
• fractional-order sliding manifold
• input-to-state stable
• globally uniformly asymptotically stable

Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Nature Science Foundation [number 61573034], [number 61327807].