Output-feedback variable gain super-twisting algorithm for arbitrary relative degree systems

ABSTRACT

This paper presents an output-feedback control strategy based on the variable gain super-twisting algorithm. The proposal achieves robust global/semi-global exact tracking results for plants with arbitrary relative degree. This is ensured in spite of parametric uncertainties and disturbances that may be state-dependent and time-varying. The construction of such controller is based on a (non)homogeneous higher order sliding-mode differentiator with dynamic gains. The gain adaptation schemes for the controller and differentiator are based on norm observers to overcome the lack of state measurement. The continuous nature of the obtained control signal alleviates the chattering phenomenon. The stability properties of the proposed controller are demonstrated by means of a Lyapunov function-based analysis. The theoretical results are verified through a simulation example, and experimentally tested on a seesaw module.

KEYWORDS:

• Uncertain nonlinear systems
• variable structure systems
• higher order sliding-mode control
• exact differentiators
• output feedback
• global/semi-global stability

Acknowledgments

This work has been supported in part by CNP_q, FAPERJ and CAPES, Brazil.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Let {λ _i } be the eigenvalues of A _c , the stability margin of A _c is defined by ${\gamma }_0:={\min }_{\mathrm{i}}[-\mathrm{Re}\left({\lambda }_{\mathrm{i}}\right)]$.