Sliding mode control of uncertain fractional order systems with delay

ABSTRACT

This paper presents a sliding mode control (SMC) based framework to design a stabilizing controller for uncertain fractional order time-delay systems (FOTDS) using the Lambert W function technique. This technique is exploited to design the fractional order (FO) sliding manifold which provides a constructive method to design an FO sliding manifold as compared to the other methods. A stabilizing switching controller is derived, that ensures the finite time reachability of the system trajectories to the sliding manifold for all subsequent time. Moreover, the conventional SMC technique can be readily applied to a particular class of FOTDS with delay free sliding mode dynamics obtained through a specific transformation. A Duffing oscillator is considered here to illustrate the proficiency of the proposed approach. Simulation results demonstrate the efficiency of the proposed method in the presence of time delay and uncertainty.

KEYWORDS:

• Sliding mode control
• fractional calculus
• Lambert W function
• delay

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Niraj Choudhary http://orcid.org/0000-0001-7595-9898

IndraNarayan Kar http://orcid.org/0000-0003-0277-1725