Robust discrete-time sliding mode control for tracking and model following of uncertain nonlinear systems

ABSTRACT

This paper proposes a discrete-time controller for robust tracking and model following of a class of nonlinear, multi-input multi-output, systems. For this purpose, a discrete-time sliding mode controller (DTSMC) is used to ensure the stability, robustness and an output tracking against the modelling uncertainties, even at relatively large sampling periods. In this way, Takagi–Sugeno (T–S) fuzzy modelling is used to decompose the nonlinear system to a set fuzzy-blended locally linearised subsystems. Implementation of the second Lyapunov theory for mismatched uncertain nonlinear T–S fuzzy models results in a set of linear matrix inequalities, which is used to design the sliding surface. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show that the proposed method guarantees the stability of closed-loop system and achieves small tracking error in the presence of parametric uncertainties at large sampling periods.

KEYWORDS:

• Nonlinear system
• Takagi–Sugeno fuzzy modelling
• mismatched uncertainty
• robust control
• output tracking and model following

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Behrooz Rahmani

Behrooz Rahmani is an associate professor of Mechanical Engineering at Yasouj University. He received his B.Sc. in Mechanical Engineering from Shiraz University, Shiraz, Iran, in 2001, his M.Sc. and Ph.D. in Mechanical Engineering from Iran University of Science and Technology (IUST), Tehran, Iran, in 2005 and 2011. His current research interests include distributed control systems, Networked control systems, sampled-data control, nonlinear control, active and semi-active control of vibrations, and control of distributed parameter systems.