Int. J. Modelling, Identification and Control, Vol. 29, No. 2, 2018 127
Copyright © 2018 Inderscience Enterprises Ltd.
A novel sliding mode controller scheme for a class
of nonlinear uncertain systems
Jalel Ghabi
LARATSI, ENIM,
University of Monastir, Tunisia
and
Department of Electrical Engineering,
ISSATK,
University of Kairouan, Tunisia
Email: jalel.ghabi@yahoo.fr
Abstract: This paper considers a continuous sliding mode control for a class of nonlinear
systems with uncertainties including both parameter variations and external disturbances. Under
the framework of sliding mode and using the upper bounds of the uncertainties, the proposed
controller is derived to guarantee the stability of an overall closed-loop system and ensure
robustness against modelling errors, parameter uncertainties and external disturbances. As for
chattering elimination in sliding mode control, a boundary layer around the sliding surface is
used and the continuous control is applied within the boundary. Moreover, an extended schema
of a higher-order sliding mode controller is developed in this paper as another solution to avoid
the problem of chattering effect. Simulation results demonstrate the efficacy of the proposed
control methodology to stabilise an inverted pendulum, which is a standard nonlinear benchmark
system. The applicability of the proposed algorithm will be extended, via suitable modifications,
to the case of multivariable nonlinear systems with uncertainties of more general type, covering a
wide class of processes.
Keywords: nonlinear systems; uncertainty; sliding mode control; stability; robustness; inverted
pendulum; higher-order sliding mode.
Reference to this paper should be made as follows: Ghabi, J. (2018) ‘A novel sliding mode
controller scheme for a class of nonlinear uncertain systems’, Int. J. Modelling, Identification and
Control, Vol. 29, No. 2, pp.127–135.
Biographical notes: Jalel Ghabi received his Master in Automatic Control and Industrial
Computing from National Engineering School of Sfax (ENIS) in 2003 and PhD in Automatic
Control from National Engineering School of Monastir (ENIM) in 2009. Currently, he is an
Associate Professor at ISSATK, University of Kairouan. His research is related to sliding mode
control and robust predictive control of nonlinear uncertain systems.
This paper is a revised and expanded version of a paper entitled ‘A sliding mode controller
schema for nonlinear uncertain systems’ presented at the Third International Conference on
Automation, Control, Engineering and Computer Science (ACECS2016), Hammamet, Tunisia,
20–22 March 2016.
1 Introduction
Recently, sliding mode control (SMC) has received
considerable amount of researches in automatic control and
has found a number of industrial applications owing to its
good performance (Utkin and Chang, 2002; Utkin, 1992;
Levant, 2001; Edwards and Spurgeon, 1998; Young et al.,
1999; Rhif, 2014; Kolsi et al., 2015; Zarrabi et al., 2015;
Vaidyanathan et al., 2015; Yue and Zhang, 2016; Boujelben
et al., 2016). This approach is recognised as one of the
efficient tools to design robust controllers for complex high-
order nonlinear dynamic plants operating under uncertainty
conditions. In the continuous-time, SMC provides
invariance and robustness properties to uncertainties
including modelling errors and external disturbances (Utkin
et al., 1977; Utkin, 1984; Hung et al., 1993). This is
achieved by assuming that infinitely fast switching between
two different control structures is possible, and that the
uncertainties are bounded. SMC has other advantages as
well, like ease of implementation, fast dynamic responses
and good transient performance. Moreover, the dynamic
performance of a system under SMC method can be shaped
according to the system specification by an appropriate
choice of switching function.
SMC consists of two phases. The first phase is the
design of a sliding surface along which the process can slide
to find its desired final value. The second one is the
synthesis of the control law in such a way that any state
outside the sliding surface is forced to reach the desired
sliding manifold in finite time and stay on it. The control