New methodologies for adaptive sliding mode control

Abstract

This paper proposes new methodologies for the design of adaptive sliding mode control. The goal is to obtain a robust sliding mode adaptive gain control law with respect to uncertainties and perturbations without the knowledge of uncertainties/perturbations bound (only the boundness feature is known). The proposed approaches consist in having a dynamical adaptive control gain that establishes a sliding mode in finite time.. Gain dynamics ensures also that there is no over-estimation of the gain with respect to the real a priori unknown value of uncertainties. The efficacy of both proposed algorithms is confirmed on a tutorial example and while controlling an electropneumatic actuator.

Adaptive Continuous Higher Order Sliding Mode Control

“…In Utkin & Poznyak (2013a) knowledge of both a 0 and a 1 are required (as is the polarity of the disturbance signal -which is not allowed to change). Also the dual-layer nested adaptive architecture involving k(t) and r(t) is clearly quite different from the schemes proposed in Plestan et al (2010). …”

“…A recent overview of this field is given in Utkin & Poznyak (2013a). The creation of new Lyapunov functions for higher order sliding mode control structures -particularly twisting and super-twisting controllers -has also rejuvenated interest in this area (Moreno & Osorio (2008)) and the literature expanding these Lyapunov ideas into the realm of adaptive sliding mode control is developing rapidly (Plestan et al (2010); Alwi & Edwards (2013); Shtessel et al (2012); Bartolini et al (2103); ). Whilst it is intuitively clear that when sliding begins to deteriorate the controller gains must be increased, devising an effective way of lowering unnecessarily large gains once sliding is achieved, has proved more elusive.…”

“…This trade-off has motivated research in what could be described as 'adaptive sliding mode control' whereby the gains in the controller, representing bounds on the uncertainty, attempt to adapt to a level where they are as small as possible and yet guarantee sliding is maintained. This research area has a long research history and key papers in this area are (Huang et al (2008); Plestan et al (2010)). A recent overview of this field is given in Utkin & Poznyak (2013a).…”

Adaptive continuous higher order sliding mode control

“…The approach is based on a novel dual layer nested adaptive scheme which is quite different to the existing schemes proposed in the sliding mode literature (Plestan et al (2010); Utkin & Poznyak (2013a)). The scheme allows the magnitude and rate of change of the controller parameters to adapt whilst guaranteeing a sliding motion.…”

Fuzzy Sliding Mode Observer with Grey Prediction for the Estimation of the State-of-Charge of a Lithium-Ion Battery

“…In this method, without the knowledge of uncertainty bounds, the gains of SMO are adjusted according to the tracking error of the battery voltage. Nevertheless, there is an over-estimation problem that the adjusted gains are unnecessarily large with respect to the upper bound of uncertainties [17,18].…”