A new approach for adaptive sliding mode control: Integral/exponential gain law

Abstract

This paper proposes a new approach for adaptive sliding mode controller (ASMC) designs. The goal is to obtain robust, smooth, and fast transient performance for nonlinear systems with finite uncertainties of unknown bounds and limited available inputs so that the phenomena of the slow response and the gain overestimation in most ASMC designs can be greatly improved. Sufficient and necessary conditions for the existence of a sliding mode in the ASMC designs are discussed. Based on the sufficient conditions, we introduce an integral/exponential adaptation law targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. An illustrative example and numerical simulations are performed to convey the discussed results.

On a new adaptive sliding mode control for MIMO nonlinear systems with uncertainties of unknown bounds

“…The newly obtained terms ‰ eq and eq are 'residual' uncertainties with unknown bounds. However, if the nominal values are sufficiently reliable (close to their actual values), the magnitudes of the new bounds for ‰ eq and eq are supposed to be smaller than those for ‰ and in (6). As a result, the control performance are supposed to be better as well.…”

“…While in conventional SMC design the bounds on system uncertainties have to be acquired a priori, the adaptive sliding mode controller (ASMC) is introduced to adaptively compensate for the perturbations of unknown bounds. The ASMC design for the ideal case has been discussed in [6]. This paper discusses the ASMC design for nonlinear dynamic systems with time-varying uncertainties of unknown bounds under the real case.…”

“…These boundary-layer ASMC designs do not require a priori knowledge of the bounds of perturbations. However, the system response to perturbations is relatively slow; the overshoot is relatively large; and the chattering level is relatively high.Generally speaking, most ASMC adaptation processes consist of two phases: compensating phase where the switching gain increases its value until it completely compensates for the perturbations and the sliding variable reaches its maximum value, and the reaching phase where the sliding variable converges to the sliding surface (or to its immediate vicinity) [6,16]. Thus, the overall reaching time includes a compensating time and a converging time.…”

Regulation control of an underactuated mechanical system with discontinuous friction and backlash

“…The proposed control law is based on integral sliding mode and H ∞ control, and also an exponential reaching law is used in order to reduce the convergence time to the sliding surface. A previous work involving an integral/exponential gain law to absorb matched perturbations is that by Zhu and Khayati (2015). In contrast to the H ∞ controller used by Rascón et al (2016), in this work the authors proposed a sliding mode controller which includes an H ∞ control stage in the sliding surface; this controller is capable of handling matched and unmatched perturbations.…”

Robust nonlinear generalised predictive control for a class of uncertain nonlinear systems via an integral sliding mode approach

“…control law for nonlinear systems is quite mature in SMC (Wang, Zong, Dong and Tian 2015, Ullah, Han and Khattak 2015, Zhu and Khayati 2015, Ghafarirad, Rezaei, Sarhan and Mardi 2015, Park and Kim 2013. However, the use of ISMC guarantees good disturbance rejection performance from the initial time instance.…”