Minimum Ultimate Band Design of Discrete Sliding Mode Control

Abstract

The paper presents a generalized understanding on the dynamics of the sliding variable for discrete time sliding mode control systems via a fresh approach involving several bands in the space of the sliding variable. Using this analysis, controller parameters can be obtained once the ultimate band is chosen. It is shown that on choosing the least ultimate band, the control becomes non-switching and Gao's reaching law becomes identical to Utkin's reaching law. On other occasions, the ultimate band obtained using this approach is clearly less than that obtained in previous works using Gao's reaching law. The analysis is presented for both state feedback and multirate output feedback cases.

Design of funnel function‐based discrete‐time sliding mode control

“…In view of Assumption 1 and [17, 18, 21], ϖ owns a magnitude of the order O ( T 2 ) or O ( T 3 ). For the commonly used definitions, such as the QSM, the QSMD and the decrement band, please refer to [29]. The following two symbols, namely, Δ SS and Δ DD , are employed in this paper to denote the width of the QSMD and the boundary of the decrement band, respectively.…”

Sliding mode control for uncertain discrete‐time systems based on fractional order reaching law

“…The definitions of QSM, QSMD (ultimate band) and the decrement band can be found in [21,40]. Δ SS represents the width of the QSMD (ultimate band) while Δ DD denotes the boundary of the decrement band.…”

“…s(k) > Δ DD and s(k) < −Δ DD . Considering [21,40], |s(k + 1)| < |s(k)| is equivalent to s(k + 1) 2 < s(k) 2 .…”

Chattering-Free Reference Sliding Variable-Based SMC

“…e reaching law approach demonstrates relative law complexity, while ensuring a reduction of the control effort in comparison to Utkin's method and providing a specified ultimate band width. erefore, it has been an inspiration for countless later publications [21][22][23][24][25][26][27][28][29][30]. Some authors modified Gao's reaching law [21][22][23][24]; others proposed new reaching functions [25][26][27][28][29][30].…”