Reaching law for DSMC systems with relative degree 2 switching variable

Abstract

This paper presents the first attempt to design a reaching law-based discrete-time sliding mode controller with a relative degree 2 switching variable. The current value of this variable is only affected by the control signal and disturbance generated two time instants ago. It is demonstrated that the new reaching law-based strategy offers a smaller quasi-sliding mode band width when compared to a similar control scheme with relative degree 1 switching variable. This in turn leads to reduced system output error in the control system proposed in the paper.

Discrete‐time higher‐order sliding mode control of systems with unmatched uncertainty

“…Furthermore, it has been proved that discrete‐time higher‐order sliding mode (DHOSM) control has better smoothness as well as robustness as compare to the first‐order sliding mode . Therefore, DHOSM control has received increased attention of the control community . There are two major frameworks in designing higher‐order sliding mode for discrete‐time system.…”

“…Following the second framework, Sharma and Janardhanan defined the concept of DHOSM and designed a DHOSM control technique. Furthermore, a few DHOSM algorithms have also been reported …”

“…In spite of the increased utility of DHOSM controllers, the existing DHOSM control techniques are designed considering only matched uncertainty. These existing DHOSM control techniques are not suitable for the systems with unmatched uncertainty due to the following reasons.…”

“…23 Therefore, DHOSM control has received increased attention of the control community. 22,[24][25][26][27][28][29][30][31][32] There are two major frameworks in designing higher-order sliding mode for discrete-time system. The first is to discretize the existing continuous-time higher-order sliding mode algorithms to obtain their discrete-time version 24,25 ; however, the discretization of continuous SMC algorithm may lead to periodic phenomena and instability in the system.…”

The problem of state constraints in designing the discrete time sliding mode controller

“…Originally, the reaching law method was introduced for continuous time systems [19], and then developed for discrete time ones [20]. Recently, a large number of new reaching laws were presented [21][22][23][24][25][26][27][28][29][30].…”