On Discretization of Continuous-Time Terminal Sliding Mode

Abstract

Abstract-In terminal sliding-mode control, the system states are brought to the origin in finite time using the concept of sliding-mode control. Though the theory of terminal sliding mode is well studied for continuous time systems, a discrete-time terminal sliding mode concept has not been investigated. This note analyses the applicability of terminal sliding-mode control in the discrete-time framework and discusses the problems involved in the discretization of continuous-time terminal sliding mode. The note also suggests a method to approach the discrete-time terminal sliding-mode control problem.

Design of generalized terminal sliding mode control for second-order systems

“…where c > 0, 0 1 , p q < < and p and q are positive odd integers [3][4][5]. Although, the conventional terminal sliding surface (2) ensures finite time convergence, it is not the only one solution.…”

“…That is, asymptotic stability does not imply finite time convergence. However, finite time stabilization is very important in many industrial applications such as motor systems, power systems, robot manipulators, spacecraft systems, and so on; thus, there have been many recent studies on finite time stabilization [1][2][3][4][5][6].…”

“…It is well known that the SMC has the invariance property to parameter uncertainties and external disturbances. Recently, to obtain finite time convergence, terminal sliding mode control schemes have been studied actively [3][4][5]. The conventional terminal sliding surfaces have been designed with a power function whose exponent is a rational number with positive odd numerator and denominator.…”

Variable structure control for satellite attitude stabilization in elliptic orbits using solar radiation pressure

“…In this section, TSMC laws are developed for the proposed system based on [37][38][39][40][41][42]. The only difference between SMC and TSMC is design of sliding surfaces.…”

“…The state tracking error converges to zero in infinite time. Recently, a new terminal sliding mode control (TSMC) is proposed [37][38][39][40][41][42] for fast, finite time convergence, and precise tracking error. Nonlinear functions were introduced into the design of sliding surfaces in such a way that the tracking error could converge to zero in finite time.…”