Discrete Time Sliding Mode Control

Abstract

This chapter discusses the concept of discrete-time sliding mode control (DTSMC) and its design procedure. It also covers how the states are brought to a predefined sliding surface mathematically and kept in a region near to the surface within a small band. This band is termed as an ultimate band in the field of DTSMC, which denotes the degree of robustness. Researchers have been working to find out different approaches to reach to that surface, but the most promising and welldefined way is reaching law approach. The idea of reaching law is discussed briefly in this chapter with examples for better understanding of the design procedure. In this chapter, a small introduction of continuous time sliding mode control (CTSMC) is given. Finally, the current state of the art is presented.

Frequency Criterion for the Existence of Sliding Processes in Control Systems with an Arbitrary Variable Structure

“…In recent years, many works have been published on sliding processes in automatic control systems [6][7][8][9][10][11][12][13][14]. These works use methods similar to the equivalent control method [5][6][7] or the second Lyapunov method [8,9].…”

“…In recent years, many works have been published on sliding processes in automatic control systems [6][7][8][9][10][11][12][13][14]. These works use methods similar to the equivalent control method [5][6][7] or the second Lyapunov method [8,9]. The results of these calculations are most often quite difficult to apply in real control systems, particularly in electromechanical control systems.…”

“…The frequency condition simultaneously analyzes processes both in the low-frequency zone-slow, and in the high-frequency zone-fast, i.e., an engineering criterion can be created that describes all the parameters of sliding processes [7][8][9].…”

“…The control object simultaneously contains several inertial links with small time constants, except for the second-order integrating link. In this case, it is quite difficult to accurately determine the sliding trajectory equation using an equivalent control method [1][2][3][4][7][8][9]. Experiments have shown that for such a system, cross-coupling based on the control signal of the electric drive-the control signal or the voltage at the motor armature-will be effective.…”

Extended Discrete-Time Quasi-Sliding Mode Control for VTOL UAV in the Presence of Uncertain Disturbances

“…This approach is widely implemented in many practical settings in the continuous-time domain by forcing the states to follow desired sliding surface [19], [24]. SMC was developed to handle uncertainties in the discrete-time domain in [32]. However, this technique has chattering problems due to the presence of a signum function in the control structure.…”