**1. Introduction**

Sliding mode control (SMC) is a commonly recognized robust control method. It is known to be independent on external disturbances [load torque in case of the induction motor (IM)] and internal changes (e.g., variation of motor parameters, due to heating). It can be successfully applied in control of all IM variables like flux, torque, speed and position [1]. However, it suffers from some characteristic negative features, such as steady-state and dynamical errors, chatter‐ ing and variable switching frequency.

Over the several past decades, researchers tried to eliminate or reduce the disadvantages of the sliding mode applied to the IM control. The steady-state speed control error has been eliminated using the sliding surface with an additional integral part in reference [2]. Integral

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part in the switching function has also been used to eliminate the dynamical and steady-state errors in the torque control [3].

Most of the papers focused on reducing the most negative feature of the SMC, i.e. chattering (large oscillations of controlled variables). Position control with adaptive continuous approx‐ imation of the sign function is proposed in reference [4]. Load torque estimator was introduced in reference [5] to reduce level of the discontinuous part of the control signal. One of the effective solutions to reduce the chattering is the application of higher-order sliding modes. They were introduced for all of the IM variables: torque in reference [6], speed (in a speedsensorless approach) in reference [7] and position in reference [8]. The IM drive control, supplied from a current source inverter with the second-order SMC is introduced in reference [9]. Integral SMC of stator current components is shown in references [10–12] to reduce the chattering.

One of the chattering sources is a discretization caused by digital implementations of the drives' control structures; therefore, the discrete SMC methods have been proposed. The IM position discrete control is proposed in references [13] and [14]. The discrete SMC of the IM speed is introduced in reference [15].

Another drawback of the SMC in a direct approach (when the control algorithm defines the transistors' control signals directly) is a variable switching frequency. In order to eliminate this phenomenon, a voltage modulator can be applied. The classical direct torque control (DTC), SMC and space vector modulation (SVM) were combined in references [16] and [17]. Similarly, the indirect field-oriented control (IFOC) method and SMC were combined in reference [18].

In the past years, there have also been the attempts to extend the robustness of the IM control over the reaching phase, not only the sliding phase. The proposed approaches can be divided into two groups. In the first one, the switching line (or a surface) is designed to include the starting point: for speed control in reference [2] and for the position control in reference [19]. The second group consists of the methods with time-varying switching lines. They have been applied mainly in the position control [20], but also for the speed control [21].

In this chapter, a comparative analysis of the SMC of all IM state variables is presented. Direct approaches that define the transistor control signals directly are described and illustrated with simulation and experimental results. The cascade connection of sliding mode controllers is proposed for speed and position regulation, presented in a unified manner. The equivalent signal-based control is used to lower the level of the chattering in regulated variables.

This chapter consists of nine numerated sections. The following section presents the mathematical model of IM. Next three sections show the control of IM variables: torque, speed and position, respectively. Sections related to the speed and position control are divided into two subsections that include the direct and the cascade control. After short conclusions section, there is an appendix with experimental setup description and tables with tested IM parameters and base values, necessary to obtain the normalized unit system.
