# Simulation Study of Two Torque Optimization Methods for Direct Torque-Controlled Induction Motors
## 1 Introduction  
There are many applications that require high-performance Induction Motor (IM) drives such as electric vehicles, mine winders, high-speed elevators, machine tools, and other more sophisticated machines. These applications usually need speed-accuracy \(\leq\)0.5%, no less than 20:1 of wide-range speed control, and a speed transient response \(\geq\)50 rad/s [1; 2; 3; 4]. Fast, transient response and accurate torque control are key to achieving a high-performance drive. Three decades ago, direct torque control (DTC) was deemed the simplest, most accurate, and fastest torque control method for IM drives [5]. Additionally, the DTC algorithm does not depend on motor parameter variations [6; 7]. Nevertheless, conventional DTC has the main disadvantage of having a wide band of inverter switching frequency, despite constant torque and flux [8]. The nature of hysteresis controllers has caused this wide inverter switching frequency to occur when being used for flux and torque. The introduction of techniques using constant sampling helped to lead to the advancement of the DTC concept. Therefore, these techniques have replaced conventional analog hysteresis controllers. Accordingly, the inverter upper switching frequency is restricted. Different additions and changes to the concept and theory of DTC regarding constant sampling frequency have been proposed by many authors [9; 10; 11; 12; 13]. The fast torque response was not considered by these researchers [PERSON] and [PERSON] [14; 15]. There have been recent efforts to support the torque response of DTC in IM drives. [PERSON] [16] introduces a direct-torque-controlled (DTC) induction motor (IM) drive that employs feedback linearization and sliding-mode control (SMC). It is a useful and simple methodology, but has many disadvantages such as torque vibrations, huge chattering, and sonic noise [PERSON] [17] obtains an enhancement of SVM-DTC algorithm performance. This occurs when the super twisting, sliding mode speed controller is used rather than the PI speed controller. The optimal design selection of voltage vectors based on a fuzzy controller is introduced by [PERSON] [18]. Nevertheless, the algorithm shows a 43% decrease in torque ripple compared to discrete SVM-DTC [19]. An optimized dynamic over-modulation approach is suggested by [PERSON] [20] to achieve a fast torque response, which decreases the response time. The downside of this approach is a poor flux response and increased harmonic content due to the use of the over-modulation procedure. The model predictive control approach has been applied to IM drives with the help of DTC principles [21; 22; 23]. The basic concept of a model predictive control is to calculate the suitable inverter voltage vector by utilizing a predefined cost function. Though this approach successfully reduces the ripples in flux and torque, as well as the switching losses of the inverter, it requires a high computation time [24]. Moreover, it shows a negligible improvement in the system dynamics and an increase in the motor parameter's dependency. Artificial intelligence approaches have been applied to the DTC of IM drive systems [25; 26; 27] and adjusted hysteresis band techniques have been implemented for the DTC of IM drives [28]. It is well known that the optimal selection of the voltage vector has proven to provide a fast torque response for the IM drive [29]. Here, two optimization methods that modify the variable frequency DTC are introduced and compared. The proposed methods greatly improve the torque and speed dynamic performance against the traditional DTC technique. The methods involve constant sampling of the DTC and optimization for a fast torque response. Finally, the two proposed methods are derived, simulated using Matlab, and compared to the conventional DTC method. A new control algorithm is established to deliver a fast torque response and the effects of the motor parameter variations on the optimization processes are studied.