## 1 Introduction  
Modern motor control methods are those that provide the power supply to the motor through a power converter that allows for the regulation of the supplied voltage and frequency. Induction motors can be viewed as complex nonlinear control systems, and there are mainly three control strategies: scalar control or V/F control, where the manipulated variables are the magnitude and frequency of each voltage or current supplied to the stator; the field oriented control (FOC), which allows one to regulate the electromagnetic torque generated by the motor; and modern control, which regulates all the states of the nonlinear or linear plant [1]. Some examples of scalar control applied to induction motors include ref. [2], where the control was implemented on the Compact RIO control board 9074, which was used along with a static frequency converter to supply the three-phase asynchronous motor with a squirrel cage rotor. Additionally, a fuzzy logic controller was developed in LabVIEW software for speed regulation, and its performance was compared to the speed control with a PI control. In ref. [3], simulations and experimental results were provided by applying a dual-mode adaptive robust controller to control the angular shaft speed of a three-phase induction motor. A microcomputer received the rotor speed using a tachometer, and Hall effect sensors were used to measure the currents of two phases of the motor. In ref. [4], LabVIEW software: [[https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464](https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464)]([https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464](https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464)) 9 bdb7a1929e989190 bd.pdf, accessed on 8 April 2024 running on a field programmable gate array, was used to design a V/F control. A general purpose inverter controller was used to control the speed of the induction motor with a pulse width modulation technique. MATLAB/Simulink, [[https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464](https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464)]([https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464](https://studyatncepu.ncepu.edu.cn/docs/2023-12/d52f754070464))9 bdb7a1929e989190 bd.pdf, accessed on 8 April 2024 and LabVIEW tools were used for the simulations and experiments. With respect to the field oriented control (FOC), in ref. [5], an adaptive indirect FOC based on a rotor flux observer was presented. Rotor flux estimation was based on the backstepping technique using the integral of tracking errors. It was implemented in real time using a dSPACE DS1104R&D board with a TMS320F240 digital signal processor and ControlDesk software: [[https://www.sciencedirect.com/science/article/abs/pii/S08883](https://www.sciencedirect.com/science/article/abs/pii/S08883)]([https://www.sciencedirect.com/science/article/abs/pii/S08883](https://www.sciencedirect.com/science/article/abs/pii/S08883)) 27017303801, accessed on 6 February 2024 for the control of the load torque and rotor speed of the 3 kW induction motor. In ref. [6], motor speed control via the FOC approach was synthesized, and constant flux control of a three-phase induction motor was calculated. It was performed using the discrete linearized three input-three output model (stator angular frequency, two components of the stator space voltage vector-rotor angular speed, and two components of the stator space flux linkage). Furthermore, a robust optimal preview control was proposed. The simulation and experimental results were presented using a dSpace DS 1104 control board. Focusing on the developed advanced modern control techniques for three-phase induction motors, in some works, including ref. [7], a quasi-linearization approach was presented that converts the nonlinear optimal control problem of a three-phase induction motor (modeled as a third order nonlinear model) into a sequence of linear quadratic optimal control problems. The simulation results are presented. In ref.