## 1 Introduction  
Electric motors have various uses in modern life, such as in household appliances, manufacturing, and transportation [1; 2; 3; 4]. The permanent magnet synchronous motor (PMSM) is one of the numerous types of electric motors and has a high performance, strength, and torque. Therefore, numerous researchers have studied PMSMs; in particular, the control of PMSMs has attracted substantial attention. Field-oriented control (FOC) is the most frequently used strategy for PMSM control. Because the FOC scheme requires information about rotor positions, PMSMs are typically equipped with a sensor to read this parameter. However, for several reasons, the necessity to use a bulky sensor needs to be avoided to reduce production costs, eliminate reliability challenges, and minimize the effect of noise that can interfere with sensor performance; this method is called sensorless control. Research on sensorless control strategies can be divided into two categories: (1) control during the initial startup and at a low speed [5; 6; 7] and (2) control at a medium or high speed [4; 8; 9]. The high-frequency injection technique is typically used for low speeds, whereas the back-electromotive force (EMF) method is used for high speeds. Some research has suggested an alternative using artificial intelligence (AI) for sensorless control [10; 11; 12; 13; 14; 15; 16]. In 2003, [PERSON] et al., showed that neural networks (NNs) are limited by long computation times because NN performance is dominated by complex recursive computations [10]. As a subset of AI, machine learning (ML) has attracted attention due to its potential applications in many engineering disciplines, including powered electronics and motor drives. ML based on an artificial NN (ANN) offers several advantages, such as a distributed design that enables it to handle multiple inputs and outputs, the ability to recognize nonlinear systems, and the ability to learn, generalize, and adapt. These characteristics indicate that ML can be used for motor control. ANNs have been widely implemented for general motor control. In [11], [PERSON] used a radial-basis function self-tuning proportional-integral-derivative (PID) NN controller to control the velocity loop of a PMSM. [PERSON] and [PERSON] implemented a back-propagation NN (BPNN) training method to track the speed of a brushless direct-current (BLDC) motor [12]. In [13], a reactive power-based model-reference adaptive-system speed estimator and an adaptive neural network for a PMSM were used to construct a sensorless speed system. Previously, AI has been used to predict rotor positions. [PERSON] successfully used an ANN to estimate a rotor position angle; trapezoidal back-EMF information from a BLDC was employed as the ANN input [14]. In another study, the Scikit-learn computation software library was successfully used, along with two currents from the Clarke transform (\(I_{\alpha}\) and \(I_{\beta}\)) as inputs, to facilitate a simulation of rotor positions [15]. The AdaBoost algorithm and Scikit-learn software libraries require enormous computational resources. Moreover, [16] described a ML observer based on a back-propagation algorithm. The sensorless ML-based observer became interesting since it uses data from a well-running control process (data-driven) instead of a formula with specified motor parameters. A sliding mode observer, another type of observer, requires certain parameter values so that the mathematical process runs well [8; 9; 17; 18]. While ML-based observers do not require detailed parameters, the proposed ML model needs to be trained using data obtained from a motor control that has been running well [15; 16]. In [15; 16], training data acquired from signal sampling at various motor-speed control operation points were used. The methods provided a favorable response for constant speed control but had difficulty with speed transitions for some implementations.