**1. Introduction**

Nowadays, Brushless direct current (BLDC) Motors are extensively used because of their characteristics. Such characteristics are high dynamic response and high-power density. Usually, these kinds of motors are controlled employing an electronic inverter of commutation composed of three-phases. Typically for controlling these types of motors, a six-step commutation and a three-phase voltage source inverter are used, where the commutation of the inverter components is determined by the state of the Hall effect sensors. In recent years, works have been reported for speed control in this type of engine based on this scheme; such is the case of the work presented by Zhao et al. [1].

There have been considerable efforts in solving the soft computing approach to control brushless motors. The work developed by Shanmugasundram et al. [2] presents a comparison of control for a brushless motor using PID, fuzzy logic, and a hybrid of neural networks which show the effectiveness of these controllers such as speed response, steady-state error, among others. Arulmozhiyal and Kandiban [3] made a fuzzy PID controller in which they present the facility to tune the PID constants using the implemented fuzzy system. For their part, Premkumar and Manikandan developed a diffuse neuro controller, which had a higher performance than the other implementations tested [4]. In [5], Al-Maliki and Iqbal have also used a fuzzy Logic Control, but this time for tuning a PID controller. In addition, Mamadapur and Mahadev [6] implemented a PID for speed control of a BLDC motor but using Neural networks.

For their part, Liu et al. [7] developed a control strategy for these types of motors that consisted of the implementation of control through an adaptive neural network for current monitoring in this system. Ibrahim et al. [8] made a comparison between the Particle Swarm Optimization techniques

and the bacterial food search technique to determine the optimal parameters of a PID speed controller for a BLDC motor. In [9], an adaptive fuzzy logic for speed control of a BLDC motor was developed using ANN and PSO techniques. Potnuru et al. [10] used a pollination algorithm for speed control of a BLDC motor. Another work that implements a speed control for a BLDC motor can be found in [11], where an adaptive neural network with a fuzzy inference core was used. Templos-Santos et al. have used bio-inspired algorithms in order for parameter tuning of a PI controller in a Permanent magne<sup>t</sup> synchronous motor (PMSM) [12]. Merugumalla and Kumar [13] used the firefly algorithm to create a motor drive of speed control for a BLDC. One last work is that developed by ELkholy and El-Hay [14], and they have evaluated the efficient dynamic performance of BLDC motor using different soft computing approaches. It is worth mentioning that the works mentioned above use a sensing mechanism to give feedback to the control system, making this more elaborate and, in some cases, more costly to implement these methods.

More focused works concerning the control of direct current motors, beginning with the work of Yu et al. [15], who used a neural network to carry out adaptive control in a PMSM. For their part, Cheng et al. [16] made use of a radial neural network for the control of a brushless DC motor with excellent results. The fusion of neural networks with a diffuse system was presented by Abed et al. [17] to diagnose failures in the bearings of a BLDC engine. In [18], Luo et al. performed the control of a brushless motor using the adaptive dynamic surface control technique modeled by a neural network. Saleh et al. [19] used wavelet neural networks to implement a speed controller for a BLDC motor. Naung et al. [20] adjusted the parameters of a controller PI to control the speed of a BLDC motor through a neural network. In [21], Dynamic Neural Networks were used to develop an intelligent control for a BLDC Motor. Finally, let us mention the work of Ho et al., who implemented a driver for a DC motor through the use of neural networks [22].

In this paper, the main motivation to study the sensorless control of a BLDC motor is the use of neural networks.The above is due to the neural networks are a better way to recognize patterns from the sample of the system which going to be controlled. Therefore, when the control of a BLDC motor wants to be made, usually, the use of observators is necessary in order to estimate, mainly, the position of the motor. These observators replace the use of sensors but are very complicated to implement. For this reason, the use of any sensorless techniques for control or estimation of the parameters of the motor. For example, in [23], the five-phase induction of the motor was modeled by means of the short-circuit fault between turns and sensorless control strategy. In [24], König, Nienhaus, and Grassohave analyzed and modeled the current ripples generated by electromagnetic actuators to estimate the inductance and carry out sensorless monitoring of the device. On the other hand, Che et al. [25] implemented a sensorless speed control for an induction motor using the sliding modes method and genetic algorithms. Another kind of motor where the sensorless technique was used is the Permanent magne<sup>t</sup> synchronous motor. In the work of Wu and Zhang [26], sensorless speed control was developed for a PMSM using terminal sliding mode and backstepping. In [27], Aguilar et al. implemented a sensorless speed tracking controller for a PMSM based on a second-order sliding mode observer and tested with load variations. Meanwhile, Kivanc and Ozturk have developed a position sensorless speed control for PMSM by means of a space vector based on four switches and three phases inverter [28]. In [29,30], interesting studies about sensorless control of PMSM are presented using estimation methods and sliding mode observer.

Next, a couple of works where the sensorless and neural networks are combined will be mentioned. One of them is [31], where a sensorless speed system was implemented based on the reactive power-based model reference adaptive system speed estimator and adaptive neural network for a PMSM. In [32], a neural network was used for a sensorless control for a PMSM oriented tor wind energy conversion.

On the side of the BLDC motor, Sreeram [33] implemented a speed regulation control of a sensorless BLDC utilizing fuzzy logic and four-switch three-phase inverter. The development presented in [34], where the radial displacement of the stator is proposed as a mechanism to improve speed control for a BLDC drive in a sensorless way. In [35], Vanchinathan and Valluvan used the Bat algorithm to control in a sensorless way the rotor speed of the BLDC motor. A study comparative of different controller techniques is presented in [36], where a controller PI, an anti-windup PI, a fuzzy logic-based, and a fuzzy controller PI are compared to validate the performance of sensorless BLDC motor at different loads and speeds. Rif'an, Yusivar, and Kusumoputrohave proposed the use of the ensemble Kalman filter (EnKF) and neural networks to predict load changes and estimates of the disturbance by simulation of a sensorless BLDC [37].

Finally, other works that made use of non-invasive methods for sensing some physical variable or detect failures in motors will be next mentioned. In [38], the technique of Signal Analysis based on Chaos using Density of Maxima(SAC-DM) technique was applied in the diagnosis of failures of BLDC motors from sound signals. In addition, Medeiros et al. [39] used the SAC-DM to detect failures in BLDC motors. Meanwhile, other works are focused on detecting faults in induction motors based on the analysis of acoustic sound and vibration signals [40–42].

For this reason, in this work, the controlling brushless DC motor through neural networks and without the need for sensing is proposed. Solving this kind of problem is essential since it is not always easy to have a sensor for the different internal parameters of a motor in order to control such parameters, especially for a BLDC driver. In addition, the neural network utilized to solve the controller of this motor is implemented only with two-layer; then, the neural network is simple and easy to port into embedded hardware to generate a non-dependent computer system.

In order to show a generalized idea of the advantages of our implementation, the highlights of our work will be listed below:


The main novelty of our approach is found in the third item of the advantages previously presented, due to the vast majority of works about this topic and that use a neural network utilizing a big number of examples to train the neural network.

The implementation and the results obtained in various tests carried out are presented in the following sections—starting with Section 2, where the typical structure for brushless motor control is shown as well as its simulation in the PSIM software [43]. In addition, in Section 2, a brief review of the neural network and its architecture used is presented. The implementation of motor control and the training of the neural network are described in Section 3. Section 4 shows the tests and results of the motor control implementation through the neural network. Additionally, a comparison against the PID control is made in Section 4, too. In order to clarify some points about the results obtained in this work a discussion was added in Section 5. Finally, the conclusions of this work, as well as perspectives for its continuation, are presented in Section 6.

#### **2. Materials and Methods**

This section presents and explains the different methods and materials used to achieve the results in this paper. First, it is necessary to present a brief description of the brushless direct current just to contextualize the functioning of the motor. In the second part of this section, a general revision about the concepts of neural networks will be presented.

#### *2.1. Motor Brushless*

A brushless motor is an electric motor controlled by an electrical signal. This type of motor lacks any form of collector or sliding ring. The motor requires some form of alternating current to rotate, either from an alternating current (AC) power supply or an electronic circuit. These motors have certain advantages over brushed motors, which are ideal for robotics projects. Some advantages and disadvantages of this type of motors are presented below: Advantages:

