**1. Introduction**

Electrical machines play an essential role in the industry and the development of society, they make up an efficient means of electromechanical conversion. The industrial modernization process increasingly requires the application of electric motors in drive systems, which often requires control of torque, acceleration, speed or position.

Variable speed drives are mainly used in applications, such as electrical vehicles, pumps, elevators, fans, ventilation, heating, robotics, ship propulsion, and air conditioning [1–3]. The benefits of squirrel-cage induction motors—high robustness and low maintenance—make it widely used through various industrial modern processes, with growing economical and performing demands [1,4].

Previously, the use of motors in industrial applications that required good performance in position and speed control were limited to DC machines. Such use was due to the inherent decoupling characteristics of the machine: one electrical circuit to impose magnetic flux on the machine (field) and another to impose torque (power), which simplifies the control of torque, position, and speed of the machine [5].

The advancement of power electronics, control theory, growth of studies in the field of microelectronics and the advancement of digital processor technology, allowed the efficient use of the electric motor in the activation of the most varied industrial loads, enabling the use of alternating current machines in applications of high dynamic performance [6,7].

Thus, the alternating current motor has become widely used in the industry since it presents characteristics such as robustness, low manufacturing cost, absence of sliding contacts and possibility of operating a wide range of torque and speed [8].

The scalar control technique is simple to implement. Although the constant voltage/frequency control method is the simplest, the performance of this method is not good enough [9–11]. Vector-based control methods enable the control of voltage and frequency

**Citation:** Gomes, R.R.; Pugliese, L.F.; Silva, W.W.A.G.; Sousa, C.V.; Rezende, G.M.; Rodor, F.F. Speed Control with Indirect Field Orientation for Low Power Three-Phase Induction Machine with Squirrel Cage Rotor. *Machines* **2021**, *9*, 320. https://doi.org/10.3390/ machines9120320

Academic Editors: Marcos de Sales Guerra Tsuzuki, Marcosiris Amorim de Oliveira Pessoa and Alexandre Acássio

Received: 27 October 2021 Accepted: 23 November 2021 Published: 27 November 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

amplitude unlike the scalar method. They also provide the instantaneous position of the current, voltage and flux vectors [12].

The dynamic behavior of the IM drives is also improved significantly using the vectorbased control method. However, the existence of the coupling between the electromagnetic torque and the flux increases the complexity of the control. To deal with this inherent disadvantage, several methods have been proposed for the decoupling of the torque and flux.

One difficulty of its use for position or speed control is its complex mathematical modeling, requiring greater computational effort for its implementation [5]. In addition, in induction machines there is no unique physical circuit for the field, and this makes its control more complex [13,14].

In Induction Machines (IM), the power phases of the machine each contribute to maintaining the concatenated magnetic flux of the machine and are thus coupled to each other through mutual inductances. To solve the problem of induction machine control, axis transformation techniques are used, which make it possible to transform the electrical and mechanical model of an induction machine so that the flux and torque of the machine can be controlled independently, known as field-oriented control or vector control [15].

The field-oriented control technique is widely used in high-performance motion control applications of induction motors. However, in real applications, accurate decoupling of torque and flux cannot be achieved with accuracy due to the uncertainties of the machine parameters present in the model. These uncertainties are associated with external disturbances, unpredictable parameter variations, and unmodeled nonlinear plant dynamics. Consequently, this deteriorates the dynamic performance of flux and speed significantly. In general, the performance of this technique is dependent on the accuracy of the mathematical model of the induction motor [16].

Field oriented control consists of concentrating the rotor flux on the direct axis of the synchronous reference system, thus achieving decoupling of the flux and torque loops, like DC machines. It is a highly computational technique that involves many mathematical transformations and requires powerful microcontrollers such as Digital Signal Processors (DSPs) and Digital Signal Controllers (DSC) [17].

In general, the field-oriented control performance is sensitive to the deviation of motor parameters, particularly the rotor time constant [7,18,19]. To deal with this problem, there are many fluxes measurement and estimation mechanisms in the published literature [18–21].

Speed information is required for the operation of vector-controlled IM drive. The rotor speed can measure through a mechanical sensor or can be estimated using voltage, current signals, and machine parameters [22,23]. The use of speed sensors is associated with some drawbacks, such as noise present in the measurement, requirement of shaft extension, reduction of mechanical robustness of the motor drive, not suitable for hostile environments and more expensive [24]. On the other hand, using the sensorless strategy reduces hardware complexity, reduces costs, elimination of the sensor cable, better noise immunity, higher reliability, and less maintenance requirements [22].

In this context, the work presents the design and commissioning steps of a three-phase frequency inverter for the activation of a small three-phase induction machine. In addition, the simulation and control of the machine will be addressed through the Indirect Oriented Field Control strategy (IFOC). In this work, the main components that make up the power circuit, current, voltage and speed measurement circuits will be presented. It is also presented the models used for the design of the current and speed controllers of the vector control and, later, the validation in the simulation environment and the experimental bench. In addition, in this work an encoder attached to the machine shaft is used to measure the position and speed of the rotor to prevent parametric variations and speed estimation errors from affecting the quality of the indirect field control. Also, the tests performed in this work are for lower speeds and without a load attached to the machine shaft.

The main contribution of this paper is to propose the design and commissioning of a low-cost converter to drive an induction machine using the indirect field control strategy with a sensor attached to the shaft.

The work is organized as follows: Section 2 will deal with the description of all the hardware used in the construction of the prototype. Section 3 will describe the dynamic modeling of the field oriented directly to the three-phase induction motor. Section 4 will describe the concepts related to Space Vector Pulse Width Modulation (SVPWM). Section 5 will display the tuning of the controllers for the current and speed loops. Section 6 is responsible for presenting the results obtained in the computational simulation as well as the practical tests performed in the prototype developed. Finally, Section 7 presents the conclusions of the work.
