Principles and Methods of Servomotor Control: Comparative Analysis and Applications

Abstract

Servomotors have found widespread application in many areas, such as manufacturing, robotics, automation, and others. Thus, the control of servomotors is divided into various principles and methods, leading to a high diversity of control systems. This article provides an overview of types of servomotors and their basic principles and control methods. Principles such as digital signal processing, feedback control principle, field-oriented control, and integration with Industry 4.0 are discussed. Based on these control principles, the article presents popular control methods: PWM control, current control, two-loop control, fuzzy-logic control, and programmable control. The article concludes with a comparison of the presented methods on several criteria, and as an example, it includes the results of modeling a servomotor using the fuzzy-logic control method.

1. Introduction

Modern production cannot do without electric motors, which are used in various fields. Various types of electric motors are employed for diverse purposes, allowing for increased productivity, energy efficiency, and cost-effectiveness in any manufacturing process [1,2,3,4]. Thanks to motors, the possibilities of production are constantly expanding, enabling the use of more complex and advanced mechanisms, and creating new development opportunities. One way of advancing production is the use of robotic systems, where servomotors are directly employed [5,6,7].

Servomotors in robots are used to enhance the precision or smoothness of a mechanism’s operation, depending on the task it performs. Therefore, the control of drives must have a similar nature, enabling the achievement of the required goals. However, the more complex the drive control method, the more intricate the control system will be, leading to additional costs but at the same time enhancing production characteristics [7,8,9,10].

The control of servomotors has not only changed in recent years but continues to evolve, revolutionizing various industries, particularly robotics and automation. Initially, these motors were controlled using analog methods, but with the advancement of digital technologies, control has become more precise and versatile [11,12,13,14].

Various technologies for servomotor control are currently employed, including digital signal processing systems, feedback systems, field-oriented control, and control systems integrated with Industry 4.0. All these types of servomotor control are used to achieve different results, each having its own merits and drawbacks, which are discussed in these works [15,16,17,18,19,20,21].

This work is a general overview of the topic of servomotors, their devices and principles of operation, popular methods of control, and ways to expand existing and new control systems. It is worth noting that motor control is constantly evolving, allowing for the exploration of new control methods, such as the transition from analog to digital systems, from open-loop systems to feedback systems, and so on. The development of control systems enables the improvement of the efficiency, precision, and adaptability of motors in various industries, leading to the conclusion that new technologies will have more complex yet integrable solutions.

The second chapter of this article provides a description of the structure and operating principles of servomotors and discusses the main objectives of their use. The third and fourth chapters introduce the control principles mentioned above and outline some methods of controlling servomotors that are suitable for a specific type of control. The fifth chapter is a comparison of the presented types of control. The chapter does not provide experimental data but rather offers a comparative characterization based on previously conducted research.

2. Servomotors: Structure, Operating Method, Types, Main Characteristics

2.1. Structure and Operating Method

A servomotor is a type of electromotor, the shaft of which can be controlled with high accuracy. A shaft of a servomotor can rotate at the required angle or with constant rotational speed. Servomotors have become widespread in robotics for these properties [22,23].

A servomotor consists of a DTC motor, gearbox with shaft, and controller with necessary sensors (encoder, position sensor, etc.). A draft of the construction of a servomotor is presented in Figure 1.

The gearbox in servomotors is used to reduce speed and increase torque on the output shaft. A potentiometer or encoder is used to track the rotation angle or speed of the shaft, thus creating a closed-loop control system with feedback [23,24,25].

A popular method of controlling a servomotor is pulse-width modulation (PWM). This method is based on determining the angle of rotation or speed of the output shaft based on the pulse length at a given frequency. The use of PWM for controlling servomotors is based on the following principles [26,27,28]:

1.

PWM generates pulses of varying width (duration) with different periods.

$$\mathrm{D}=\frac{{\mathrm{T}}_{\mathrm{O}\mathrm{N}}}{{\mathrm{T}}_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}}}\times 100,$$

(1)

where D—pulse duration, T_ON—the ON time of the signal, and T_period—the total period of one PWM cycle.

$$\mathrm{f}=\frac{1}{{\mathrm{T}}_{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}}},$$

(2)

where f—PWM frequency.

2.

To control the speed of the servomotor, the width of the pulses is changed, allowing the regulation of the power supplied to the motor.

$$\mathrm{P}\mathrm{W}=\mathrm{D}\left({\mathrm{P}\mathrm{W}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{P}\mathrm{W}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right)+{\mathrm{P}\mathrm{W}}_{\mathrm{m}\mathrm{i}\mathrm{n}},$$

(3)

where PW—pulse width and PW_max and PW_min—the maximum and minimum pulse width supported by the servomotor.

3.

Control of the position of the servomotor is possible using feedback. To adjust the position, the voltage applied to the motor, after the PWM signal is converted, is compared to the desired voltage, resulting in a control signal.

$$\mathsf{\alpha }=\mathrm{D}\left({\mathsf{\alpha }}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathsf{\alpha }}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right)+{\mathsf{\alpha }}_{\mathrm{m}\mathrm{i}\mathrm{n}},$$

(4)

where α—angular position of the servomotor and α_max and α_min—the maximum and minimum angles of the servomotor.

4.

PWM is also used to regulate a smooth trajectory of movement from one point to another for the servomotor.

5.

In addition to PWM, PID controllers and microcontrollers are applied to enhance the efficiency of regulation and control.

This method has gained popularity due to its simplicity of implementation and low cost. PWM also provides high efficiency in speed and positioning control, making it applicable in applications requiring a high response to control input and precise control. Examples of such applications may include non-dynamic systems such as fans, pumps, or conveyors [29,30]. However, to achieve the best results, other principles of controlling servomotors are applied, which will be discussed below.

2.2. Servomotor Types

Currently, servomotors are divided into several types based on six different criteria: the type of motor used, the type of current, the type of construction, the function performed, the signal processing method, and the type of gearbox.

Based on the type of motor used and the type of current, servomotors are classified as synchronous or asynchronous, and using alternating or direct current, respectively. Considering that asynchronous motors are more powerful, this type of servomotor is produced only for alternating current. Synchronous motors have lower power but provide greater accuracy; in conjunction with direct current, they allow for achieving smaller motor dimensions and using this type of servomotor for autonomous mechanisms [31,32,33,34,35].

In terms of construction, servomotors are divided into brush motors, coreless motors, and brushless motors. Unlike brush motors, brushless models have a wider range of rotation speeds, allowing them to be used in processes requiring high-speed movement. However, controlling a brushless motor requires the presence of a PLC, regardless of the tasks it performs [33,36,37,38].

According to the function performed, servomotors are divided into two groups: maintaining a specified rotation angle or rotational speed. Based on the names, the first group of servomotors is used to bring mechanisms to the required position, such as locks, dampers, cranes, etc. The second group of servomotors is used to move objects in the working area and is employed in manipulators, various CNC machines, etc. Depending on the function performed, the main control parameter in the servomotor will differ: the motor’s rotation range or moment of inertia for the first or second group of motors, respectively [15,17,39,40,41,42].

In terms of signal processing, servomotors are divided into analog and digital motors. The main difference between these groups is the control principle. Analog motors use microchips, while digital ones use microprocessors. Due to technological advancements, digital servomotors have replaced analog ones due to their increased response speed to the control signal. Consequently, these servomotors have increased positioning accuracy and the ability to maintain a constant torque [43,44,45,46].

For example, in Figure 2, a servomotor used in a Hirata Cartesian robot (Hirata Corporation, Kumamoto, Japan) is depicted. It is a synchronous alternating current motor with the function of maintaining a constant rotational speed, as it is used to move the robot axis along the working area [47,48].

Motors with the function of maintaining a constant rotational speed are also used in laboratory setups of a digital twin of a wind generator [49], as well as in diagnosing damage to bearings [50,51] depicted in Figure 3a,b. Motor control is carried out using a frequency converter, allowing the selection of an appropriate motor control mode, adjustment of controller settings for different operating conditions, calibration of control to eliminate malfunctions, and more.

For example, in bearing fault diagnosis setup, discrete motor control is used to maintain a constant rotational speed. The use of a potentiometer to set an analog speed signal is not appropriate because there is a high probability of additional disturbances that would affect the rotational speed of the output shaft. For the digital twin setup of a wind generator, modeling methods are used, since, to maintain a constant rotational speed, the input speed signal is converted from a database stored in the cloud.

2.3. Servomotor Characteristics

The main technical characteristics of servomotors are as follows [18,52,53,54,55,56,57]:

• Torque (shaft force).
• Operating voltage.
• Rotational speed.
• Maximum rotational angle.
• Dimensions and weight.
• The torque indicates the rate of acceleration of the output shaft and its ability to overcome the resistance to the rotation of the load. The ability to realize the full potential of the servomotor is directly proportional to the torque.
• The rotation speed of the servomotor indicates the time it takes for the output shaft to turn by 60°. For example, a rotation speed of 0.07 s means that the servomotor shaft will turn by 60° in 0.07 s. The working voltage of the servomotor power supply affects both the rotation speed and the torque.
• The maximum rotation angle indicates the angle to which the output shaft of the servomotor can turn. In modern production, servomotors with continuous rotation are used, meaning that the maximum rotation angle is 360°. However, in some mechanisms, motors with smaller rotation angles, such as 120°, 180°, 270°, etc., are used.
• The dimensions of the servomotor affect the choice of the motor used to produce the mechanical structures in which they will be installed. This parameter is important for devices where speed, lightness, and compactness are crucial, such as drone models.
• Of the technical characteristics mentioned above, only three directly influence the control of servomotors: torque, rotation speed, and rotation angle. Depending on the selected control mode, the control parameter of the servomotor will differ.

For example, the main technical characteristics of the servomotor mentioned above are presented in

Table 1. The main technical characteristics of the Hirata Cartesian robot servomotor [47,58].

Characteristic	Value
Torque	2.4 Nm
Input (operating) voltage	116 V AC
Rotational speed	3000 r/min
Output power	0.75 kW

.

3. Basic Principles of Servomotor Control

As mentioned above, four main principles exist for controlling servomotors: digital signal processing, feedback control, field-oriented control, and integration with Industry 4.0.

3.1. Digital Signal Processing in Servomotors

Digital signal processing has allowed for the optimization of servomotor control, expanding boundaries in control methods and opening up new possibilities. Digital signal processing enables the limitations of analog control systems to be bypassed, thus laying a new foundation for more effective servomotor management. Based on [59,60,61,62], it is possible to identify the key aspects in the construction of this principle and draw conclusions about its advantages and disadvantages.

Key points in digital signal processing for servomotor control include:

• Precision control. Digital signal processing allows the use of advanced control algorithms that enhance control accuracy. This is achieved as digital controllers can receive, process, and respond to changes in input signals in real time, skipping many stages in tuning the control action.
• Adaptive control. Since servomotors operate in dynamic environments with changes in load and the occurrence of various errors, the principle of digital signal processing helps integrate adaptive control for servomotors. This type of control neutralizes disturbing influences in real time and adjusts control depending on new conditions, thus improving the performance and efficiency of servomotors.
• Noise filtering. In real production environments, servomotors are subject to interference and noise from other devices, production line structures, additional loads, etc. The principle of digital signal processing allows the identification and neutralization of noise to maintain the accuracy of the control signal at the required level.
• Network interaction and communication. The communication of servomotors within a unified system is facilitated by the principle of digital signal processing. Coordinating actions, adjusting control, and other networking capabilities enable synchronized control of servomotors in complex manufacturing processes, such as robotic technological lines.

However, along with the merits of digital signal processing, there are some drawbacks to this principle:

• Computational power. Implementing digital signal processing algorithms requires significant computational resources. To ensure real-time signal processing, it is necessary to accurately calculate the processing time and controller signal responses to fully realize the potential of the entire control system.
• Integration with existing control systems. Integrating control based on digital signal processing with other systems may pose challenges due to compatibility issues and the need for proper design of the control interface.

3.2. Feedback Control Principle in Servomotors

Feedback control systems are closed-loop control systems that compare the actual output signal with the desired one. Based on the difference between these values, they adjust the control settings, thereby changing the system’s behavior to minimize the deviation of the output signal. In the case of servomotors, feedback control systems provide a specified value for the position, speed, or any other output parameter of the motor. Based on [63,64,65,66,67], it is possible to identify the key aspects in the construction of this principle and draw conclusions about its advantages and disadvantages.

A feedback control system consists of the following components:

• Sensor. In the case of servomotors, encoders or potentiometers are mainly used to continuously track the speed or position of the motor’s output shaft.
• Controller. This is the part responsible for processing feedback signals and generating control actions through an integrated controller to the motor. Most control systems use a PID controller for its speed and minimization of output error.
• Desired output signal. This is the target value that the motor control system aims to achieve. Any parameter can be taken as the desired value, forming the basis for the control system.

The working principle of a feedback control system is quite simple and operates on a clear algorithm. The sensor continuously monitors the output value in real time and sends data to the controller. The error is then calculated by comparing the signals, and a control action is output. Using the controller and its components, a control signal is generated to minimize the deviation and increase the stability of the control system.

Advantages of feedback systems include:

• Accuracy. Continuous control of the output value allows feedback systems to achieve high levels of maintaining the desired output signal.
• Dynamic response. Feedback control systems provide a quick response to changes in load, disturbances, or noise, allowing servomotors to be used in changing conditions.
• Reduction in static error. The controllers used in these systems minimize static error and reduce the transient process time.
• Stability. The closed-loop control increases the overall stability of the control system.

3.3. Vector Control Principle in Servomotors

Vector control is a control method that allows the optimization of the control of alternating current (AC) motors and synchronous motors with permanent magnets. This control method uses an approach where the torque and current flux of the motor are separately considered. The main idea is to transform the three-phase current and voltage into a rotating coordinate system, aligning the magnetic flux with the rotor’s magnetic field. This enables independent control of the torque, leading to better dynamic response of the control system, reduced additional noise, and increased efficiency. Based on [68,69,70,71,72], it is possible to identify the key aspects in the construction of this principle and draw conclusions about its advantages and disadvantages.

The main components of the field-oriented control system are:

• Coordinate transformation. Vector control relies on transforming currents into a coordinate system using Park and Clarke transformations, simplifying the control task and optimizing the motor’s operation.
• Current control. Precise control of currents is crucial. Independent torque control allows for minimizing losses and improving efficiency.
• Use of PI controllers. Using controllers of this type helps reduce control errors, enhance responsiveness, and provide continuous support for the desired motor performance.

The key advantages of the vector control principle include:

• Improved dynamic response. Fast and accurate motor control enables instant dynamic response.
• Reduction of torque disturbances. This significantly reduces torque fluctuations, ensuring smooth motor operation.
• Increased efficiency. Optimization of motor currents and minimization of losses lead to improved overall motor efficiency.
• Increased power density. The design of more compact and lightweight servomotors with higher power can be achieved, making them suitable for use in limited spaces.

3.4. Integration with Industry 4.0 Principle in Servomotors

Industry 4.0 enables the use of smart technologies that alter the behavior of mechanisms in the industry, with servomotors being one of the key elements in smart technologies due to their provision of precision and efficiency. Thanks to integration with Industry 4.0, new opportunities have emerged in predictive management and seamless communication of production processes and mechanisms. Based on [16,73,74,75,76,77], it is possible to identify the key aspects in the construction of this principle and draw conclusions about its advantages and disadvantages.

The main points of integration with Industry 4.0 are:

• Internet of Things (IoT) connectivity. Servomotors connected to Industry 4.0 are part of a unified Internet of Things network. This connection allows real-time monitoring of motor conditions, collecting a wealth of data such as operational parameters, temperature, vibration, etc.
• Data analysis and predictive maintenance. Modern methods of data analysis allow the collection of data streams from servomotors into a unified database. This systematic organization of data enables the prediction of motor behavior and planning maintenance and repairs, thus avoiding unjustified equipment downtime.
• Remote monitoring and control. Servomotors connected to Industry 4.0 can be remotely controlled. This is beneficial in large-scale manufacturing where engines are distributed over a large area, requiring remote control and monitoring of engine conditions for timely management adjustments without on-site intervention. Remote monitoring reduces delays and increases overall production efficiency.
• Standardization. The use of specific standards, such as Open Platform Communications Unfired Architecture (OPC UA), facilitates the integration of servomotors into a unified network with other production components.
• Adaptive control. Integration with Industry 4.0 allows the development and use of flexible servomotor control systems. Control systems can adapt promptly to changing conditions and respond to disturbances, thereby reducing setup time and downtime.
• Energy efficiency. By connecting servomotors to a unified network using Industry 4.0 protocols, it is possible to reduce the energy consumption of production and optimize processes to use a more logical distribution of energy resources.

4. Control Methods of Servomotors

According to the principles of servomotor control outlined above, the basic common control methods are distinguished: PWM control, current control, two-loop control, fuzzy-logic control, and programmable control. PWM control has been described earlier in the article; it should be noted that this type of control is based on the principle of digital signal processing, allowing control of the position, speed, and trajectory of the output shaft of the servomotor.

4.1. Current Control

Current control, also known as torque control, is based on changing the current in the windings of the servomotor. This method allows precise regulation of the torque on the motor shaft because the current magnitude is proportional to the torque. Current control, which provides high accuracy in torque control, is suitable for applications where load control is required, as well as the need for overload protection. Examples of such applications include systems where maintaining stable control is important, such as industrial robots and autonomous motion systems [78,79].

The basis of current control is the principle of feedback and regulation. Feedback on the current is applied to the servomotor, the current is measured in the windings, and the value is sent to the controller for comparison with the set value (Equation (5)). When the measured value deviates from the set value, the regulator generates a control signal for the power amplifier. The power amplifier, in turn, adjusts the voltage on the motor windings to bring the current value to the desired level [80,81].

$$\mathrm{e}={\mathrm{I}}_{\mathrm{s}}-{\mathrm{I}}_{\mathrm{m}},$$

(5)

where e—deviation error, and I_s and I_m—the set and measured value of the current.

The regulator in this type of control method consists of three parts and their combinations: proportional, integral, and differential.

The proportional component uses the following equation for increasing performance:

$$\mathrm{P}{=\mathrm{e}\mathrm{K}}_{\mathrm{p}},$$

(6)

where P—proportional control signal, and K_p—proportional coefficient.

The integral component uses the following equation for error elimination:

$$\mathrm{I}{=\mathrm{K}}_{\mathrm{i}}\int \mathrm{e}\mathrm{d}\mathrm{t},$$

(7)

where I—integral control signal, and K_i—integral coefficient.

The differential component uses the following equation for reducing the amount of overshoot:

$$\mathrm{D}{=\mathrm{K}}_{\mathrm{d}}\frac{\mathrm{d}\mathrm{e}}{\mathrm{d}\mathrm{t}},$$

(8)

where D—differential control signal, and K_d—differential coefficient.

The main advantages of this method include the following [82,83]:

• High precision in regulating torque.
• Quick response to changes. Current control allows easy adaptation to external changes.
• Energy savings. Efficient energy use is due to the adaptive properties of current control.
• Impact on positioning accuracy. Strict control of torque allows controlling the position of the shaft in the final position.

The main drawbacks of the method, which differ from other methods and negatively affect further development, are the requirements for the accurate measurement of torque and flux parameters and sensitivity to changes in motor parameters, namely inductance and resistance [82,83].

4.2. Two-Loop Control

Two-loop control connects feedback loops, typically consisting of positional and velocity loops. This method enhances the efficiency of motor control by ensuring precision in positioning and speed. Two-loop control allows a balance between system dynamics and control accuracy to be maintained, so the application of this control method is common in medical devices and automatic manufacturing lines.

The positional loop is designed to control the position of the servomotor’s output shaft and sets the direction of its movement to a specified point. A control signal for the electric motor is created by comparing the current position with the set position using a potentiometer. The control signal is generated to minimize positioning errors [42,84].

The velocity loop aims to stabilize the rotational speed of the servomotor’s output shaft. The feedback from the velocity loop measures the current rotational speed and compares it with the desired speed, calculated based on the positioning error from the positional control loop [42,84].

The mathematical apparatus of the two-loop control is dame such as current control. The difference between these two apparatuses is the amount of regulators used for each loop.

The advantages of two-loop control include the following [84,85,86]:

• Precision in positioning.
• Stability of the speed control system.
• Dynamic response. Interaction between both loops allows the servomotor control system to respond promptly to changes.
• Integration with other methods. A two-loop control-based system easily integrates with control systems based on other methods, such as field-oriented control.

The main drawback of two-loop control is the requirement for the precise tuning of the regulator coefficients in both loops. Achieving optimal control and stable system operation demands more complex mathematical calculations. However, the mathematical calculations required are much less than that of more advanced methods, such as FOC and fuzzy logic [84,85,86].

4.3. Field-Oriented Control

Field-oriented control (FOC), based on the vector control principle, is a method of controlling current and voltage in a servomotor, considering the direction of the magnetic field rotation. FOC supports system control dynamics and efficiency, which is suitable for high-performance systems and mechanisms with high precision. Examples of applications may include CNC machines and laser cutting machines [72].

The field-oriented control method involves transforming the magnetic field into a rotating coordinate system known as the “d-q” system. The d-axis is aligned with the magnetic flux, while the q-axis is perpendicular to the d-axis. This transformation aligns the magnetic flux inside the motor along one axis, and the variable current is aligned along the other axis, which is the torque axis. Therefore, control is carried out based on the variable current [71,87].

The mathematical equation for Park transformation is:

$$\left[\begin{array}{c}{\mathrm{i}}_{\mathsf{\alpha }}\\ {\mathrm{i}}_{\mathsf{\beta }}\end{array}\right]=\left[\begin{array}{cc}\mathrm{c}\mathrm{o}\mathrm{s}\left(\mathsf{\theta }\right)& -\mathrm{s}\mathrm{i}\mathrm{n}\left(\mathsf{\theta }\right)\\ \mathrm{s}\mathrm{i}\mathrm{n}\left(\mathsf{\theta }\right)& \mathrm{c}\mathrm{o}\mathrm{s}\left(\mathsf{\theta }\right)\end{array}\right]\left[\begin{array}{c}{\mathrm{i}}_{\mathrm{d}}\\ {\mathrm{i}}_{\mathrm{q}}\end{array}\right],$$

(9)

where i_α and i_β—stator currents in fixed axes, i_d and i_q—stator currents in rotated axes, and θ—magnetic flux rotation angle.

The mathematical equation for Clark transformation is:

$$\left[\begin{array}{c}{\mathrm{i}}_{\mathrm{d}}\\ {\mathrm{i}}_{\mathrm{q}}\end{array}\right]=\left[\begin{array}{cc}\mathrm{c}\mathrm{o}\mathrm{s}\left(\mathsf{\theta }\right)& \mathrm{s}\mathrm{i}\mathrm{n}\left(\mathsf{\theta }\right)\\ -\mathrm{s}\mathrm{i}\mathrm{n}\left(\mathsf{\theta }\right)& \mathrm{c}\mathrm{o}\mathrm{s}\left(\mathsf{\theta }\right)\end{array}\right]\left[\begin{array}{c}{\mathrm{i}}_{\mathsf{\alpha }}\\ {\mathrm{i}}_{\mathsf{\beta }}\end{array}\right],$$

(10)

The feedback system measures the magnetic flux and then, using Park and Clarke transformations, converts them from the stator coordinate system to the rotating d-q coordinate system. The use of a PI controller in a field-oriented control system allows maintaining the specified flux for each axis. The Clarke transformation is used to create d-q coordinates, and the inverse Park transformation is used to transform the currents back into the stator coordinate system [71,87,88].

The equations for motor voltage and torque are as follows:

$${\mathrm{T}}_{\mathrm{e}}=\frac{3}{2}\mathrm{p}\left(\mathsf{\psi }{\mathrm{i}}_{\mathrm{q}}+\left({\mathsf{\psi }}_{\mathrm{m}}-\mathsf{\psi }\right){\mathrm{i}}_{\mathrm{d}}\right),$$

(11)

$${\mathrm{V}}_{\mathrm{e}}={\mathrm{R}}_{\mathrm{s}}{\mathrm{i}}_{\mathrm{s}}+{\mathrm{L}}_{\mathrm{s}}\frac{\mathrm{d}{\mathrm{i}}_{\mathrm{s}}}{\mathrm{d}\mathrm{t}}+{\mathrm{e}}_{\mathrm{s}},$$

(12)

where V_s—stator voltage, R_s—stator resistance, L_s—stator inductance, i_s—stator current, p—number of pole pairs, ψ—rotor flux, ψ_m—maximum rotor flux, T_e—electromagnetic torque, e_s—back EMF.

Advantages of the field-oriented control method [71,87,88]:

• Precision control. This method allows for increased precision in controlling both the torque and speed of the servomotor.
• Low noise and vibration levels. FOC reduces mechanical and electrical noise in the operation of the servomotor.
• High energy efficiency. The method reduces losses and allows for increased energy utilization efficiency.

The development of FOC faces two of its most significant drawbacks: complexity of implementation and sensitivity to motor parameters. The more complex the mechanism control system, the more difficult the algorithm implementation and the more precise the behavior model should be. In turn, changes in motor parameters lead to the revision of the entire control algorithm [71,87,88].

4.4. Fuzzy-Logic Control

The use of fuzzy logic in servomotor control allows for optimizing and adapting the motor control system to changing input conditions. Fuzzy-logic control primarily provides flexibility and adaptability in conditions of fuzzy tasks and a lack of complete data. Accordingly, fuzzy logic finds its application in applications with variable loads, mechanisms operating in a changing environment, and robotic systems. Fuzzy logic-based control is built on the following stages [89,90,91]:

• Identification of input conditions: In the case of a servomotor, the input variables are typically the position or speed of the output shaft.
• Definition of fuzzy rules: Creating fuzzy sets with different degrees of membership for each input variable and establishing rules that link the conditions into a unified system.
• Fuzzy logical inference: Applying the defined rules to each input value.
• Aggregation: Combining the applied rules to determine the control action.
• Defuzzification: Converting the overall control action rule into a specific value that is then applied to the servomotor.

Although fuzzy logic does not require an exact mathematical model, tuning this method is quite labor-intensive. The development of the method is also influenced by the difficulty of predicting its behavior under different conditions and achieving optimal performance without loss of computational efficiency [89,92].

Considering that for fuzzy logic there is no need to use special and accurate mathematical models, the structure of the algorithm can be illustrated as in Figure 4.

Unlike binary logic, where variables are divided based on the values of true or false, fuzzy logic determines the degree of membership of a variable to 0 or 1. The use of this type of control allows for adapting the control system to operate in changing conditions, even under the influence of various stochastic disturbances such as changes in load, detection of mechanical errors, etc. Fuzzy logic control is effective in situations where predicting the behavior of the mathematical model of the system is challenging, and there is no possibility of its precise determination [89,92].

Such systems include digital twins, which, when working with real-world objects, have a significant degree of uncertainty. Therefore, the adaptability of a control system based on fuzzy logic is an ideal solution for managing a digital twin and can also serve as a tool for creating a multitasking control system.

4.5. Programmable Control

Programmable control of a servomotor is based on the use of specialized software and external controllers to manage the speed, positioning, and torque of the motor. This method is associated with the principle of integration with Industry 4.0. Programmable control, depending on the task, provides adaptive control and tuning, allowing integration with other control systems. Accordingly, this method of servo motor control finds its application in automated production control systems and robotics [93,94,95].

By using an external controller, programmable control allows a range of desired positions to be defined through corresponding commands and supports various motion variations, such as smooth start and stop, acceleration profiles, maintaining constant speed or torque, and so on [81,96].

The use of feedback in the programmable control system is essential, and the feedback can be either incremental or absolute. Measuring the position or rotational speed of the servomotor’s output shaft allows for a clearer response to errors that may occur during positioning and a smooth response for their elimination. The flexibility of control is also supported using different coordinate systems (including relative or external) [97,98,99].

Interaction with other devices in the control system through the software method is ensured by using various protocols, such as EtherCAT, Modbus, etc. Additionally, the software method allows the creation of Supervisory Control and Data Acquisition (SCADA) systems for interaction between machines and humans. The use of different programming languages, as well as proprietary servomotor libraries, allows optimizing costs for control and integration of the motor into existing control systems [100,101,102,103,104].

Programmable control, based on its features, has such drawbacks as programming complexity and implementation due to the presence of many disparate control systems, and depending on computational power, there may be a loss of real-time performance. It is also worth noting that this method is the only one among all those analyzed in this paper that requires constant debugging and maintenance of all involved systems.

Programmable control is illustrated using the example of a digital twin of a wind turbine, presented at the beginning of the article. This method is ideal for integrating multiple different interfaces into a unified system and enables the quick analysis of input data from various sources, making it a versatile approach to software methods.

4.6. Other Modern Methods

In addition to the methods of servomotor control discussed above, there are new methods emerging that have not yet gained widespread use in industrial, robotics, and other fields, and therefore are not considered in comparison with the presented methods. However, it is worth noting that modern servo motor control methods are a very promising direction in the development of control systems. Such methods include Model Predictive Control (MPC), Neural Network Control (NNC), piecewise linear control, and others.

MPC is a control method where the use of an accurate mathematical model of a mechanism or process can create a behavior model and determine performance criteria in advance [105]. This control finds its application in areas where control of systems with delays or variable characteristics is necessary, such as chemical production and long-acting robotic systems [106,107]. However, even though MPC allows optimization of system performance based on the desired criteria, the computational power of this method remains a significant downside that limits its proliferation. Creating a complex mathematical model, as well as computing the optimal solution at each time step, is a challenging task for most mechanisms and productions [21,108].

NNC is a control method that uses neural networks and principles of artificial intelligence to approximate nonlinear control functions and the mathematical model of the process. This type of servo motor control is used in systems where it is impossible or difficult to create an accurate mathematical model, such as multi-level autonomous control systems [109,110]. This method resonates with fuzzy logic-based control methods and possesses similar positive qualities such as flexibility, adaptability of control, and the ability to react quickly to external influences [111]. However, unlike fuzzy logic, training a neural network requires a huge amount of data and resources, as well as a significant amount of time, which is an obstacle in the real world where fast decision-making based on unexplored data is required.

Piecewise linear control of servo motors is a control method that allows the motor control curve to be divided into separate linear segments to achieve control points with sufficiently high precision [112]. This method is characterized by its simplicity of implementation and discretization of control space, with each control segment having its own characteristics. This method is an optimal solution where the use of complex algorithms is too costly and the number of computational resources is significantly limited [113,114]. However, this method is quite a specific solution and has many limitations when applied to solving complex and dynamic tasks [115].

5. Comparison of Servomotor Control Methods

Comparison of servomotor control methods may vary to some extent for each technical solution; therefore, this work proposes a general comparison based on several parameters: speed, accuracy, adaptability, energy efficiency, popularity, ease of implementation, and material resource costs. These are general indicators that can be used to assess the effectiveness of the presented control methods and choose the most suitable one for a specific case.

Each characteristic plays a key role in building a control system and is evaluated on a five-point scale:

• Speed is necessary to evaluate the responsiveness of the control system to incoming disturbances and changes in input parameters (1—low speed, 5—high speed).
• Accuracy is the primary parameter for systems based on positioning (1—low accuracy, 5—high accuracy).
• Adaptability is responsible for the degree of adaptability of the control system to changing conditions (1—low flexibility, 5—high flexibility).
• Energy efficiency indicates the amount and quality of consumed energy (1—increased energy consumption, 5—low energy consumption).
• Popularity not only indicates the degree of method dissemination in the industry but also access to reliable information on creating a control system based on a particular method (1—low popularity, 5—high popularity).
• Ease of implementation is important for assessing the complexity of developing and maintaining the created control system (1—easily implemented, 5—difficult to implement).
• Material resource costs influence the economic factor of developing a control system, its costliness, and payback period, considering efficiency and performance aspects (1—high costs, 5—low costs).

A visual comparison of characteristics is provided in Figure 5.

As seen from the comparison, the most popular and energy-efficient method today is the programmable control of servomotors. However, the simplest to implement is PWM control, and in terms of adaptive control, fuzzy logic algorithm is considered. In terms of accuracy, three control methods stand out: two-loop control, FOC, and fuzzy logic control. In summary, when choosing a method for servomotor control, it is advisable to consider the initial characteristics of the desired control, i.e., to select control parameters that bear greater responsibility for performing specific operations.

In the control of the Hirata Cartesian robot’s servomotor operations, direct control based on fuzzy logic algorithm is used. This is because the algorithm is not only used for motor control but also for diagnosing mechanical damage in the robot’s transmissions. Therefore, important characteristics for servomotor control include accuracy, adaptability, and control speed. Additionally, the adaptability of fuzzy logic, coupled with high precision, allows its utilization in configuring digital twins for modeling various conditions and behavioral variations. Fuzzy logic facilitates the development of a control system along multiple directions, enabling the digital twin to emulate human logic based on external factors. This human-like decision-making ability is crucial in scenarios where rigid rule-based systems may fall short, providing a more nuanced and realistic approach.

6. Fuzzy Logic Control of the Hirata Cartesian Robot Servomotor

The speed and torque control of Hirata Cartesian robot servomotor is based on the frequency and amplitude of the vibration signal that occurs because of mechanical damage in the robot’s transmissions. This correlation is based on several reasons, namely the detection of damage in the transmissions and the robot’s operation under conditions of damaged transmission.

Control based on fuzzy logic operates by defining linguistic variables and constructing a fuzzy set of data. Therefore, the fuzzy logic algorithm does not require the determination of an exact mathematical model of the robot for servomotor control.

Fuzzy sets for linguistic input variables related to the amplitude and frequency of vibrations are illustrated in Figure 6.

The shape of the membership function is chosen to align with the logic of the robot’s operation under specified conditions. For instance, the nominal vibration of the robot during work operations is 0.3 g for the nominal motor rotation speed at which the maximum speed of the robot’s working element is achieved. Therefore, for the fuzzy set of amplitude, trapezoidal and triangular functions are chosen, while only trapezoidal functions are selected for frequency. Gaussian functions are chosen for the output parameters of the speed and torque of the servomotor to ensure smoother regulation of these parameters.

Fuzzy sets for linguistic output variables related to the speed and torque of the servomotor are presented in Figure 7.

As a result, based on the presented fuzzy sets and the derived fuzzy rule base, patterns for the speed and torque of the servomotor can be obtained. The simulation results are illustrated in Figure 8.

As seen from the simulation results, the speed parameter is inversely proportional to the torque of the servomotor. This is implemented to overcome the consequences of mechanical damage to the robot’s transmission. When a fault is detected, the robot’s movement speed decreases, and the torque increases to mitigate the impact of undesirable consequences on other parts of the robot. This also helps reduce the influence on its fundamental characteristics, such as positioning accuracy, performance, and energy efficiency.

7. Conclusions

In this work, the structures, implementation, types, and basic principles and methods of servomotor control are described while highlighting its benefits, limitations, and application possibilities. PWM control, utilizing digital signal processing, proves effective in controlling position, speed, and trajectory. Current control, or torque control, stands out for its high precision in regulating torque, quick response to changes, energy savings, and impact on positioning accuracy.

Two-loop control, integrating positional and velocity loops, enhances motor control efficiency, offering precision in positioning, stability in speed control, dynamic response, and integration with other methods. Field-oriented control (FOC), based on the vector control principle, ensures precision control, low noise and vibration levels, and high energy efficiency through the transformation of the magnetic field.

Fuzzy-logic control, relying on fuzzy sets and logical inference, enables adaptive motor control in changing conditions, making it ideal for uncertain systems like digital twins. Finally, programmable control, associated with Industry 4.0, utilizes specialized software and external controllers, offering high flexibility, efficiency, easy integration, and interaction with various protocols and SCADA systems.

The comparison of servomotor control methods presented in this work provides a comprehensive overview of various parameters crucial for assessing the effectiveness of different control techniques. The parameters of speed, accuracy, adaptability, energy efficiency, popularity, ease of implementation, and material resource costs serve as valuable indicators in making informed decisions about the choice of a control method based on specific requirements.

The analysis reveals that programmable control stands out as the most popular and energy-efficient method, while PWM control is the simplest to implement. For adaptive control, the fuzzy logic algorithm is considered, and for accuracy, two-loop control, FOC, and fuzzy-logic control are highlighted.

Each method has its niche and strengths, and the choice depends on the specific requirements of the application. The adaptability of fuzzy-logic control and the efficiency of programmable control make them particularly versatile, addressing challenges in uncertain environments. As technology advances, the selection of a servomotor control method should align with the evolving demands of precision, adaptability, and efficiency in diverse industrial applications.