Effectiveness of Field Oriented Control and Direct Torque Control

Methods for Induction Motor Speed Regulation

SOHAIL AHMAD, HA THU LE

Department of Electrical and Computer Engineering,

California State Polytechnic University, Pomona,

Pomona City, California 91768,

UNITED STATES OF AMERICA

Abstract: – Induction motors are used extensively in many sectors, including manufacturing, power generation,

healthcare, and transportation. Robust speed regulation of inductor motors is a key requirement for ensuring

their intended usage and increasing their effectiveness. This study analyzes two advanced and popular methods

for regulating the torque and speed of induction motors, namely, field-oriented control (FOC) and direct torque

control (DTC). Detailed mathematical modeling of both methods is described, providing the in-depth

perspective of the control algorithms and problem variables. This is followed by a thorough analysis of the

performance of the control methods. Different control scenarios have been analyzed using simulation with

MATLAB Simulink under different speed and loading conditions. The outcomes show that FOC provides

better performance in terms of reduced torque jitter, smooth torque, and speed tracking response for highly

variable load and reference speed profiles. Further, the FOC is found to generate better current waveforms. This

leads to improving the power factor, decreasing electrical noise, and enhancing the motor performance.

Meanwhile, the DTC demonstrates a strong capability to handle large speed changes and provide faster torque

response, but it suffers from considerable torque variation. The simulation outcomes also suggest that the

method selected to tune PI controllers is effective. The findings contribute to enhancing the efficient operation

of induction motors and fostering their applications in diverse sectors for improved productivity and service,

and superior economic gain.

Key-Words: - Controller tuning, direct torque control, field-oriented control, induction motor, motor speed

control, PI controller, torque jitter, vector control.

Received: December 1, 2023. Revised: December 20, 2023. Accepted: December 27, 2023. Published: December 31, 2023.

1 Introduction

Three-phase induction motors (IM) have established

themselves as industrial workhorses. Their

applications are diverse, and include power

generation, manufacturing, healthcare, and multiple

other sectors. One of the most important

characteristics that make IM a ubiquitous choice in

large-scale applications is versatility, efficiency, and

reliability. Due to their direct influence on the

performance of motors, efficient control techniques

are vital to be used in their design schemes. Multiple

control techniques have been developed for

induction motors with various performances.

Understanding the advantages and disadvantages of

the control techniques is of great importance for

correct application.

Induction machines are used as industrial drives

for a variety of equipment, such as drilling

machines, saws, conveyors, elevators, power tools,

and robotics arms. Correct control of these motors is

crucial to ensure the effective operation of industrial

equipment. A small variation in speed may cause

faulty products, instability in driven equipment,

discomfort for users, and lower effectiveness of

manufacturing processes, [1], [2].

In efforts to reduce carbon emissions in the

transportation sector, countries around the world

have implemented policies and set goals to

transition from gasoline-fueled to electric vehicles.

Induction motors are used as drives in multiple

electric vehicle models, [3], [4], [5], [6]. This is

another stimulant for seeking effective methods to

regulate induction motor speed. Electric motors

must provide smooth driving by being able to

accelerate and decelerate quickly in response to

changes in road conditions, as well as in compliance

with traffic rules. Further, they must efficiently use

energy to extend the vehicle range, [7], [8], [9],

[10].

Another important application of induction

machines is found in renewable energy areas,

including wind power generation (wind farms),

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solar PV, and concentrating solar plants. Here,

again, speed control plays a critical role. Induction

machines are used as generators in wind turbines.

Additionally, they are used as motors to drive

supporting systems in wind turbines, such as blade

pitching drive and yaw drive. Solar PV systems use

sun trackers to maximize their energy capture where

induction motors are the system drives. Accurate

control of the motors is key for efficient operation

of the wind turbines and the solar trackers.

Health care is another sector where induction

machines play an important role. One example is

Magnetic Resonance Imaging (MRI) equipment

where correct control of motor speed is a must for

the system to function properly. Another example is

infusion pumps which rely on precise motor control

for correct administration of fluid and medicine for

patients.

The above analysis and examples suggest an

increasingly important role of induction machines

which goes beyond industrial and manufacturing

sectors to reach other critical areas, such as

transportation, renewable energy, and healthcare. It

motivates us to conduct a study to analyze some

advanced control methods to obtain a better

understanding of their characteristics and

performance. The study findings are expected to

contribute to the ongoing progress of motor control,

increasing efficiency and fostering diverse

applications of induction machines.

First, our study will provide a brief literature

review of important induction motor speed control

methods. Then, we will focus on analyzing two

recent and popular control methods, namely Fiend-

Oriented Control and Direct Torque Control,

concerning their precision, torque and speed

behaviors, and related characteristics. The analysis

is performed using MATLAB Simulink and a

realistic modeling motor and control system.

1.1 Voltage-Frequency Control (V/f Control)

Voltage-Frequency control, also known as scalar

control or V/f control, is a powerful method for

regulating the speed of induction motors. It involves

changing the motor supply voltage magnitude and

frequency simultaneously. By doing so, the motor

speed can be regulated without impacting the

motor's maximum torque capability. There are

different ways where the V/f ratio is varied to

provide a special operating performance. The most

common method is fixed, or constant, V/f ratio. V/f

control methods can maintain constant speed across

a wide range of loads. However, they may not suit

all applications that require variable speed operation

and may lack the precision required for demanding

applications, [8], [9], [10], [11], [12].

1.2 Vector Control (Field-Oriented Control)

Field-Oriented Control (FOC) is an advanced vector

control technique, which is widely used for

induction motor speed control. The core of the FOC

method involves decomposing motor stator current

into a magnetic field-generating part and a torque-

generating part. These current components are then

controlled separately using PI controllers to obtain

desirable speeds and performance. FOC

implementation requires expensive sensors and a

complex control algorithm. Though, it is capable of

high-performance motor control with smooth

rotation over the entire speed range, as well as fast

acceleration and deceleration, [10], [11], [12], [13].

1.3 Direct Torque Control (DTC)

Direct torque control (DTC) is another advanced

vector control method. It involves estimating

(decoupling) motor magnetic flux and torque using

measured voltage and current. The estimated flux

and torque are compared with their reference values.

If the estimated flux or torque deviates far the

reference values, the motor variable speed drive

(VFD) is operated to bring the flux and torque errors

within their tolerance bands as quickly as possible.

An advantage of DTC is that torque and flux can be

changed very fast by altering the references.

Further, there is no need for PI current controllers.

The VFD operates electronic switches to reduce flux

and torque errors. However, DTC needs highly

accurate voltage and current measurements, which

may be difficult to obtain. In addition, the control

equipment must be very fast to prevent the flux and

torque from deviating far from the tolerance bands.

Hence, DTC requires a complex motor model and

complex control algorithms while potentially having

considerable torque ripple, [14], [15], [16], [17],

[18], [19], [20], [21], [22], [23].

1.4 Sensorless Control

Many induction motor speed control systems require

speed and position sensors, such as absolute

encoders and magnetic resolvers. These sensors can

be expensive and require frequent maintenance.

Sensorless control techniques, such as sensorless

vector control and back EMF estimation, do not

require sensors. Advantages of sensorless motor

drives include reduced cost, increased reliability,

lower complexity of drive circuits, and less

maintenance requirement. Sensorless methods

utilize the estimation of motor model parameters

and are employed in applications where sensors are

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either unsuitable or too expensive, [22], [24], [25],

[26].

1.5 Sliding Mode Control

Sliding mode control (SMC) is a nonlinear control

method that, by applying a set-valued control signal,

forces the controlled system (such as an induction

motor) to "slide" along a cross-section of the

system's normal behavior. SMC may be viewed as a

special case of a hybrid dynamical system because

the system flows through a continuous state space

while moving through different discrete control

modes. SMC can keep the intended motor speed

constant under disturbance conditions, thanks to its

superior capability to handle disturbance and

uncertainty. This is achieved by constructing a

"sliding surface" on which the motor's state

variables converge to desirable values. However, in

some applications, SMC may produce high

harmonics and cause acoustic noise, [15], [19], [25],

[27], [28], [29], [30].

The following sections present an investigation

of FOC and DTC, the two advanced and popular

vector control methods. The goal is to obtain a

better understanding of their torque and speed

behaviors, related characteristics, and effectiveness

in regulating the induction motor speed.

2 Analysis of Field Oriented Control

of Induction Motor

As said previously, the core of the FOC method

involves decomposing motor stator current into a

magnetic field-generating part and a torque-

generating part. These components are then

controlled separately using PI current controllers to

achieve desirable speeds and performance. The

following section presents FOC mathematical

representations that underline it.

2.1 Variable Frequency Drive, [31], [32]

The induction motor speed is regulated using a

Variable Frequency Drive, which changes the

magnitude and frequency of the voltage applied to

the motor. This adjustment is critical to achieve

optimal motor performance, efficiency, and

responsiveness.

 󰇛󰇜

(1)

where Vs, Vm and  are the source voltage,

maximum voltage, and angular frequency,

respectively.

2.2 Clarke Transformation, [31], [32]

Clarke transformation is used to transform the motor

stator phase currents, Ia, Ib, and Ic, into the alpha-

beta frame. This transformation converts the three-

phase currents into two-phase currents, simplifying

the control of the motor in a two-dimensional frame.

 







(2)

2.3 Park Transformation, [31], [32]

As a next step in the control process, after Clark

transformation, the alpha-beta frame currents are

transformed into dq-coordinates using Park

transformation. Park transformation decouples the

active and reactive power components (a magnetic

field-generating part and a torque-generating part),

making it possible to control them independently.

2.4 Slip Speed Estimation and Position

Generation

The speed feedback from the motor is added to the

slip speed estimator. This estimator block

determines the slip speed by taking the reference

stator current in the dq frame:

   



(3)

where, s, r and s represent the slip, synchronous,

and rotor speeds respectively.

The estimated slip speed is then summed and

fed to the position generator to generate the angle

which is input to the Park transform block and

influences the dq currents for control.

2.5 PI Controller for FOC Control Block

The PI controller's objective is to maintain the speed

and current within their frames. The controller

inputs are motor currents and speed while the output

is the duty cycle for the two-level converter.

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Fig. 1: Block diagram representation of Field Oriented Control (FOC) [31]

Fig. 2: MATLAB Simulink representation for FOC simulation

(Data are provided in Table A1, Table A2, Table A3 and Table A4 of Appendix)

2.6 Implementation

Error calculation: The error is computed as the

difference between the desired and actual motor

torque or flux.

PID controller operation: For each sampling period

 Compute the proportional term as P

multiplied by the error.

 Compute the integral term by accumulating

the error over time and then multiplying by

I.

 Compute the derivative term by determining

the change in error from the last period and

then multiplying by D.

 Duty cycle computation: Combine the P, I,

and D outputs to determine the inverter duty

cycle.

2.7 Performance and Adjustment

After initial tuning, it is crucial to evaluate system

performance. If overshooting or slow system

response occurs, make necessary adjustments to the

PID parameters:

 If the system oscillates, the P gain might be

too high.

 If the system responds slowly, the P gain

might be too low or the I gain too high.

 If the system overshoots and takes a while

to settle, the D gain might need adjustment.

2.8 Tuning Methodology

Various tuning methodologies exist, but for the

purpose of this study, the following PID control

tuning method as explained in the following study

was used.

The methodology is explained as, Setting Gain

Controls for the FOC Algorithm. The regulator

gains are calculated by the implementation of the

pole-zero cancellation technique. This methodology

has the main advantage over other systems as it does

not influence the order of the system. The inner loop

transfer function of the controller is given using the

following equation, [31], [32].



  󰇛󰇜 

󰇛󰇜

󰇛󰇜  

Similarly, the outer loop transfer function of the

controller is tuned as,





󰇛󰇜 󰇛󰇜  

 󰇛󰇜    󰇛󰇜 󰇛󰇜  

(5)

󰇛󰇜

󰇛󰇜

All other relevant equations are given in [31],

[32]. The calculations for Kp and Ki are done for

the following constant values in the motor.

All these values were substituted into the above

equations with the values of a1, a2, a3, a4 and a5

calculated as,





(6)





(7)







(8)





(9)

 







   



(10)

    





(11)

Table 1. Constant parameters of induction motor

used for testing the control algorithm, [31]

Parameters

Values

Supply Voltage (V)

460 V

Power (kW)

111.85 kW/150 HP

Stator Resistance (Rs)

0.0302 ohm

Rotor Resistance (Rr)

0.01721 ohm

Stator Inductance (Ls)

0.000283 H

Rotor Inductance (Lr)

0.000283 H

Mutual Inductance (Lm)

0.01095 H

Inertia (J)

2

Friction Factor (f)

0.0

Pole Pairs (p)

2

Frequency (F)

60 Hz

Nominal Speed

(rad/sec)=2*pi*f

376.9914 rad/sec

Nominal Torque

(Nm)=9.548*Power/N

600 Nm

Table 2. Calculated parameters for tuning PI

controller coefficients, [32]

Constants for calculating control parameters used in

the study

a1

14.28

a2

60.25

a3

-137.819

a4

-6.414e-4

a5

20

(4)

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Table 3. Tuned PI regulator parameters

for current control

Table 4. Tuned PI regulator parameters

for voltage control

Control Parameters

Kp

Ki

450

6426

320

4569

260

3714

200

2857

140

2000

Calculation of gains for current controller

  

(12)

where Kp can be assumed.

Calculation of gains for speed controller

  

(13)

where Kp can be tuned by trial-and-error as in the

current controller. The values of Kp were assumed

and the best value was taken in terms of response.

2.9 Simulation Results for FOC

The FOC diagram is shown in Figure 1 and the

control method is implemented using MATLAB

Simulink (Figure 2) to regulate the speed of an IM.

Table 1, Table 2, Table 3 and Table 4 contain

induction motor and PI controller parameters for the

FOC simulation. The simulation data are also

provided in Table A1, Table A2, Table A3 and

Table A4 of Appendix for reader convenient

reference. Various simulation scenarios are

considered. The goal is to better understand the

behavior of torque in relation to variation in

reference speed for the controller. Different set

points were analyzed in the final assessment of the

designed model. The reference speed (ref) in rpm,

reference flux (phi_ref) in Vs, and reference torque

and current are represented in different subplots.

The simulations were done by varying the motor

speed at different time instants, namely, 0, 1.5, and

2.5 seconds. The reference speed was set at

1785rpm, 1500rpm, and 500 rpm, respectively. The

IM is run at different load torque values, namely

50%, 60%, 70%, 80%, 90%, and 100% of the

nominal torque. The results are presented in Figure

3, Figure 4, Figure 5, Figure 6, Figure 7 and Figure

8.

As evident Figure 3, Figure 4, Figure 5, Figure 6,

Figure 7 and Figure 8, all the reference and set

points were very efficiently tracked by the controller

and the current drawn by the motor is also free from

any non-sinusoidal components. Since the

simulation was run for a significant time, the flux

tracking was also achieved with a very smooth and

critically damped response. The results

demonstrated that the model contained all these

discussed characteristics and performed better than

any other contemporary or even better models.

Analysis of motor behavior of Figure. 3:

Initially, the motor draws a larger current (bottom

plot) than its rated value due to low torque at start-

up. The motor runs a load magnitude equating to

50% of its rated value. Once the motor attains its

rated speed, the in-rush current is stabilized. This

current remains constant unless the speed or torque

requirements are varied. This is evident from the

time stamp ranging from 1.5s to 1.6s where the

speed is varied and consequently, the torque is also

changed. The overshoot during these changes

remained within permissible limits of 2% which

advocates the significance of the PI controller

tuning.

The first plot of Figure 3 (speed) shows that the

motor speed follows the reference speed closely.

The 3rd plot (torque) shows that the torque produced

by the motor (Blue) matches the Reference torque

generated by the controller (Light Yellow, not

visible as it is obscured by the Blue curve) in

response to variable speed command. The motor

torque waveform has some variation, but the

average value is relatively stable. In the meantime,

load torque (Dark Yellow) is maintained at two

constant values. The initial load is set lower to

enable the motor to start and accelerate.

Analysis of motor behavior of Figure 4, Figure 5,

Figure 6, Figure 7 and Figure 8:

We observe similar behavior as that of Figure 3 in

terms of current, speed, and torque when the motor

is run at 60%, 70%, 80%, 90%, and 100% of its

rated load value. The motor speed follows the

reference speed closely. The motor produced torque

matches the Reference torque generated by the

controller.

Overall, the outcomes of Figure 3, Figure 4,

Figure 5, Figure 6, Figure 7 and Figure 8 suggest

that the FOC-based control system can regulate the

Control Parameters

Kp

Ki

0.15

3

0.1

2

0.05

1

0.02

0.4

0.01

0.2

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motor speed over a wide range of loading in a

steady and smooth manner.

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Fig. 3: Results at 50% nominal torque (FOC)

Fig. 4: Results at 60% nominal torque (FOC)

Fig. 5: Results at 70% nominal torque (FOC)

Fig. 6: Results at 80% nominal torque (FOC)

Fig. 7: Results at 90% nominal torque (FOC)

Fig. 8: Results at 100% nominal torque (FOC)

3 Analysis of Direct Torque Control

of Induction Motor

Because of its fast dynamic reaction and lower

complexity when compared to the field-oriented

control method, Direct Torque Control (DTC) is a

common control method for induction motors. A

DTC diagram is shown in Figure 9 and a brief

explanation of the DTC mathematical model is

presented below.

3.1 Induction Motor Modeling, [32], [33]

The mathematical model of an induction motor is

given by the following equations.

   

 

(14)

   

 

(15)

Where the subscript s represents stator and v and i

represent voltage and current respectively. R is the

resistance, and the flux linkage is represented by .

3.2 Stator Flux Modeling, [32], [33]

The modeling of stator flux linkage can be

represented using the following equations.

    

(16)

    

(17)

3.3 Torque and Flux Modeling, [32], [33]

The following equations approximate the torque

produced by the motor.









(18)

3.4 Procedure for Implementation of the

Control Algorithm, [32], [33]

The primary idea behind DTC is to use the inverter's

voltage vector to manage the stator flux and torque

within their respective hysteresis regions.

 Examine the estimated torque and stator flux in

relation to their reference values.

 Using a lookup table, select the appropriate

voltage vector to change the stator flux and

torque based on the inaccuracy.

 Use this voltage vector to run the motor via the

inverter.

Fig. 9: Basic block diagram for Direct Torque Control (DTC) of induction motor, [33]

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3.5 Simulation Results for DTC

The direct torque control method was also simulated

using MATLAB Simulink (it is similar to that of

Figure 2, not shown for brevity) for different torque

loading conditions to obtain the controller

responses. The speed of the motor was initially set

equal to the rated speed and the torque varied

between values ranging from 50%-100% of the

rated value. Figure 10, Figure 11, Figure 12, Figure

13, Figure 14 and Figure 15 show the results. The

reference parameters of speed (ref), torque (Tref),

and current (Ia_Motor) are calculated in their SI

units.

Analysis of motor behavior of Figure 10:

The inrush current in the case of the DTC method

remained confined to a considerably lower value

compared to the FOC method. This is evident from

the 4th plot of Figure 10 where the motor runs at

50% of its nominal load. The inrush current almost

remained in its rated limit with decreased frequency

at starting. This decreased frequency is significant

for a reduction in iron losses in the motor during

start-up. Hence, the saturation point of the motor is

also changed to a higher value due to this decreased

frequency of inrush current.

As the motor runs at 50% of its rated load torque,

the speed initially reaches the rated value of

1875 rpm. After that, the torque is stabilized and

reaches its reference value of 300 Nm (Figure 10).

The motor speed follows the varying speed

command, as shown by the 1st plot of Figure 10.

However, the motor-produced torque waveform has

lots of ripples, as visible from the 3rd plot of Figure

10.

Fig. 10: Results at 50% nominal torque (DTC)

Fig. 11: Results at 60% nominal torque (DTC)

Fig. 12: Results at 70% nominal torque (DTC)

Fig. 13: Results at 80% nominal torque (DTC)

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Analysis of motor behavior of Figure 11, Figure 12,

Figure 13, Figure 14 and Figure 15:

A similar behavior is observed in terms of the motor

speed and torque of the Figure 11, Figure 12, Figure

13, Figure 14, and Figure 15 where the motor is run

at 60%, 70%, 80%, 90%, and 100% of its load

torque. The motor follows the varying speed

command closely. However, the motor has

considerable torque jitter issues where the torque

waveform has lots of variations and noise.

Notably, the DTC demonstrates an impressive

capability to handle large speed changes. Taking

Figure 14 as an example, at a 2.5s time stamp, the

reference speed was decreased by 2.5 times from

1250 rpm to 500 rpm; the motor torque reduced

almost immediately, facilitating the motor to

decelerate to 500 rpm. As the motor speed reaches

the desired value of 500 rpm at around 3.57s time

stamp, the motor torque also stabilizes. Similar

performance of the DTC is observed in Figure 10,

Figure 11, Figure 12, Figure 13 and Figure 15.

4 Comparative Analysis of Advantages

and Disadvantages of FOC and

DTC Algorithms

Speed regulation under changing conditions:

The FOC algorithm performed exceptionally well in

keeping precise and steady control in a variety of

speed situations. This is an essential function,

particularly in applications where fluctuating speed

conditions are commonplace. For systems requiring

high precision in speed control, the FOC is a more

dependable option due to its strong regulation,

which guarantees consistent performance.

However, DTC demonstrates a strong ability to

handle large speed changes.

Torque jitter and harmonics:

FOC torque waveform shows noticeably lower

levels of jitter and harmonics, as compared with that

of DTC. This is another area where it excels over

the DTC. Jitter, or the variations in torque seen in

DTC, can result in mechanical strains and decreased

motor operation efficiency. The ability of FOC to

reduce these fluctuations results in longer equipment

life, smoother motor operation, and higher system

efficiency overall.

However, the DTC torque response is faster

than that of FOC. To address the torque jitter issue,

the current DTC could be combined with a

secondary filter or another control algorithm. The

suggested fixes could work to improve the

effectiveness of the DTC technique.

Current waveforms:

For induction motors to operate efficiently, current

waveform quality is essential. When compared to

DTC, the FOC method was found to generate better

current waveforms. This leads to improved power

factor, decreased electrical noise, and enhanced

motor performance. Better current waveforms also

suggest less strain on the drive electronics and

motor windings, which can result in longer motor

life and lower maintenance costs.

5 Conclusion

The conducted study analyzes behaviors of two

advanced and popular control methods, namely,

Field-Oriented Control (FOC) and Direct Torque

Control (DTC), for regulating the torque and speed

of induction motors. First, the mathematical

modeling of both methods is described. Then,

diverse control scenarios are simulated using

MATLAB Simulink. The outcomes have led to the

following conclusion:

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Volume 18, 2023

Fig. 14: Results at 90% nominal torque (DTC)

Fig. 15: Results at 100% nominal torque (DTC)

a) Field Oriented Control provides better

performance than Direct Torque Control in

terms of reduced torque jitter. However, the

DTC torque response is faster than that of

the FOC.

b) Both FOC and DTC provide good speed

tracking responses for highly variable load

and reference speed profiles. The FOC

performs well in keeping precise and steady

control in a variety of speed situations while

the DTC demonstrates strong capability to

handle large speed changes.

c) Furthermore, the FOC algorithm is found to

generate better current waveforms. This

leads to improving the power factor,

decreasing electrical noise, and enhancing

the motor performance.

d) The simulation outcomes show that the

method that we selected and adjusted for

tuning the PI controllers of FOC is

effective. It can be used as a sample for

engineers to tune similar controllers.

Overall, our study contributes some in-depth

understanding of the core characteristics of FOC

and DTC, namely, speed, torque, and current

behaviors. It should be noted that tuning parameters

of the PI controllers play a crucial role in ensuring

proper functionality of the FOC-based control

system. We contribute a sample of the tuning

technique for tuning similar PI controllers. The

study models are designed for the electrical

requirements of the United States. However, the

data can be extrapolated and used for other

locations. The study findings are helpful for the

operation of induction motors to increase their

performance. They also foster applications of

induction motors in diverse sectors for better

productivity, enhanced service, and superior

economic gain.

Acknowledgment:

The student author wants to acknowledge and thank

Professor Ha Thu Le, the project advisor, for

providing guidance and assistance throughout his

master's study. Furthermore, the authors would like

to thank the Master project committee members,

Dr. Tim Lin and Dr. Dennis Fitzgerald, for their

time and feedback.

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APPENDIX

Data used for MATLAB Simulink FOC

simulation

The simulations were completed for specific motor

data and the results can be extrapolated for further

applications in different other schemes. The main

parameters used in the study are given in the

following tables.

Table A1. Constant parameters of induction motor

used for testing the control algorithm, [31]

Parameters

Values

Supply Voltage (V)

460 V

Power (kW)

111.85 kW/150 HP

Stator Resistance (Rs)

0.0302 ohm

Rotor Resistance (Rr)

0.01721 ohm

Stator Inductance (Ls)

0.000283 H

Rotor Inductance (Lr)

0.000283 H

Mutual Inductance (Lm)

0.01095 H

Inertia (J)

2

Friction Factor (f)

0.0

Pole Pairs (p)

2

Frequency (F)

60 Hz

Nominal Speed

(rad/sec)=2*pi*f

376.9914 rad/sec

Nominal Torque

(Nm)=9.548*Power/N

600 Nm

Table A2. Calculated parameters for tuning PI

controller coefficients, [32]

Constants for calculating control parameters used in

the study

a1

14.28

a2

60.25

a3

-137.819

a4

-6.414e-4

a5

20

Table A3. Tuned PI regulator parameters for current

control

Control Parameters

Kp

Ki

0.15

3

0.1

2

0.05

1

0.02

0.4

0.01

0.2

Table A4. Tuned PI regulator parameters for voltage

control

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

- Sohail Admad: Identification of research issues,

system data acquisition, design and

implementation, simulation, writing an original

draft, and revising.

- Ha Thu Le: Refining research issues and scope,

methodology, technical advising, refining

simulation scenarios, review of results, formatting

and editing the final draft, revising the reviewed

paper to meet publisher requirements.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors declare that they have no known

competing financial interests or personal

relationships that could have appeared to influence

the work reported in this paper.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

_US

Control Parameters

Kp

Ki

450

6426

320

4569

260

3714

200

2857

140

2000

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Volume 18, 2023