International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 9 (2019), pp. 1406-1412© International Research Publication House. http://www.irphouse.com

AC Inductor Motor Control Using Neuro-Fuzzy Network
Udeze, Chidiebele C1 Umoh, Joan Benedict2, Eneh, Joy Nnenna3, Ozue, Izichukwu ThankGod4 , Sochima V. Egoigwe5
1, 2, 3, 4, 5

Department of Electronics Engineering, Faculty of Engineering, University of Nigeria, Nsukka, Nigeria.
ORCID ID: 0000-0002-1732-8796

2Jose’ Vieira in his work compared the different neuro-fuzzyarchitecture and evaluates their performances [1]. His article
gave a comparison analysis on the general vision of the area
describing the most common hybrid neuro-fuzzy techniques,
their advantages and disadvantages. He explained the different
types of neuro-fuzzy systems, their structures and application.
His work gave great recommendation on the need for the hybrid
approach of controlling an inductor motor.

Abstract
Induction motors have gained wide acceptance with respect toindustrial and domestic drives due to their minimal
maintenance requirements and low costs. However, speed andposition control of an AC induction motors exhibits complex
characteristics, various control methods have been adopted forthe speed and position control of the motors which haveexhibited certain limitations like poor accuracy and highharmonic distortion. A hybrid network which combines the
Neural Network and the Fuzzy Logic System known as theneuro-fuzzy networks is developed in this work to control the
speed and position of a three phase inductor motor. The stator
voltage model was used to generate the data used to train theneuro-fuzzy network for the control of an inductor motor’s
position while a speed-frequency model was used to generate
the data used to train the network for speed control of a typicalindustrial three phase inductor motor. Developed network for
position control was implemented directly in matlab using
neuro fuzzy tool box while the developed network for thecontrol of speed implementation was done in the existing statevector pulse width modulation (SVPWM) technique for speed
control of inductor motor. The integrated scheme known as
neuro-fuzzy state vector pulse width modulation (NFSVPWM)
was implemented in Simulink. Results show that neuro-fuzzy
network for position control which achieved complete 360
degree detection and also having 50% improvement on theaccuracy of the existing methods. The NFSVPWM improved
the accuracy of SVPWM by 1.87% while achieving a zero total
harmonic distortion (THD). These results can be deployed toindustries by implementing them digitally using
microcontrollers as target devices.

The combination of neural network and fuzzy logic
complements each methods by combining their advantages andalso avoiding their limitations. Gurpreet S. Sandhu and Kuldip
S. Rattan in their research employs a different algorithm whichenables Fuzzy logic controller to be interpreted as neuralnetwork instead of integrating neural network into certain partsof the FLC [2].
Abolfazi Vahedi in his work formulated a novel sensorless
adaptive neuro-fuzzy speed controller for inductor motor
drives. Using their individual complementing techniques, theobtained result shows that the adaptive neuro-fuzzy speed
controller can gain a very satisfactory performance and a fast
response time even though his control strategy was based onbounded rationality [3]. He used the Neural Network inlearning data and the Fuzzy Logic for understanding theknowledge learned by the ANN (that is combing the FLC to thetail of the ANN. Its feedback was handled by the critic model.
Comparatively, combining neural network and Fuzzy Logic
controllers have given significant improvement to the system.
Existing Neuro-Fuzzy Systems have been achieved using
different combination techniques such as Cooperative neurofuzzy system, concurrent neuro-fuzzy network system andhybrid neuro-fuzzy network system [1]. This research wishes
to adopt a more effective approach of control.

Keywords: Artificial intelligent, Neuro-Fuzzy Network,
Inductor motor, Backpropagation algorithm, Control systems.

Mathematical Representation of Position and Speed of aThree Phase Induction Motor

INTRODUCTION

Three phase induction motor adopts the principle ofelectromagnetic induction [4]. When a three phase sinusoidal
voltage is connected across the windings of the stator of an
induction motor, varying/rotating magnetic fields are develop
around the windings [5]. These magnetic fields have the same
frequency as the source voltage, and are 120 degrees apart if
the source voltage is balanced [5]. The rotational speed of themagnetic field is known as the synchronous speed ws of the
motor [6][7].

Although the techniques behind inductor motor remains
unchanged. Artificial intelligent (AI) has a significant influencewhen controlling an inductor motor and has several advantages
over conventional controllers. The main goal of this study us todesign a suitable method of controlling an AC inductor motor.
This paper adopts a hybrid technique thereby combining the
Neural Network and the Fuzzy Logic control (termed as NeuroFuzzy Network) as each individual properties complement eachother. In this approach, a neuro-fuzzy controller architecture is
proposed which is an improvement on the existing neuro-fuzzyarchitecture.

The magnetic fields cuts through the rotor induce
electromagnetic force (emf). A secondary magnetic field is1406

International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 9 (2019), pp. 1406-1412© International Research Publication House. http://www.irphouse.com
produced around the rotor circuit by this induced emf. Theinteraction between the two windings (primary and secondary)produces forces which turns the rotor.
Now the mathematical representation of a balanced three phasevoltage source is given by equations 1 to 3 [5].
𝑉𝑎 = 𝑉𝑚 𝑆𝑖𝑛(𝑤𝑡)-1

𝑉𝑏 = 𝑉𝑚 𝑆𝑖𝑛(𝑤𝑡 + 120)-

2

𝑉𝑐 = 𝑉𝑚 𝑆𝑖𝑛(𝑤𝑡 − 120)-

3

Where 𝑉𝑎 , 𝑉𝑏 , 𝑉𝑐 are the instantaneous phase voltages of thethree source generator while 𝑉𝑚 is the amplitude of the source
voltage. It is important to observe that the balanced phasevoltages are 120 degrees apart.

Figure 1: High level description of digital technique for
Speed and Position of control three phase induction motor
The digital switching algorithm leverage on neuro-fuzzytechnique to control the speed and position of the three phaseinduction motor through the motor actuator. The graphical userinterface (GUI) was used to view the speed and position of the
motor while the feedback was used to sense the present state of
the motor with respect to the speed.

The relationship between the inductor motor speed, 𝑛 and the
speed, 𝑛𝑠 of the rotating magnetic flux is given as𝑛 = (I − s)𝑛𝑠-4

Where s is the slip [8].
Given the relationship between the frequency, 𝑓 and the speed
ns as
𝑛𝑠 = 120𝑓/𝑃-

The Design of the Digital Switching Algorithm for the
Speed and Position Control of Three Phase Induction
Motor.

5

Consider the source voltage equations for a balanced threephase induction motor

Where 𝑃 is the number of pole pairs in the stator windings [8].
While examining equations 4 and 5, it is observed that the speed𝑛 of induction motor can be controlled when the synchronous
speed is controlled which means controlling the source voltage
frequency.
Neglecting the induced voltage in the stator winding of the
motor, the equation obtained by relating the supply voltage V
and the rotating flux 𝜙 is [8].
V 𝛼 𝜙𝑓-𝑉𝑎 = 𝑉𝑚 𝑆𝑖𝑛(𝑤𝑡)-7𝑉𝑏 = 𝑉𝑚 𝑆𝑖𝑛(𝑤𝑡 + 120)-

8

𝑉𝑐 = 𝑉𝑚 𝑆𝑖𝑛(𝑤𝑡 − 120)-

9

For w= 2𝜋f where f = 50 Hz, the graphical representation ofequations 7 to 9 considering a single cycle is shown in figure 2.

6

To obtain an optimal operation, a constant value of the flux 𝜙maintained and rated for operation of a specific induction
motor. It means that for efficient control of speed of an
induction motor to be achieved, the voltage and frequency of
the input voltage to the motor must be controlled [8].
Now, the position control of an induction motor means
specifying exactly the angle of rotation of the motor per time[6]. In ac domain, it is quite difficult to control the inductor
motor’s frequency and position. So the next section discussed
digital technique for voltage, frequency and position control of
ac induction motor.

Figure 2. Balanced three phase ac voltage
The angle displacement, θ, of the motor is given by

Digital Techniques for Speed and Position Control of Three
Phase Induction Motor

𝑑θ

=𝑤

-

10

dθ = 𝑤𝑑𝑡

-

11

𝑑𝑡

Speed and position of an induction motor can be controlled by
employing the ability of a digital switching technique whichswitches the motor to any desired position or speed. Figure 1 isa high level block diagram for the digital switching techniquebeing used in this work.

This means that integrating the angular speed of the motor
gives the position of the motor.
That is,θ = ∫ 𝑤𝑑𝑡

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International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 9 (2019), pp. 1406-1412© International Research Publication House. http://www.irphouse.com
The Design of position control Inductor Motor using Statematrix method

Neuro-Fuzzy Network for Speed Control of Inductor
Motor

Table 1 shows the matrix design of how to detect the positionof a three phase inductor motor based on the state matrix ofthe induction motor.

The mathematical relationship between inductor motor speed
and the frequency of the supply voltage can be established bysubstituting equation 14 in equation 15. That is,Table 1: State matrix design of position control of three phaseinduction motor𝑛 = (I − s)𝑛𝑠-13

𝑛𝑠 = 120𝑓/𝑃

-

14

-

15

𝑛 =

120∗(1−𝑠)∗𝑓𝑃

Equation 15 shows that the speed of an inductor motor is
directly proportional to the frequency supplied.
Given the following specifications for an industrial three phasesquirrel cage inductor motor.
Speed: 1501-2000 RPM; No of poles = 2; rated slip = 0.42, Vph= 220 [45].
Equation 15 then becomes

If F is the reference frequency of the source voltage, then T=1/F. Digitally, table 1 can be implemented using neuro-fuzzy
logic

n=

120 ∗ (1 − 0.42) ∗ 𝑓
2

n = 34.8 ∗ 𝑓

Neuro-Fuzzy Network for Position Control of Three Phase
Inductor Motor-

16

Equation 16 gives the specific equation relating the motor
speed and the frequency of the supply voltage. The speed of the
motor can vary from 1501 to 2000 rpm. For a variation of speed
from 1501 to 2000 rpm, the frequency variation is from
43.1322 to 57.4713 Hz. Both the speed and the frequency canbe categorized into nine different membership functions asshown in table 2. Figure 5 shows the membership function plot
relating to the speed variable while figure 6 shows the fuzzy
rule base to be integrated in Neuro-fuzzy network for the motor
speed control. Figure 7 shows the neuro-fuzzy network
developed from the rule based. It is made up of two externallayers and three hidden layers.

Figure 3. Neuro-Fuzzy network for position control of threephase induction motor

Equation 16 was used to generate the data used in training the
network. The network was trained to achieve zero error using
hybrid propagation algorithm at epoch number of 1 as shownin figure 8.

The network of figure 3, is made up of two external layers
representing inputs and output. The inputs to the network are
Va, Vb and Vc while the output is the position of the motor. The
three hidden layers represent the fuzzification, inference anddefuzzification of the network. The characterization of the
network was done by training using artificial neural backpropagation method leveraging on instantaneous values of thephase voltages for time t = 0 to 11T/8 at a step of0.0000763889. The data used in the training was generatedusing equations 7 to 9.

Table 2: Membership functions for speed control of a typicalthree phase inductor motor.

Figure 4: Training result for position control of three phaseinductor motor
The figure 4 shows the error goal that was achieved at epochs
1.

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International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 9 (2019), pp. 1406-1412© International Research Publication House. http://www.irphouse.com
of PWM block for optimized control of the speed of theinductor motor. Figure 9 shows the block diagram of theexisting SVPWM scheme while figure 10 is the integrated
scheme proposed in this work.

Figure 5. Membership function plots of speed variable

Figure 9. Description of the existing SVPWM scheme

Figure 6. Rule base for neuro-fuzzy network for speed controlof the inductor motor
Figure 10. Integrated hybrid scheme for speed control of
inductor motor

The integrated hybrid scheme called neuro-fuzzy state vector
pulse width modulation (NFSVPWM) was implemented in
Simulink using SIM Power tool box. DC source was use as thesource voltage. The inverter is implemented using a three arm
bridge leveraging on insulated gated bipolar transistor (IGBT)
and diodes as power electronic devices. Three squirrel cage
inductor motor was used as the motor having a default
frequency of 50 Hz and phase voltage of 220 volt. To
implement the pulse width generation block, a three phase-six
pulse width generator with external reference signal(frequency) was used. The neuro fuzzy network was
implemented by importing the trained network into the
Simulink environment. Figure 11 shows the complete Simulink
model for the implementation of the speed control of threephase inductor motor using NFSVPWM.

Figure 7. Neuro-fuzzy network for speed control of the threephase inductor motor

Figure 8. Training result of neuro-fuzzy network for speed
control of the inductor motor

Implementation of the Neuro-Fuzzy Network for Speed
Control of Three Phase Induction Motor.
In this section, neuro-fuzzy network (NFN) is integrated in thestate vector pulse width modulation (SVPWM) scheme
leveraging on the NFN for variable selection of the frequency

Figure 11. Implementation of NFSVPWM scheme in
Simulink

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International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 9 (2019), pp. 1406-1412© International Research Publication House. http://www.irphouse.com
RESULT DISCUSSION

Figure 16. Motor position in state 1 at t=0.000343 second

Figure 12. Position of the three phase induction motor
at t= 0.00273 second

Figures 12 and 13 show that the angle position of the threephase inductor motor at time t = 0.00273 second is 56.2, andthe position at t = 0.00274 is 56.3. It means the resolution of
the network is 0.1. Theoretically, the change in position fromt = 0.00273 to 0.00274 can be calculated using equation below;dθ = 𝑤𝑑𝑡,dθ = 2 ∗ 𝜋 ∗ 50 ∗ 0.00001
dθ = 0.00314.
So this means that theoretically a change of 0.00314 in position
can be detected. The neuro-fuzzy network was able to detect achange of 0.1 in position of the motor. A deviation of 0.09686
from the ideal value. Figures 14 to 16 shows that the positionof the inductor motor is not static within a state.

Figure 13: Position of the three phase induction motor
at t= 0.00274 second

Discussion on the Results of Speed Control of Three Phase
Induction Motor

Figure 14. Motor position with all the state variables in state1
Figure 17. Response of NFSVPWM scheme at reference
speed of 1500rpm

Figure 15. Motor position in state 1 at t=0.000342 second
Figure 18. Response of NFSVPWM scheme at reference
speed of 1700 rpm

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International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 9 (2019), pp. 1406-1412© International Research Publication House. http://www.irphouse.com

Figure 19. Response of NFSVPWM scheme at reference
speed of 1800rpm

Figure 23. Signal statistics at reference speed of 1700 RPM

It is also shown in figure 23 that the steady state error atreference speed of 1700 rpm is 1. So, average steady state errorof the NFSVPWM scheme is 1. This corresponds to accuracyof (1700-1)/1700 = 0.9994. That is 99.94%.

PERFORMANCE ANALYSIS
To show a better improvement of the NFN control method,
Fuzzy logic control was analysed (through simulations) for the
position control while the existing SVPWM for the speed
control.

Figure 20. Response of NFSVPWM scheme at reference
speed of 1950 rpm
Figures 17 to 20 show that the proposed NFSVPWM scheme isable to achieve control objectives in 0.35 second at various
instances tested. At reference speed of 1950 rpm the peak topeak steady state value is 1949 giving a steady state error (SSE)of 1 as shown in figure 21.

Comparison of Position Control of Three Phase Inductor
Motor Using Neuro-Fuzzy Network and Fuzzy Logic.
Results of position control of three phase inductor motor wasachieved using developed fuzzy logic membership functions
and fuzzy rule, the results show that the position control of thethree phase inductor motor using fuzzy logic approach has aresolution of 0.2 a deviation of 0.19686 from value. So theneuro-fuzzy network brought an improvement of 0.19686 0.09686 = 0.1 on the precision of the existing fuzzy logic
method of inductor motor position control. This represents 50%
improvement on the accuracy of the fuzzy logic method.
The result also revealed shows that with fuzzy logic method,that the position of the motor can only assume eight states as
only the increment of 45 degrees will be detected by the logic.
The neuro-fuzzy network is able to detect an increment of 0.1
in position even within a state. When approximated to nearest
integer, it means the network achieved a position detection 360
states meaning that it improved fuzzy logic method by a factorof 360/8 = 45.

Figure 21. Signal statistics at reference speed of 1950 RPM
Similarly, at reference speed of 1800 rpm the peak to peaksteady state value is 1799 giving a steady state error (SSE) of 1
as shown in figure 22.

Comparison of Speed Control of Three Phase Induction
Motor Using NFSVPWM and SVPWM Methods
Using the existing state vector pulse width modulation(SVPWM) method [9], the simulation achieved responses atdifferent speed, the steady state error (SSE) at reference speedof 1500 rpm is 26. At reference speed of 1700 is 39. Also, when
the reference speed is 1800, the SSE is 32 while SSE forreference speed of 1950 is 34. It is clear that the existing
SVPWM method or technique exhibits variable SSE at
different speeds. The Neuro-fussy state vector pulse width

Figure 22. Signal statistics at reference speed of 1800 RPM

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International Journal of Engineering Research and Technology. ISSN 0974-3154, Volume 12, Number 9 (2019), pp. 1406-1412© International Research Publication House. http://www.irphouse.com
modulation (NFSVPWM) method has constant SSE
irrespective of speed of operation. This is an improvement on
SVPWM method.

Recommendations for Further Research
The networks developed in this work were implemented atsimulation level. This work can be further validated by
implementing the developed concepts practically using digital
methods leveraging on micro controllers as target devices.

Now, the average SSE of the SVPWM method is 32.75. Usinga reference speed of 1700 rpm, it corresponds to accuracy of(1700-32.75)/1700 = 0.9807 which is 98.07%. It means that the
NFSVPWM method brought an improvement of 1.87% in theaccuracy of SVPWM method.

REFERENCES.
[1]

Jose` Vieira et al, “Neuro-Fuzzy Systems; A survey”.
WSEAs Transaction on systems pp 414-419, 2004

[2]

Demuth, Howard and Beale, Mark. Matlab neuralnetwork tool box documentation. 2004

[3]

Haykin Simon “An Introduction to Feed Forward
Networks”. 1999

[4]

Vo, T., Nguyen, V., Anh, D., & Pham, T. (2017).
Sensorless speed control of a three phase induction
motor:anexperimentapproach.
International
Conference on System Science and Engineering (ICSSE)(pp. 331 - 1336). IEEE.

[5]

Pustovetov, M. Y. (2016). A mathematical model ofthree phase induction motor in three phase stator
reference frame describing electromagnetic andelectromechanical processes. 2016 Dynamics ofSystems, Mechanisms and Machines (Dynamics) (pp. 15). IEE.

[6]

Tsutomu, T., Atsushi, H., & Masaya, I. (2012).
Independent speed and position vector control of two
permanent magnet synchronous motors fed by a five-leg
inverter with space vector modulation. 2012 IEEE
Industry Applications Society Annual Meeting. IEEE.

[7]

Http://www.youtube.com/watch?r=AQqyGNOP_3o[8]Sara, A., Salinda, B., Mahdi, T., & N, R. (2013).
Sensorless speed estimation of induction motor based on
feed-forward neural network algorithm. 2013 IEEE
Conference on Clean Energy and Technology (CEAT)(pp. 71-75). IEEE.

[9]

MathWorks. (2018, May 15). Simulate Variable Speed
Motor Control. Retrieved October 1, 2018, fromhttps://www.mathworks.com/help/physmod/sps/powers
ys/ug/simulating-variable-speed-motor-control.html

Performance Evaluation of the NFSVPWM Method
Figure 24 shows the analysis of total harmonic distortion
produced in the three phase inductor motor while being
controlled using NFSVPWM Method.

Figure 24: Harmonic analysis of the induction motor

It is observed that within the maximum frequency of operationconsidered for the motor, there is a zero harmonic distortion!
This means that the NFSVPWM method did not only achieve
an improved efficiency of the speed control, but also did not
distort the stator current of the motor. Distorting the statorcurrent causes an internal heating which affects negatively theefficiency, and ultimately life span of the motor.
From this analysis, the results show that neuro-fuzzy network
for position control which exhibits a complete 360 degree
detection improved the existing fuzzy technique (FT) by factorof 45 while having 50% improvement on the accuracy of the
FT. The NFSVPWM improved the accuracy of SVPWM by
1.87% while achieving a zero total harmonic distortion (THD).

[10] Srinivas Singirikonda, Yellaiah Ponnam and Sravan
Kumar Palarapu, “Ziegler-Nichols (Z-N) Based PID
Plus Fuzzy Logic Control (FLC) For Speed Control of
A Direct Field-Oriented Induction Motor (DFOIM)”,
Int. Journal of Engineering Research and Applications
ISSN: 2248-9622, Vol. 3, Issue 6, Nov-Dec 2013,
pp.755-762

CONCLUSION
This work developed a neuro-fuzzy network for position
control of three phase induction motor. The network achieved
a position detection of 360 states meaning that it improved
fuzzy logic method by a factor 45.
It also developed neuro-fuzzy network for speed control ofthree phase induction motor. In comparing with the existing
control method, it is seen that the proposed NFSVPWM gives
an improvement by giving a constant SSE irrespective of thedifferent speed the motor operates.

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