Nigerian Journal of Technology (NIJOTECH)

Vol. 36, No. 3, July 2017, pp. 867 – 875

Copyright© Faculty of Engineering, University of Nigeria, Nsukka,
Print ISSN: 0331-8443, Electronic ISSN: 2467-8821
www.nijotech.com
http://dx.doi.org/10.4314/njt.v36i3.29

SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER (A CASE

STUDY OF EMERGENCY LUBE OIL PUMP MOTOR OF H25 HITACHI
TURBINE GENERATOR)
I. I. Ekpoudom1,*, I. E. Archibong2 and U. T. Itaketo3
1,2,3 DEPT. OF ELECTRICAL/ELECTRONIC AND COMPUTER ENGR., UNIVERSITY OF UYO, UYO, AKWA IBOM STATE, NIGERIA

E-mail addresses: 1 highpointer7@yahoo.com, 2 idoren2001@yahoo.com, 3 engr1easy@yahoo.com

ABSTRACT
This paper presents the development of a fuzzy logic controller for the driver DC motor in the lube oil system of the H25
Hitachi gas turbine generator. The turbine generator is required to run at an operating pressure of 1.5bar with the low
and the high pressure trip points being 0.78 bar and 1.9 bar respectively. However, the driver DC motor speed drifted
from the desired speed of 1450 revolutions per minutes (rpm) to as low as 1414 rpm. It is against this backdrop, that this
project work was envisaged to design a controller capable of controlling the speed of the DC motor in order to achieve the
desired speed rating of 1450 rpm. In modelling the motor, the transfer function method was used to develop a linear
approximation to the actual motor. After computing the total inertia of the motor shaft, the motor model was simulated
for the speed response in MATLAB and Simulink environment, and the response showed that the motor attained an
actual maximum speed of 1414 rpm at settling time of 0.3 seconds. Based on expert knowledge of the lube oil system, a
fuzzy logic controller was designed and this resulted in the issuance of a control action to correct the actual speed of the
motor from 1414 rpm to the desired speed of 1450 rpm.

Keywords: dc motor, fuzzy logic controller, modelling, membership function, speed of response

1. INTRODUCTION control system in which the control output is compared

The need to control the motor speed is borne out of the with a reference, and if there is an offset, the controller
necessity to achieve the desired vendor motor speed takes action to minimize the error to as low as
which has actually drifted overtime. The lube oil system practicable [3].
pressure depends on the speed of driver motor. In gas
turbine engines, the lubrication system is maintained at a 2. METHODOLOGY
predetermined pressure by the manufacturer and this 2.1 The Lube Oil System of the H25 Hitachi Gas Turbine
pressure has acceptable limits. If the pressure falls System
outside the limits or the operating envelope, there could The lube oil is stored in a large reservoir from where it is
be serious impact on the performance and availability of pumped to the bearings and control system by the main
the rotating parts of the gas turbine. Besides, severe oil pump. In gas turbine engines, pressure circulating
pressure drop in the lube oil system of gas turbine lubrication system is used and this is sometimes called
generator can cause the Human Machine Interface (HMI) forced-feed lubrication system. The lube system majorly
to shut down the turbine while it is on load [1]. consists of lube oil reservoir, main lube oil pump,
Obviously, design shows that the discharge pressure of auxiliary lube oil pump, emergency lube oil pump,
the lube oil pump is directly dependent on the speed of pressure relief valve, bearing header pressure regulator,
the driver motor. Hence, if the driver motor develops a heater and lube oil filter. All these components work
fault that results in speed drop, there is a corresponding together to circulate oil throughout the entire turbine
reduction in the discharge pressure. systems [1].
Fuzzy Logic differs in concept and content from the When the lubricating oil pressure gets too low turbines
traditional multivalued systems. Fuzzy logic systems are stopped by a hydraulic trip. The safety philosophy
make use of linguistic variable instead of numbers or requires an automatic dump valve to release oil from a
crisp values [2]. Fuzzy logic controllers are widely used trip cylinder to shut off the fuel supply whenever the
in various and varied control schemes and in most lube oil pressure gets too low. A simplified schematic
instances positioned in the forward path of a feedback

* Corresponding author, tel: + 234 – 803 – 799 – 0505

 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

diagram of the turbine lube oil system is shown in Figure

1. There is a linear relationship between the torque
developed by the motor, the air-gap flux and the
armature current and is as follows:

where, is magnetic flux in the air gap

Tm is motor torque and ia is armature current
Substituting equation (1) in (2), results in the expression
below

In this project work, the lube oil pump driver is a field

current - controlled DC motor which is known to having
substantial power amplification. In this type of DC motor,
the armature current is kept constant while the field
current is varied as the voltage input into the electrical
circuit [6]. In Laplace transform notation, equation (3)
Figure 1: Simplified Diagram of the Gas Turbine Lubrication becomes,
System, Source:[11]

2.2 Mathematical Modelling of DC Motor In (4), = is a constant armature current,

There are basic sources of driving lubrication oil pump in ( ) is defined as the motor constant. It is
gas turbines engines which include, pneumatic, hydraulic worth mentioning that the field current is related to the
and electric. In this project case study, the lube oil pump field voltage as in equation (5) [7]
is being driven electrically with the use of a DC drive
( )
motor. The DC motor converts direct current electrical
power to mechanical power. A major fraction of the Applying Laplace transform methods to equation 5,
torque generated in the armature is available to drive the results in
inertial load of the lube oil pump. In modelling the motor, ( )
the transfer function method was used to develop a
linear approximation to the actual motor. Second-order 2.2.2 Mechanical Characterization of the DC Motor
effects such as hysteresis and voltage drop across the A greater portion of the torque developed by the motor
brushes were neglected [4]. The DC motor wiring was delivered and used to drive the lube pump load and
diagram is given in Figure 2. the relation may be expressed as

In (7), is the torque requirement of the motor from

the pump and is the disturbance torque, which is often
negligible. However, it is advisable to consider the
disturbance torque in systems subjected to external
forces [8]. Assuming the lube-oil pump is directly
coupled to the motor shaft as shown in figure 1, the total
available load torque is written as:

where is the total inertia of the pump impeller and

motor rotor
is the angular speed of the motor shaft and is the
Figure 2: DC Motor wiring diagram [5].
viscous friction coefficient. The total inertia that the
motor shaft is subjected to is:
2.2.1 Electrical Characterization of the DC Motor
The input voltage to the motor was applied to the field
Where is the inertia of the pump impeller, is the
terminal. The field current is proportional to the
inertia of the motor rotor.
magnetic flux of the air-gap that exists in the motor
Substituting equation (8) in (7), it follows that
provided the field is remaining unsaturated and the
expression is given as:

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 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

Figure 3: Block Diagram of Field-Controlled DC Motor for Driving Lube Oil Pump

Taking Laplace transform of equation (10), rearranging pump (m), is acceleration due to gravity g =9.81ms−
equation 6 and combining these, the result is written and is the pump efficiency.
from [3] as: Equations 13 and 14 were used to estimate the mass
inertia of the pump impeller, depending on the
parameter given by the pump manufacturer.
Therefore the transfer function of the motor-pump load
combination, with is: 2.2.4 Design and Modelling of Fuzzy Logic Controller
The success of any designed FLC is based on heuristic
[( ) ] and expert knowledge of the system that is to be
The block diagram of the field-controlled DC motor is controlled [9]. Typically, a fuzzy logic controller has at
shown in Figure 3. least two inputs and one output. A fuzzy inference
system (FIS) maps given inputs to outputs using fuzzy
2.2.3 Estimation of Lube Oil Pump Inertia logic membership functions. A membership function
The pump torque was dependent on the inertia of the (MF) is a shape that defines how each point in the input
pump impeller directly coupled to the motor shaft and space is mapped to a membership value (or degree of
the angular speed of the drive shaft. Hence, it was membership) between 0 and 1. The input space is
necessary to accurately determine this parameter as the sometimes referred to as the universe of discourse which
motor torque requirement is greatly associated with it. needs to be specified by the designer. There are two
However, the inertia of a pump impeller is its resistance styles of FIS used in fuzzy logic controllers and these are
to changes in angular velocity as it rotates about its shaft. Mamdani and Sugeno styles. Mamdani's fuzzy inference
This accounts for the rotational mass of the impeller and method is the most commonly used methodology and
is typically 10-15% of the motor inertia. Accurate values can make do with different membership functions in its
of the pump impeller inertia are usually available from inputs and outputs [10].
the vendor and can be used where possible [1].During For this design, the input and output is defined as
transient analysis it is often most conservative to follows: since FLC requires at least two inputs and one
underestimate the pump moment of inertia, particularly output, the first input will be the speed error while
for fluids with high vapour pressures. Pumps with a the second is the changein error of the speed . The
lower moment of inertia will spin down faster, more DC motor shaft rotational speed is the output , and the
abruptly slowing the fluid at the pump outlet while fluid equations relating these are written in equations 15, 16
further down the pipe line continues to flow due to and 17.
momentum. While it is advisable to always obtain inertia −
data from vendors, it is not always readily available. In − −
these circumstances the pump moment of inertia was − −
estimated using equation 13. where, is the time factor, is the actual
speed achieved by the motor, is the desired
( ) speed required by the lube oil pump to provide the
Where, P is pump power (kW) and is pump speed optimum oil pressure for the turbine.
(rpm).
The shaft power of the pump was calculated from 2.2.5 Membership Function Definition and Rules
equation 14 as shown below Formulation
However, one needs to define all the linguistic terms that
would be used for specifying our membership functions -
Where is density of lube oil (kg/m3), is the MF. These terms formed the sets of antecedents and
volumetric flow rate (m /s), is differential head of the
3 consequents in the fuzzy rule-based table which are

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 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

employed in quantifying the input and output values or (output fuzzy set) is defuzzified into crisp value using the
degree of membership in the fuzzy sets. Table 1 shows centre of gravity method. Moreover, FIS mapped given
the linguistic term for MF. inputs to outputs using fuzzy logic rules via the
There were two MF used for modelling the FLC, and membership functions.
these include the triangular and the trapezoidal. The
membership functions types used for the DC motor of the 2.2.6 Modelling and Simulation of Lube Oil Pump DC
lube oil pump has universe of discourse of , and as Motor and FLC
− , − and − respectively. Table 2 The mathematical models of the lube oil pump DC motor
now shows the initial rules formulated for this FLC and the fuzzy logic controller developed were simulated
design. in MATLAB and Simulink environment. MATLAB as a
The rules were actually formed in fuzzy logic toolbox and high-level technical computing language and interactive
translated into the table above. In Table 2, the grey environment was employed for algorithm development,
coloured row and column represent the linguistic terms modelling, simulation, data visualization and analysis.
that constitute the antecedents of fuzzy rules with
respect to the heuristic variables, speed error and change Table 1: Membership Function Terms
in speed error. The middle section of the table with a MF Terms Description
clear background is actually the consequents of the rules. NL Negative Large
The shapes of the membership functions used are NM Negative Medium
presented in Figure 4. The triangular and trapezoidal NS Negative Small
membership functions are often used because these Z Zero
curves make it flexible and easy to represent the PS Positive Small
proposed ideas and facts of the model, and with less PM Positive Medium
computational time requirement. Then in order to obtain PL Positive Large
the output of the FLC, the rotational speed of the motor

Table 2: Fuzzy-based Initial Rules

Speed Error
NL NM NS Z PS PM PL
NL NL NL NL NL NM NS Z
NM NL NL NL NM NS Z PS
Speed Error NS NL NL NM NS Z PS PM
Change Z NL NM NS Z PS PM PL
PS NM NS Z PS PM PL PL
PM NS Z PS PM PL PL PL
PL Z PS PM PL PL PL PL

Figure 4: Initial Membership Functions for the FLC

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 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

It essentially offers the platform on which the behaviour 1414rpm. A very short settling time of 0.3 sec is
of the system could be investigated under different evident from the plot above. This speed
operating conditions. is lower than the optimum speed (
1450rpm) needed to supply the required lubrication oil
2.2.7 Modelling and Simulation of Lube Oil Pump DC pressure to the turbine during idling.
Motor and Fuzzy Logic Controller. Therefore, it would be necessary to model a controller to
The mathematical models of the lube oil pump DC motor enable the optimal speed for the motor to be achieved.
and the fuzzy logic controller were actually simulated in Also, figure 7below illustrates the angular position of the
MATLAB and Simulink environment. In order to model motor shaft in radians which is directly tied to the
the DC motor, its parameters are obtained from the case rotational speed of the motor. The angular position
study industry using the Lube-Oil Pump Motor of the increases linearly with time and recorded an
H25 Hitachi Turbine Generator at Bonny Oil and Gas approximate value of in 1 sec. This implies a
Terminal. Appendix I shows the required parameters for total angle of revolution of the shaft of
the field-controlled DC motor while Appendix II shows which is about . Hence, the motor
the lube oil pump parameter for computing impeller shaft would certainly climb as high as 1414 rev in 60 sec.
inertia
Using equation (12), the lube oil pump motor was 3.2 Model Evaluation Criteria
modelled in Simulink environment and shown in Figure There are many performance indices used in control
5. Before simulating the model for the speed response, engineering design for evaluating how well a designed
the total inertia on the motor shaft must be computed. system would perform in practice. In this work, only time
First, from Equations (13) and (14), the pump impeller domain response indices are used. Figure 8 shows the
inertia was calculated and substituted in Equation (9) to response of the system to a standard test input. In
obtain the total inertia on the motor shaft. This was done computing the system step response, Simulink software
by writing MATLAB code in a script which detailed all the first linearizes the nonlinear mathematical relationship
parameters of the model. However, the final transfer in equation 18 about the input and output points of the
function in equation (12) for the motor is evaluated and model shown in Figure 5.
presented in equation (18). The system has a rapid and smooth response to step
input. The overshoot of % indicated that the
system step response is not chaotic. This is because the
system has no complex poles and no zeros, a pointer to
3. RESULTS AND ANALYSIS the fact that there are virtually no internal delays. Table
3.1 Model Simulation Results 3 summarizes all the performance indices for the step
The model was simulated for period of 1 second and the response. The transient response disappears beyond the
DC motor speed and angular position responses are rise time of and finally gives way to the steady-
depicted in Figures 6 and 7. The speed response showed state response at the settling time of .
that the motor attained an actual maximum speed of

60/(2*pi) motor_speed

Motor
rad/s-rpm
Speed

1 If(s) Tm(s) TL(s) 1 w(s) theta

110 Km 1/s angle
Lf.s+Rf J.s+b
Input Motor Integral Angular
Voltage Field Motor-Pump Position
Constant Load
0 Td

Figure 5: Simulink Model of Lube Oil Pump Field-Controlled DC Motor

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 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

Table 3: Step Response Performance Analysis DC Motor

for Lube Oil Pump
Performance Indices Values Units
Peak Amplitude −
Peak Time
Rise Time
Settling Time
Overshoot
Steady State Error −

The steady-state error is equally low at , and this

means it is . This can be driven low or zeroed
whenthe FLC is introduced into the system.
Figure 6: Speed Response of DC Motor for running an
Emergency Lube Oil Pump in H25 Hitachi Gas Turbine 3.3 Speed Response of the DC Motor with the Fuzzy Logic
Generator Controller.
The Simulink model of the FLC used for correcting the
actual speed of the motor from to the desired
speed of is shown in Figure 9. The content of
the DC motor subsystem, if double clicked in Simulink
environment, is exactly the same model in Figure 5. This
FLC-DC motor model is simulated for a period of 1 sec
and speed response is shown in Figure 10.

The speed response indicated that the FLC controller is

able to issue a control action which finally corrected
motor speed to the required optimum speed
of .
Figure 7: Angular Position Response of DC Motor for
running an Emergency Lube Oil Pump in H25 Hitachi Gas 3.4 FLC Model Adjustment and Performance Analysis
Turbine Generator. Adjusting the shapes of the membership function can
greatly enhance the performance of the FL controller. A
common practice during FLC fine-tuning is to make the
adjacent sides of the MF shapes or fuzzy set values to
overlap one another by 25%, thereby improving both
efficiency and performance. In addition, if the areas of
the membership functions that extend far away from the
Z region are broadened, the response of the controller
becomes faster. Also, performance improvement is
accomplished by systematically reducing the weight of
the fuzzy logic rules which is otherwise known as
Figure 8: Response of DC Motor for running an reduction in rules severity. The number of rules was
Emergency Lube Oil Pump in H25 Hitachi Gas Turbine reduced from 49 to 19. After FLC model adjustment and
Generator rules reduction, the inputs and output MFs, and the
Overshoot and the settling time represent the degree of nonlinear control surface is represented in Figures 11
closeness of the step response to the desired response. and 12. Comparing Figure 4 with Figure 11, it can be
The final peak value of the step response occurred at an seen that the shapes of the membership functions have
amplitude of in . These low rise and peak been adjusted.
times actually demonstrate how swift the system is to
step input signals, and the optimality of the system
dampness.

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 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

E(t)
225.68 e(t) w(t) speed_f uzz
w speed
reference
speed dE(t) Speed
Fuzzy Logic DC Motor
Controller
du/dt
Derivative

Figure 9: Simulink Model of FLC and DC Motor.

Figure 10: Speed Response of DC Motor with FLC for Running an Emergency Lube Oil Pump in H25 Hitachi Gas Turbine
Generator

Figure 11: Adjusted Triangular and Trapezoidal inputs and Output Membership Functions.

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 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

Figure 12: Speed Response of DC Motor with Adjusted FLC for Running an Emergency Lube Oil Pump in H25 Hitachi
Gas Turbine Generator

The adjusted FLC was reintroduced into the Simulink 5.5KW, H25 Hitachi Turbine Generator at Bonny Oil and
model of the DC motor loop and simulated for a period of Gas Terminal, has been presented. The results from the
1 sec. the speed response plot in figure 12 above shows motor modelled and simulated indicated that based on
that the controller still maintains the speed at industry parameters, the motor attained a maximum
but with a much faster response. Consequently, the speed of . However, the developed FLC was
model performance indices earlier described are equally introduced into the control loop to correct the speed of
affected as shown in Table 4.A linear model is first the DC motor to the required operating speed of
computed from the nonlinear Simulink model of the FLC for the lube oil pump. The simulation results
before the linear response is plotted. During simulation, were obtained using MATLAB/Simulink. The results
the software linearizes the portion of the model between showed that the overshoot, settling time, peak time and
specified linearization inputs and outputs, and plots the control performance improved greatly by using fuzzy
response of the linear system. logic controller. Time domain performance indices such
as peak time, rise time, settling time and steady state
Table 4: Performance Indices of DC Motor with Adjusted error showed that the FLC enabled the DC motor to
FLC perform faster and better when the shapes of the
Performance Indices Values Units membership functions of the controller were adjusted
Peak Amplitude accordingly.
Peak Time
Rise Time
Settling Time 5. REFERENCES
Overshoot [1] Byington, C. “Intelligent Monitoring of Gas Turbine
Steady State Error − n in Lub i tion y t ” Association of
Research Libraries, Vol. 98, Number 10, 1998, pp 23-
It is clear from Table 4 that there is an improvement in 28.
the performance of the DC motor and the fuzzy logic [2] Marks, R. J. II (Ed.), ”Fuzzy Logic Technology and
controller except for a slight increase in system A li tion ” IEEE Technology Update Series, Vol.
overshoot. This is because FLC is inherently robust and 19, Number 26, 1994, pp 19-24.
nonlinear with elements of uncertainties in its structure. [3] Chandra, R. and Kumar, M. ”Speed Control of S.E.D.C.
Motor by Using PI and Fuzzy Lo i Cont oll ”
4. CONCLUSION International Journal of Soft Computing
The modelling of Fuzzy Logic Controller (FLC) for and Engineering, Vol. 3, Number 2, 2013, pp 143-
controlling the speed of a field-controlled DC motor of an 153.
emergency lube oil pump, during idling operation of a

Nigerian Journal of Technology Vol. 36, No. 3, July 2017 874

 SPEED CONTROL OF DC MOTOR ON LOAD USING FUZZY LOGIC CONTROLLER I. I. Ekpoudom, I. E. Archibong & U. T. Itaketo

[4] Guillaume, S. and Charnomordic, B. “Fuzzy Inf n [11] (http://www.pall.com/images/Aerospace-Defense-

Systems: An Integrated Modelling Environment for Marine/aerospace_engine_lube_systems_chart1.jpg).
Collaboration between Expert Knowledge and Data
U in Fi o” Expert Systems with Applications, Vol.
39, Number 10, 2012, pp 8744-8755. 6. APPENDIX I: Lube Oil Pump DC Motor Parameters
[5] Dorf. R. C. Electric Circuits, John Wiley and Sons, Parameter Name Symbols Values
Paperback, New York, 1996 Power ( ) 5.5
Input Voltage ( ) 110
[6] Vas, P n D uy W “ l t i l M hin n Input Current ( ) 61.1
D iv : P nt n Futu ” 8thMediterranean
Speed ( ) 1450
Electro technical Conference, Vol. 1, Number 6,1996,
Resistance ( ) 1.8
pp. 404-408.
Inductance ( ) 0.0195
[7] Niasar, A. H., Moghbelli, H. and Vahedi A “ Inertia ( ) 0.0002215
Control of a Brushless DC Motor Drive via Adaptive Torque Constant ( ) 0.0128
Neuro-Fuzzy Controller Based on Emotional Viscous Damping
L nin Al o ith ” Proceedings of the Eighth 0.005283
Coefficient ( )
International Conference on Electrical Machines and
Systems. ICEMS,N anjing, China, 2005. Vol. 1, pp.
7. APPENDIX II: Oil Pump Parameter for Computing
230-234, 27-29.
Impeller Inertia
[8] Dorf, R. C. and Bishop, R. H. Modern Control Systems, Parameter Name Symbols Values
Prentice Hall, Paperback, New York, 2001 Pump efficiency ( ) 95
[9] Kosko, B. Fuzzy Engineering, Prentice Hall, Specific Speed ( ) 1450
Paperback, New Jersey, 1997. Density of Oil-SAE-50 ( ) 890.8
Differential head ( ) 5
[10] Jurado, F. Ortega, F. M., Cano, A. and J Carpio, J.” Acceleration due to gravity ( ) 9.81
Neuro-Fuzzy Controller For Gas Turbine in Biomass- Volumetric flow rate ( ) 0.5
B l t i Pow Pl nt” Electric Power Systems
Research, Vol. 60, Number 3, 2002, pp 115-119.

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