JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
IMPLEMENTATION OF A FUZZY LOGIC SPEED CONTROLLER FOR A PERMANENT
MAGNET BRUSHLESS DC MOTOR DRIVE SYSTEM.
J. A. Oyedepo and A. Folaponmile
Department of Computer Engineering, Kaduna Polytechnic, Kaduna
Abstract
In this paper DC motor control models were mathematically extracted and implemented using fuzzy logic speed
controller. All control systems suffer from problems related to undesirable overshoot, longer settling times and
vibrations while going from one state to another. To overcome the maximum overshoot, fuzzy logic control
technique has been used in the controller architecture. Fuzzy logic controlled model of the DC motor was
implemented. The purpose is to achieve accurate trajectory control of the speed of permanent magnet brushless
DC Motor, especially when the motor and load parameters are unknown. Based on the mathematic model of
BLDCM, a fuzzy logic controller is designed, and the membership function is composed by Gauss function. This
fuzzy logic speed control of BLDC motor was simulated using MATLAB/SIMULINK and the result obtained
showed that excellent flexibility and adaptability as well as high precision and good robustness are obtained by
the proposed strategy.
Key words: Brushless DC motor, fuzzy logic control, speed controller
Introduction
There are mainly two types of dc motors used in the
industry. The first one is the conventional dc motor
where the flux is produced by the current through the
field coil of the stationary pole structure. The second
type is the brushless dc motor (BLDC MOTOR)
where permanent magnet provides the necessary air
gap flux instead of the wire wound field poles
(Tipsuwanporn et al 2002).
tools, industrial automation equipment and many
other recent ones as studied by researchers like Lee
and Ehsani 2003, Hong eta l, 2007 and Akkaya et al
2007.
Many machine design and control schemes have been
developed for the purpose of improving the
performance of BLDC motor drives. In order to
implement an effective control in simulation, the
model of the motor has to be known. Various
researchers (i.e. Safi et al 1995; Figueroa et al, 2003
and Hung et al, 2007) have proposed some simulation
models based on state – space equations, Fourier
series, d – q axis model and variable sampling for the
analysis of this type of motor drives. From control
point of view, DC motors exhibit excellent control
characteristics because of the decoupled, nature of the
field and armature mmf’s. Recently, many modern
control methodologies such as non linear control
(Hemati et al, 1990), optimal control (Pelezewski and
Kunz, 1990), variable structure control ( Lin et al,
1999) adaptive control (Cerruto et al; 1995) and
particle swarm optimization strategy (Nasri et al,
2007) have been widely proposed for linear brushless
permanent magnet DC motor.
With the rapid development of microelectronics and
power switches, most adjustable – speed drives are
now realized with ac machines. Permanent Magnet
Synchronous Motor (PMSM) with sinusoidal shape
back – EMF and BLDC motor with trapezoidal shape
back – EMF have been extensively used in many
applications, ranging from servo to traction drives due
to several distinct advantages. In short BLDC motors
have some advantages over conventional brushed DC
motors and induction motor. Some of these
advantages are: better speed versus torque
characteristics, high dynamic response, high
efficiency high power density, large torque/ inertia
ratio, long operating life, noiseless operations, higher
speed ranges. In addition, BLDC motors are reliable,
easy to control and inexpensive (Yedamale, 2009).
BLDC motors have favourable electrical and
mechanical properties, thus they are widely used in
servo applications such as automotive, aerospace,
medical instrumentation, actuation, robotics, machine
There are two methods of controlling BLDC motors
namely sensor control and sensor less control. The
latter has advantages like cost reduction, reliability,
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JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
elimination of difficulty in maintaining the sensor etc.
it is also highly advantageous when the motor is
operated industry or oily environment, where cleaning
and maintaining of Hall sensors is required for proper
sensing of rotor position, and they are preferred when
the motor is in less accessible location. Classical
control methods can be implemented in well – defined
systems to achieve good performance of the systems.
This paper deals with the implementation of fuzzy
logic speed controller for BLDC motors. The fuzzy
logic control has adaptive characteristics that can
Ref.
Current
Generator
achieve robust response to a system with uncertainty,
parameter variations and external load disturbance.
Modeling of BLDC motor drive system
Fig, 1 shows the Block diagram of the proposed
control system, which contain two loops. The first
loop is the current control loop that accomplishes
torque of BLDC motor while the second loop is the
speed control loop, which adjusts the speed of the
BLDC motor.
PWM
Current
Control
3 - ph
VSI
BLDC
Motor
Current Control loop
- Rotor Position
Fig 1 Block diagram of BLDC motor
Position and
Speed Detector
Actual speed
In the analysis of the BLDC motor the following
assumptions have been made for simplification and
accuracy; BLDC motor saturated, state resistances are
equal, self and mutual inductances are constant, semi
conductor devices of inverter are ideal, iron losses are
negligible, Back – EMF waveforms of all phases are
equal. For the purpose of analysis, equivalent circuit
of BLDC motor and VSI of fig. 2 will be used
BLDC motor
Three Phase VSI
o
Fig 2 Configuration of BLDC motor and VSI System
From fig.2, the dynamic equations can be derived as follows:
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JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
(1)
Where:
and are phase voltages
R is resistance, L is inductance
M is mutual inductance, , and
The motion equation is then expressed as
and
are trapezoidal back – EMFs.
(2)
By substituting eqn. (3) and (4) into (5),
defined as;
Where:
is the electromagnetic Torque,
is the load torque in
,
J is the moment of inertia in
,
B is the frictional coefficient in
is rotor speed in mechanical in
.
is rotor speed in electrical in
.
(6)
By making the damping factor negligible the
relationship between speed and torque of BLDC
motor can be rewritten as;
=
(7)
Modelling of trapezoidal back EMF
Voltage source inverter (VSI)
The trapezoidal back – EMF wave forms are modeled
as a function of rotor position so that rotor position
can be correctly calculated according to the operation
speed. The back emf are expressed as
As shown in fig 2, only the two phases are excited
through the conduction operating modes. According
to Lee and Ehsani, (2003), voltage and current
equations can be obtained as follows:
, and
Where
+
(3)
+
is back emf constant
is function of rotor position
The
named as trapezoidal shape functions with
limit values between +1 and -1 is defined as;
and
(5)
can be
(8)
+
Where
are the loop currents ,
are the line – to – line back emfs from fig 2
=
,
and
=
the phase currents are;
and
and
and
By using the switching function S. a,b, c which is
obtained from hysteresis block,
and
in
reference to midpoint of DC supply voltage
can
be calculated as (Cunkas and Aydogdu, 2010);
=
=
(4)
can be obtained in a similar way.
The electromagnetic torque is redefined using the
back emfs as follows;
=
67
=
JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
Design of fuzzy logic controller
=
=
(9)
Then the inverter line – to – line voltages can be
derived as;
and
The complete block diagram of the fuzzy logic
controlled BLDC motor drive system is as shown in
fig 3 and that of the fuzzy logic controller with two
inputs
and one output
is shown in fig 4.
(10)
Fuzzy
Controlle
r
PWM
Current
Control
Reference
Current
Generator
3 - ph
VSI
Position and
Speed Detector
- Rotor Position
speed
BLDC
Motor
Rotor Speed
Fig 3 Block diagram of fuzzy logic controlled BLDC motor drive system
Knowledge Base
Normalization
Fuzzifier
Inference
Mechanism
Defuzzifier
Denormalization
U
Fig 4 Block diagram showing structure of fuzzy logic controller
From fig 3, the error, e is calculated by taking the
difference between the reference speed and actual
rotor speed as follows;
(11)
And the change in error, ce is obtained as,
parameter
for the output. In normalization
process, the input values are scale between
and in denormalization process, the output values of
fuzzy controller are converted to a value depending on
the terminal control element.
The fuzzy values obtained from fuzzy inference
mechanism have to be converted to crisp output value,
, by defizzifier process. Initial rule base that can be
used in drive systems for a fuzzy logic controller
consist of 49 linguistic rules as shown in table 1, and
gives the change of the output of fuzzy logic
(12)
Where
is the previous error value.
In fig 4, there are two normalization parameters
for input and one denormalization
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JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
controller in terms of the two inputs. The membership
functions used to fuzzify the two inputs values
and defuzzify output
are given in fig. 5.
Table 1: Rule base of fuzzy controller
Ce
NB
NM
NS
Z
PS
PM
PB
NB
PB
PB
PM
PM
PS
PS
Z
NM
PB
PM
PM
PS
PS
Z
NS
NS
PM
PM
PS
PS
Z
NS
NS
Z
PM
PS
PS
Z
NS
NS
NM
PS
PS
PS
Z
NS
NS
NM
NM
PM
PS
Z
NS
NS
NM
NM
NB
PB
Z
NS
NS
NM
NM
NB
NB
Rule Matrix for Fuzzy Speed Control
Membership functions:
Fig. 5 : Membership function for e
69
of the fuzzy logic controller
JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
Fig. 6 : Membership function for ce
Fig.7: Simulink Model for the Fuzzy Logic Controller
Table 1. Specification of the Permanent Brushless DC Motor
PARAMETERS
VALUE
Armature resistance(Ra)
0.6Ω
Armature inductance (La)
0.012 H
Armature voltage (Va)
400 V
Mechanical inertia(jm)
0.15 Kg.m2
Friction coefficient (bf)
0.008 N.m/rad/sec
Back emf constant (k)
1.8 V/rad/sec
Rated speed
2100 r.p.m
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JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
Simulation results
FIG. 8 OUTPUT SPEED RESPONSE WITHOUT FLC FOR DC MOTOR
Fig.8. OUTPUT RESPONSE OF FLC COMPARED WITH PID FOR BLDC MOTOR
In this paper, the Characteristics of permanent
brushless DC motor, its steady state operation and its
Conclusion
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JORIND 9(2) December, 2011. ISSN 1596 – 8308. www.transcampus.org., www.ajol.info/journals/jorind
various torque-speeds/torque-current characteristics
are studied. Fuzzy logic basic definition and
terminology was studied with the help of MATLAB.
Due to simple formulas and computational efficiency,
both triangular MFs have been used to design fuzzy
Logic
controllers
especially
in
real-time
implementation. The speed of a BLDC Motor has
been successfully controlled by using fuzzy logic
controller technique. A comprehensive analysis of
brushless DC drive system has been performed by
using fuzzy logic controller. Furthermore, the control
algorithms, FLC and PID have been compared by
using the developed model. It can be seen that the
desired real speed and torque values could be reached
in a short time by FLC controller, though it has slower
rise time when compared with PID, its settling time is
better than PID.
Hong W, Lee W and Lee B.K (2007), “Dynamic
Simulation of Brushless DC Motor
Drives Considering Phase Commutation for
Automotive Applications", Electric
Machines & Drives Conference.
Lee B.K and Ehsani M (2003), “Advanced Simulation
Model for Brushless DC Motor
Drives”, Electric Power Components and Systems
Vol. 31, pp. 841–868.
Lin F.J, Shyu K. K and Lin Y.S (1999), “Variable
structure adaptive control for PM synchronous servo
motor drive,” IEE Proc. IEE B: Elect. Power
Applications, Vol. 146, pp. 173–185.
Nasri M, Neezamabadi-Pour H and Malihemaghfoori
(2007), “A PSO – Based Optimization of PID
Controller for a linear BLDC Motor”, Proc. Of World
academy of Science, Engineering and Technology
Vol. 20.
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