Implementation of a Fuzzy Logic Speed Controller Using Scalar Method for Induction Machine Drive

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Implementation of a Fuzzy Logic Speed Controller Using
Scalar Method for Induction Machine Drive

Y. Miloud, A.Miloudi A. Draou
University Center of Saida Dr.A. Draou, A. Professor Senior MIEEE,
BP 138, En – Nasr, Saida 20000, Algeria PO Box 105276 Madina, Saudi Arabia
miloudyahiadz@yahoo.fr adraou@yahoo.com


1. Introduction

Scalar control as the name indicates, is due to
magnitude variation of the control variables only, and
disregards the coupling effect in the machine. Scalar-
controlled drives have been widely used in industry the
fact that they are easy to implement [1], [3], [4], [5].
In this paper, a scalar control method is associated
with fuzzy logic control to regulate the speed of an
induction motor. A conventional PI controller is
compared practically to fuzzy logic controller using a
simple cassy card. The robustness of the fuzzy logic
controller (FLC) is also verified by changing the load
torque and speed tracking at full load. The first part of
this paper concerns the presentation of the volt/hertz
scalar control scheme. Then, the topology of the fuzzy
logic controller is presented. The results obtained
experimentally with fuzzy logic controller are compared
with classical PI controller.


2. Control Strategy

2.1 Scalar Volts/Hertz control

The proposed strategy is based on simplified
volts/Hertz control scheme with stator frequency
regulation ωs as shown in figure 1. For adjustable speed
applications, voltage is required to be proportional to
frequency so that the
(
ess
V
ωψ
/
=
), neglecting the stator resistance
drop. Figure 1 shows the block diagram of the volts
/ Hz speed control method [2]. The power circuit
consists of a diode rectifier with three-phase ac supply,
LC filter, and PWM voltage-fed inverter. Neglecting the
small slip frequency ω
command ωe is generated through the regulator and
limiter. The frequency command ωe also generates the
voltages command (
,
function generator, which incorporates the low-
frequency stator drop compensation, (V
voltage V0 is added so that the rated flux and
corresponding full torque become available down to
zero speed. At higher frequencies the boost voltage
becomes negligible. The ωe signal is integrated to
generate the angle signal
θ , and the corresponding
,,
cba
vvv
flux remains constant
s
R
sl of the machine, the frequency
, ) through a volts/Hz
a
v*
b
v*
c
v*
0). The boost
e
phase voltages (
expressions shown in figure 1.
signals) are generated by the
***
Figure 1 : Scalar Control Scheme

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3. Design of a fuzzy logic controller

The fuzzy logic is utilized to design controllers for
plants with complex dynamics that often cannot be
precisely known. In a motor control system, the function
of a fuzzy logic controller is to convert linguistic control
rules into control strategy based on heuristic
information or expert knowledge. The fuzzy logic
control approach is very useful for induction motor
speed drives since no exact mathematical model of the
induction motor or the closed-loop system is required
[6].
A fuzzy logic controller (FLC) has a fixed set of
control rules, usually derived from expert’s knowledge.
The membership function (MF’s) of the associated input
and output linguistic variables is generally predefined
on a common universe of discourse. For the successful
design of FLC’s proper selection of input and output
scaling factors (SF’s) and/or tuning of the other
controller parameters are crucial jobs, which in many
cases are done through trial and error to achieve the best
possible control performance [1],[6].
The block diagram showing the implementation of
the FLC is illustrated in Fig. 2. It includes four major
blocks: knowledge base, fuzzification, inference
mechanism, and defuzzification. The knowledge base is
composed of a data and a rule base. The database,
consisting of input and output membership functions,
provides information for the appropriate fuzzification
operations, the inference
defuzzification. The rule base is made of a set of
linguistic rules relating the fuzzy input variables to the
desired fuzzy control actions. The actual inputs to the
fuzzy system are, eN and ∆eN , which are a scaled
version of the speed error and the change in speed error
as defined by (1) and (2) .
The gains Ge and G∆e, can be varied to tune the fuzzy
controller for a desired performance.

The output gain, G∆u can also be tuned.

eN = Ge (Ω*-Ωr ) = Ge e (1)

∆eN = G∆e ∆e (2)

1-Fuzzification, Inference and defuzzification

The input variables are normalized to an ‘universe of
discourse’ with scaling factors.
Using these normalized quantities, the fuzzy logic
controller inputs can be described by membership
factors for every linguistic code. This operation which is
called ‘’Fuzzification’’,
requires the definition of linguistic sets and their
membership functions. We have chosen three linguistic



mechanism and

sets (NB, ZE, PB) for the error, the change of error and
for the output.
We have used symmetric triangular shapes for the
change of error and output (except the two MF’s at the
extreme ends) which are trapezoidal and asymmetric
triangular shapes for the error. The membership
functions are defined in the interval [-1, 1]. The values
of the actual inputs e and ∆e are mapped onto [-1, 1] by
the input SF’s Ge and G∆e , respectively.
The inference engine, based on the input fuzzy sets,
uses the appropriate IF-THEN rules in the knowledge
base to make decisions, where the Max operation is
used for the premises and the Min operation is used for
the implication.
The implied fuzzy set is transformed to a crisp output
by the center of gravity defuzzification technique as
given by the formula (3) ,
is the numerical output at
)(
µ
corresponds to the
the ith number of rules and
value of fuzzy membership function at the ith number
of rules as shown in Fig. 3. The summation is from one
to n, where n is the number of rules that apply for the
given fuzzy inputs. The output of the fuzzy controller is
integrated to give the stator speed command.
iz
iz
Fig 2 : Fuzzy Controller block
Figure 2 : Fuzzy Controller block
Figure 3 : Input and output membership
functions
-1-0.8-0.6 -0.4-0.20 0.20.4 0.60.81
0
0.2
0.4
0.6
0.8
1
NBZEPB
ωe
Ge
Ge
G∆e
G∆e
∆e
G

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Z0 =
( )
z
µ
∑
=
i
∑
=
i
n
i
n
ii
zz
1
1
)(.
µ
(3)



2 -The Fuzzy Rule Base

The fuzzy controller’s strongest asset is the
knowledge base. By carefully designing the knowledge
base, the expert’s experience is incorporated into the
fuzzy controller.


Table 1: Fuzzy controller rule base



∆ ∆e / e
NB ZE

NB
NB NB

ZE
NB ZE

PB
ZE PB


This experience is synthesized by the choice of the
input-output membership functions and the rule base. In
general uniformly distributed triangular membership
functions are used in order to simplify the digital
implementation.
This paper uses uniformly distributed triangular
membership functions for the error, change of error and
output membership functions. The range for the input
and output membership functions are as shown in Figs.
3 . The complete control rules used in our system are
shown in table. I. They are developed based on expert
knowledge. The linguistic labels contained in the table
are :


PB

ZE

PB

PB



NB
ZE
PB


Given these rules and membership functions, the
fuzzy controller produces the crisp and continuous non-
linear I/O map as shown in figure 4.

4. Implementation

4.1. Description of the control system

The fuzzy control is implemented on the test bed on
figure 5. This variable speed drive includes a 1 Kw
three-phase induction motor fed by an IGBT (Insulated
Gate Bipolar Transistor) PWM voltage source inverter.
The rotor speed is captured with a speed sensor . A DC
generator allows to produce simple load variations. The
control algorithms are developed in Turbo Pascal
language in a Pentium I. A cassy card is used to
transfer the input speed to the computer after being
filtered and then will be compared to the reference. The
speed error is then introduced to the regulator to give
the frequency command ωe which will be used as an
input to the inverter through the cassy card. The
sampling frequency for the FLC controller is 600 Hz
whereas for the PI controller is almost 1 Khz and the
maximum frequency for the cassy card is only 1 Khz.
However, the program for the FLC should be optimized
to have less computational time. For that reason, only 9
rules are used.

4.2. Experimental results

In this section, the experimental results for a 1 Kw
cage rotor induction machine, using the fuzzy controller
described in section III, is compared to a conventional
controller PI. The machine parameters are given in table
II.
Fig.6. and Fig.7. show the disturbance rejection of
each controller when the machine is fully loaded and
operated at 2000 rpm and a load disturbance torque ( 1-
Nm) is suddenly applied, first, at 7.8 s and then at 13 s.
The fuzzy controller rejects the load disturbance very
quickly with no overshoot and with a negligible steady
state error. Whereas the PI controller takes much longer
to return to speed command and presents an overshoot
at the starting. The PI controller’s disturbance rejection
performance can be improved by readjusting the gains
at the expense of speed tracking performance. For
example, larger integral gains can be used to reduce the
errors, but will cause serious speed overshoots.
Fig. 9 and Fig. 10. show the speed tracking
performance with load, for both PI and Fuzzy
controllers respectively. The PI controller tracks the
command speed with an overshoot at starting of 15 %
but the FLC controller tracks the command speed with
no overshoot.
:
:
:
Negative Big
Zero
Positive Big
Fig 4: Output of fuzzy logic controller
Figure 4: Output of fuzzy logic controller

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5. Conclusion

A comparison between a FLC controller and a PI
controller for scalar control has been presented in this
paper. The proposed FLC controller consisting of three
linguistic sets in the output of the rule base and
uniformly distributed triangular membership functions
gave very satisfactory results in terms of load
disturbances rejection and tracking speed. The
implementation of the whole system was carried out by
using very simple equipment with good experimental
results .









(a) Structure of the test bed
Table 2: Induction Machine Parameters
Number of pairs of poles
Rated power
Rated frequency
Rated speed
Rated voltage
Rated current
Stator resistance
Rotor resistance
Stator inductance
Rotor inductance
Mutual inductance
Moment of inertia
Friction coefficient
p = 1
1 KW
50 Hz
2880 rpm
220/380 V
3.8/2.2 A
Rs = 6.18 Ω
Rr = 4.38 Ω
Ls = 695 mH
Lr = 695 mH
Lm = 678 mH
J = 0.0125 kg.m2
f = 0.0033 kg.m2/s



6. Reference

[1] B.K. Bose, “Modern Power Electronics and AC
Drives”, Prentice-Hall, Upper Saddle River , NJ :
2002.
[2] F. Betin, D. Depermet, P. Floczek, A. Faqir, V.
Lanfranchi, D. Pinchon, C. Goeldel, A. Capolino, “
Fuzzy Logic Scalar Control For Induction Machine
Drive : Comparison
Drive”.International AEGEAN Conference on
Electrical Machines and Power Electronics. 27 – 29
June 2001, pp 646-651.
[3] I. Kioskeredis, N. Margaris , “ Loss Minimization
in Scalar-Controlled Induction Motor Drives with
Search Controllers”, on Power Electronics, Vol. 11,
No. 2, March 1996, pp 213-220.
[4] A.M. Garcia, T. A. Lipo, D.W. Novotny, “ A New
Induction Motor V/f Control Method Capable of
High-Performance Regulation at Low Speeds,
IEEE Trans on Industry Applications, Vol. 34, No.
4, July/August 1998, pp 813-221.
[5] K. Koga, R. Ueda, and T. Sonoda, “Constitution of
V/f Control for reducing the steady state speed
error to zero in induction motor drive system”, in
Conf Rec. IEEE-IAS Annu. Meeting, 1990, pp-
639-646.
[6] Y. Miloud, A. Draou, “Fuzzy Logic Speed Control
of an Indirect Field-Oriented Induction
Machine Drive”, Conf. Rec. IEEE/IECON’01
Denver, USA, pp. 2111-2116, Nov. 2001.









With Classical
(b) Test bed photograph
Figure 5 : Test bed

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(a)
(a)
Speed (rpm)
Time (sec)
Phase current (A)
Time (sec)
Speed (rpm)
Speed (rpm)
Phase current (A)
666 rpm /div ; 2s/div
666 rpm /div ; 2s/div
(b)
(b)
Phase current (A)
Phase current (A)
Figure 6 : Experimental PI controller
Load Torque Disturbance (± 1Nm);
(a) Speed, (b) Phase Current
Figure. 7 : Experimental Fuzzy controller
Load Torque Disturbance (± 1Nm);
(a) Speed, (b) Phase Current
666 rpm /div ; 5s/div 666 /div ; 5s/div
Speed tracking (rpm)
Speed tracking (rpm)
Time (sec)
Time (sec)
Figure 8 : PI Experimental Speed
Tracking
Figure. 9 : Fuzzy Experimental Speed
Tracking