Robot and Servo Drive Lab.
Fuzzy Logic Torque Ripple Reduction by
Turn-Off Angle Compensation for Switched
Reluctance Motors
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 48, NO.
3, JUNE 2001
M. Rodrigues, P. J. Costa Branco, and W. Suemitsu
教授:王明賢
學生:莊博翔
Department of Electrical Engineering
Southern Taiwan University
2016/7/12
Outline






Basic knowledge of SRM
I. INTRODUCTION
II. TORQUE RIPPLE
III. RIPPLE REDUCTION BY TURN-OFF ANGLE
COMPENSATION
IV. EXPERIMENTAL RESULTS
V. CONCLUSION
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Basic knowledge of SRM

現有的高效馬達中，「永磁同步馬達」是最具效率的代表
性馬達，但是此種馬達需要使用稀土當作材料，而稀土近
年來價格逐漸高漲，加上大陸限制稀土出口，故磁阻馬達
成了許多國家的研究重點

優點：結構簡單、堅固、耐高溫、又具有容錯能力，製造
容易、成本亦低廉

缺點：轉矩漣波大造成震動與噪音，降低效率
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

實際運轉時，若不是在正電感區運轉時，會產生負轉矩及
轉矩漣波，造成振動與噪音
因此下圖為電感與轉矩對應圖，驅動馬達時必須在θ2到θ3
之間激磁，否則會產生負轉矩
L
Tr
Lmax
Lmin
1
2
3
4
5
6 
Te

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i1
i2
i3
Lm
Current(A)
i1
i2
i3
 off 1  off 2  off 3
Position(degree)
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Turn –off
angle for T1
Turn –on
angle for T1
Turn –on
angle for T2
Turn –off
angle for T2
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Abstract

Abstract—A fuzzy-logic-based turn-off angle compensator for
torque ripple reduction in a switched reluctance motor is
proposed. The turn-off angle, as a complex function of motor
speed and current, is automatically changed for a wide motor
speed range to reduce torque ripple. Experimental results are
presented that show ripple reduction when the turn-off angle
compensator is used.
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INTRODUCTION


Significant torque ripple, vibration, and acoustic noise are the
main drawbacks of the switched reluctance motor (SRM) to
achieve high performance.
More recently, a method was proposed in [6] that allows the
motor to be tuned up for maximum efficiency, maximum
torque, or minimum torque pulsation, by selecting different
operating modes. These approaches, however, are not very
practical for industrial systems considering a wide motor speed
operation
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
The dynamic torque, for instance, which is used in most torque
ripple minimization schemes, is a variable difficult to measure,
and torque sensors have low reliability. The technique shown
in this letter proposes that the motor speed and current signals
can be used directly in an offline training system to
automatically produce the turn-off angle that minimizes torque
ripple for the current machine’s operating condition.Therefore,
it is a technique appropriate for a converter programming on a
test rig at the factory.
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TORQUE RIPPLE
To the H-bridge converter, the phase current of the SRM
during its deenergizing process is given by
where i0 is the initial current, -V is the deenergizing voltage,c1 =L(  off )/R (1)
is the deenergizing time constant, L(  off ) is the phase inductance at the
turn-off angle, and Rx is given by
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Deenergizing process:
(1)
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
The time td to take the phase current to zero is, thus, given by
where (1) and (2) were used. Equation (3) shows that the deenergizing
time t d can be adjusted by the turn-off angle o for an initial phase
current i0 and motor speed ! by Rx . This fact also agrees with the
effect that different turn-off angles have on the torque ripple, as shown
in Fig. 1.
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(a) Electrical torque produced by phases 1 and 2.
(b) Resulting torque.
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(c) Torque ripple for different turn-off angles.
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III. RIPPLE REDUCTION BY TURN-OFF ANGLE
COMPENSATION

The SRM initially operates with a certain turn-off angle  off |initial
, which in our experiment had a value of 30°. To generate the
necessary compensations at the initial turn-off angle toward its
value reducing torque ripple, an increment  can be added to it
as
From the previous section and considering relation (4), the
value will be defined by a relation as  (  , I ref ).
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
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
Acquisition of the Compensating Relation:
Based on data obtained by the SR drive system simulation, a
fuzzy modeling algorithm was employed to extract the rules
relating the motor speed and phase current values to  angle.
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Fuzzy control

The algorithm considers each input variable to be equally
divided by symmetric membership functions of triangular
type, the output variable uses singleton fuzzy sets, and the
algorithm uses the t-norm max to select the degree to which
two fuzzy sets match. The rules in the fuzzy model have the
following form:
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Fuzzy control


where R (1) is the lth rule, x j are the antecedent variables, and z
is the consequent variable. For the SRM, x j will be the motor
speed  And current I ref signals, and z will be  the increment
(1)
added to the initial  off angle. Symbols A j represent the fuzzy
(1)
v
sets, and
is the rule conclusion that has to be learned, being
a real number (fuzzy singleton).
The firing degree of each rule is given by
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Fuzzy control

with the membership values of each input variable defined for
every fuzzy set composing the 1th rule, and combined using
the algebraic product operator ( *). The terms denoted by
are the corresponding numerical values of
, and expressions
denote
the membership functions associated to each fuzzy set
respectively.
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Fuzzy control

Each rule is represented as a fuzzy implication with its
implication degree given by
where the operation symbolized by “ ＊” is the inference product.
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Fuzzy control

The fuzzy algorithm is described in detail in [8]. Therefore, we
resume next only its main procedures to obtain the fuzzy rules.
For each antecedent and consequent numerical value, x and z ,
respectively, their membership degrees are computed in each
fuzzy set. This operation associates each numerical value to a
vector with a number of membership degrees equal to the
number of fuzzy sets previously given to the respective
variable. The highest degree in the vector indicates the fuzzy
set that better expresses the numerical value
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Fuzzy control

The inference method is based on the centroid-defuzzification
formula
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Fuzzy control


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(a) Fuzzy sets attributed to

I ref and 
I ref
(b) Compensation relation.
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Fuzzy control
TABLE I
FUZZY RULES FOR DETERMINATION OF
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
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Block diagram of proposed compensator
Fig. 3. Block diagram of proposed compensator.
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IV. EXPERIMENTAL RESULTS

The output of the compensating function is added to the  off |initial
angle, which generates the final turn-off angle to the SR drive
system, as Fig. 3 shows. To verify the proposed technique, a
prototype was implemented in the laboratory consisting of an
H-bridge insulated gate bipolar transistor (IGBT) power
converter with a hysteresis current control, a 4-Nm 750-W
150-V 6/4 SRM, and a microcomputer with an AD/DA
interface where both speed controller and the fuzzy
compensator were achieved.
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
Two procedures were used to measure the torque smoothness
when the compensator was included: the variance value of the
change of speed error and its frequency spectrum.
 From the speed error signal:
(9)
e    ref
and replacing (9) in the motor mechanical equation
d
(10)
J
 T  T1
dt
Result in
J
d (ref  e )
dt
 Jp[
dref
dt

de
]  T  T1
dt
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(11)
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
For constant speed reference signals
dref
dt

 0.0
and constant load, the change of speed error is related to the
electrical motor torque by
de T  T1

dt
J

(12)
(13)
Therefore, the change of speed error signal can indeed be a
good measurement of motor torque ripple.
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Frequency spectrum (a) before and (b) after compensation for 50 r/min.
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(c) Decreasing of power spectrum components for 50 r/min.
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Frequency spectrum (d) before and (e) after compensation for
1500 r/min.
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
The effects of the proposed turn-off angle compensator on
other SRM performance can be summarized as follows:
• Since torque ripple is decreased, the torque average
increases. However, since the SR drive contains a speed
control loop giving the phase current reference, the controller
decreases its value to maintain the motor speed in its reference,
if the load is maintained constant during the compensation
step.
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• The motor acoustic noise, caused mainly by the torque ripple,
is most important for low-speed operation of the SRM. The
proposed compensator is then capable of reducing the acoustic
noise and also the machine vibrations.
• Finally, drive efficiency remains at the same value which
occurred when the turn-off angle compensator was not
presented
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V. CONCLUSION

The proposed compensator offers a significant reduction in
torque ripple for a wide range of motor speed operation. No
torque signal was used, which increases the compensator
simplicity and reliability. Better results may be obtained if an
autotuning process could be incorporated in the fuzzy logic
compensator, which is currently under development
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