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904 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 5, OCTOBER 1999
High Robustness of an SR Motor Angle EstimationAlgorithm Using Fuzzy Predictive Filters
and Heuristic Knowledge-Based RulesAdrian D. Cheok, Member, IEEE, and Nesimi Ertugrul, Member, IEEE
Abstract In this paper, the operation of a fuzzy predictivefilter used to provide high robustness against feedback signalnoise in a fuzzy logic (FL)-based angle estimation algorithm forthe switched reluctance motor is described. The fuzzy predictivefiltering method combines both FL-based time-series prediction,as well as a heuristic knowledge-based algorithm to detect anddiscard feedback signal error. As it is predictive in nature,the scheme does not introduce any delay or phase shift in thefeedback signals. In addition, the fuzzy predictive filter does notrequire any mathematical modeling of the noise and, therefore,can be used effectively to control non-Gaussian impulsive-typenoise. An analysis of the noise and error commonly found inpractical motor drives is given, and how this can effect positionestimation. It is shown using experimental results that the FL-based scheme can cope well with erroneous and noisy feedbacksignals.
Index TermsAdaptive filters, error analysis, fuzzy logic, fuzzysystems, nonlinear filters, parameter estimation, reluctance motordrives.
I. INTRODUCTION
I
N THE SWITCHED reluctance (SR) motor drive, the rotor
position must be known, because excitation of SR motor
phases needs to be synchronized with the rotor position. Posi-
tion sensors are commonly employed to obtain rotor position
measurements, but in many systems, these are undesirable.
Hence, as extensively detailed in reference [1], a diverse range
of indirect, or sensorless position estimation methods, has
previously been proposed.
A major concern is that, in these schemes, measured motor
feedback signals are used to calculate the motor position in
real time. However, motor drives are electrically noisy envi-
ronments, and practical measurement equipment is imperfect.
Thus, the feedback signals will usually be corrupted by noise
and error.
Hence, the previously developed estimation schemes maynot be useful in practical drives unless their reliability and
robustness against noise and error is proven. Existing literature
on the effects of errors in SR motor position estimation
schemes has been sparse. In [2], only the time and amplitude
Manuscript received September 17, 1998; revised May 31, 1999. Abstractpublished on the Internet June 18, 1999.
A. D. Cheok is with the Department of Electrical Engineering, NationalUniversity of Singapore, Singapore 119260.
N. Ertugrul is with the Department of Electrical and Electronic Engineering,University of Adelaide, Adelaide 5005, Australia.
Publisher Item Identifier S 0278-0046(99)07247-0.
quantization errors due to digital implementation of a single
linear inductance-based scheme was discussed. The issue was
further discussed in [3], where specific types of SR motor
physical designs were proposed to improve the robustness of
position estimation to error.
To improve the performance of the SR motor drive with po-
sition estimation, some form of conventional filtering method
could be used to reduce the noise and disturbance on the feed-
back. Yet, there are both practical and theoretical limitationsto this approach.
In practice, the algorithms and implementation of conven-
tional filtering methods introduce some time delay. This may
not be acceptable due to the time constraints of the real-time
position estimation and control of the motor [4].
In addition, theoretical problems emerge due to the fact that
the feedback signal noise in real motor drive environments is
often impulsive or non-Gaussian in nature [5]. Using conven-
tional filtering methods to decrease this noise is difficult, due to
the fact that non-Gaussian noise is difficult to mathematically
model and predict and, therefore, difficult to filter [6].
Hence, in this paper, a novel method is given to decrease
the problem of signal corruption in the feedback signalsinvolved in SR position estimation. The method can be applied
to all feedback-based SR motor sensorless schemes, can be
used for all physical SR motor designs, and addresses both
Gaussian noise and non-Gaussian noise. The fuzzy predictive
filter method combines both adaptive fuzzy logic (FL)-based
prediction, and a heuristic knowledge-based algorithm im-
plemented with fuzzy rules, to detect and discard noise on
the feedback signals. The scheme does not introduce any
delay or phase shift in the feedback signals because it is
predictive in nature. In addition, an important feature of the
method is that the fuzzy predictive filter does not require any
mathematical modeling of the noise and can be used effectivelywith non-Gaussian impulsive noise [7]. The fuzzy predictive
filter method can be applied in conjunction with any sensorless
position detection method where motor feedback signals are
used. Furthermore, the FL algorithm uses simple calculations,
which provides the benefit of fast real-time execution.
Before detailing the filtering method, the angle estimation
scheme used in conjunction with the fuzzy predictive filter
is discussed. An analysis of the noise and error commonly
found in practical motor drives will be given, and it will be
shown how the feedback noise can affect position estimation.
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Fig. 1. Block diagram of the FL-based position estimation algorithm.
The theory of the algorithm will then be discussed. Next, by
demonstrating the fuzzy predictive filters use with a developed
sensorless motor drive, it will be shown that the filter brings
a high robustness and reliability to position estimation by
increasing the quality of the feedback signals.
II. FL-BASED ANGLE ESTIMATOR
The fuzzy predictive filter method described in this paper
was applied to an FL-based rotor-position estimation scheme.
A block diagram of the FL-based angle estimation algorithm
can be seen in Fig. 1.The details of the estimation scheme have been previously
described in [8] and [9]. In conjunction with an FL-rule-
based SR motor model, the scheme estimates the position
from input measurements of the phase currents and phase flux
linkages. Analog integrators can be used to estimate the flux
linkages of the motor, but these often have the problem of
drift in the output signal due to temperature sensitivity and
the need for compensation [10]. Therefore, in the FL-based
position-sensing algorithm, the estimation of flux linkage was
performed using digital real-time trapezoidal integration. This
required digitized phase voltage and current signals that were
measured using analog-to-digital (A/D) converters [(1)]
(1)
(2)
where is phase flux linkage, is phase resistance,
is phase voltage, is phase current, is sample number,
and is sampling period.
Hence, the feedback signals that are used for the real-time
estimation of rotor position are the motor currents and esti-
mated flux linkage. However, as mentioned above, measuredsignals are subject to noise and imperfect measurements in
real motor drive environments. This noise will lead to errors
in the reading of the currents and voltages and
in Fig. 1. Any error in the measurement of currents
and voltages will correspondingly lead to an error in the flux
linkage found from integration in Fig. 1] and,
consequently, the estimated position in Fig. 1].
Before investigating the details of the fuzzy-predictive-
filter-based error correction method, it is first instructive to
consider the cause and effect of feedback signal error in the
SR motor. This will be given in the following section.
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TABLE ISOURCES OF FEEDBACK ERROR
Fig. 2. Examination of error of flux linkage and angle in flux-linkage characteristics.
III. ANALYSIS OF NOISE AND ERROR SOURCES
IN SR POSITION ESTIMATION
The feedback error can be defined as the difference between
the actual physical motor quantities of current, voltage, and
flux linkage, and the corresponding feedback values used
for position estimation. In this case, the various sources of
feedback error [3] can be classified under four groups, as
shown in Table I.
Fig. 2 shows the effect of errors in both the flux linkage
and current feedback values. The feedback flux and current
provide a point on the magnetization or curves that
correspond to a certain rotor position. The true values will
correspond to the correct point of rotor position, whereas the
erroneous values will lead to different points on the curvesand, thus, an erroneous rotor position.
To consider the sources of flux-linkage error, firstly it is
useful to define the measured quantities with finite errors
(3)
(4)
where and are the measured values of voltage and
current, and are the physical values of voltage and
current in the motor, and and are the respective error
components.
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TABLE IIANALYTICAL ERROR EXPRESSIONS
If in addition, is taken as the change in stator resistance
from nominal value, then from (1) it can be seen that, for
samples after the initial integration sample, the corresponding
accumulated error in the flux-linkage estimate will be
(5)
From (5), analytical expressions for the effect on flux-
linkage error of the error-producing sources can be found atsample This total flux linkage error will be approximately
equal to
(6)
where is the total flux linkage error, is the offset
error, is the amplitude error, is the time quanti-
zation error, is the amplitude quantization error,
is the mean signal noise error, and is the error due to
change in resistance.
In [3] and [11], analytical analyses of the flux-linkage errors
were given. For reference, Table II summarizes some of theresults.
If there are flux-linkage estimation errors due to one or more
of the above-explained effects, there will be a correspondingerror in the rotor-position estimation. In this present analysis,
it is assumed that there is no filtering of the feedback signals,
in order to consider the worst case. The angle error for a
given flux error will be given by
(7)
In the above equation, the quantity , or density of angle
variation with flux, is defined for a given motor current
such that
(8)
where is the number of curves separated by one
rotor angle degree in the flux region at
constant current
Similarly to the flux linkage, the current measurement will
be affected by offset error, amplitude error, and noise. For a
given error in the current measurement the angle error
will be given by
(9)
where, similarly to (8), for a given flux linkage , a quantity
, or density of angle variation with current, is defined such
that
(10)
where is the number of curves separated by one
rotor angle degree in the current region
at constant currentTherefore, the above analysis demonstrates that the error on
the position estimation due to error on the feedback signals
is a nonlinear function of the measured feedback signal noise,
the instantaneous level of the current and flux linkage in the
measuring instant, and the actual rotor position. In addition,
as mentioned above, the noise and error will normally be non-
Gaussian in nature and, therefore, difficult to model and filter
using conventional methods. Hence, a mathematical model
free fuzzy predictive filtering method was used to decrease
the effect of feedback error and noise. This method will be
discussed in the following section.
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IV. FUZZY PREDICTIVE FILTERS
In this section, details will be shown of the developed
method that was used in conjunction with the angle estimation
algorithm to detect and discard noise on the feedback signals
without using conventional filtering methods. The method
allows reduction of feedback signal noise, without any delay in
the feedback signals, by using FL-based prediction algorithms
and heuristic decision-making techniques. The fuzzy predictivefilters of flux linkage and angle as used in the position
estimator were shown in Fig. 1. As seen in the figure, there
are both flux linkage and angle fuzzy prediction and decision-
making blocks. These work together in conjunction to form a
fuzzy predictive filter block for both angle and flux linkage.
A. Prediction of Flux Linkage and Position
The prediction algorithm used is implemented using FL,
and its purpose is to predict future values, so that if a
measurement inaccuracy occurs, the predicted value may be
used to lower the error and, therefore, effectively filter the
feedback signal using prediction. To achieve this, a comparisonbetween estimated and predicted rotor position and flux values
is made during each iteration. Then, some combination of these
is chosen in order to lessen the effect of errors.
The purpose of the predictor can be better understood if the
ideal case is taken in the first instance. In the ideal case of
accurate prediction, the estimated values of flux linkage (from
integration) and position (from the output of the fuzzy motor
model) could be predicted accurately using the prediction
algorithm. Now, consider the case where, for a short instant
of time, the measured values of flux linkage and position
are erroneous. At this time, the predicted values (which are
predicted from the previous correct values of flux linkage and
position) will be good approximations of the actual values offlux and position in the machine, if the prediction algorithm
is accurate. In this case, the estimated values can be ignored,
and instead the predicted values can be used. However, this
does not offer an ideal solution. The first question that arises
is: If the estimated and predicted values are different, which
is actually the more correct value?
Human intuition is required to try to answer this problem,
and this will be discussed later.
The problem of predicting the flux linkage and angle in
future steps of time is a problem of time-series prediction. It
has been demonstrated that FL systems are excellent solutions
for time-series prediction [12], [13]. In addition, a wide array
of FL-based prediction algorithms has been developed [7],[14], [15]. In this work, real-time motor drive implementation
is an important issue and, thus, the table lookup learning
scheme [13] was used. This is because fast one-pass learning
and simple computations are features of the table lookup
scheme.
The FL predictor using table lookup learning operates by
generating fuzzy rules from the numerical inputoutput data
pairs of previous data points, each separated by a constant
step of time, and creating an adaptive predicting fuzzy rule
base. The rules of this predicting fuzzy rule base define the
relationship between the present value of data and past values
of data. The fuzzy predictor can then make a prediction from
this fuzzy rule base.
For example, consider as a time se-
ries of previous rotor-position values (or previous flux-linkage
values), each separated with a constant time interval (equal
to the rotor-position computation period of the sensorless
algorithm). If the future value of at time step in
the future, is to be determined from a window of previous
measurements then
inputoutput pairs can be formed. These inputoutput pairs
will be
(11)
In the above equation, the symbol indicates some FL-
based function relating a future output value (e.g.,
with previous values (e.g.,
As mentioned above, the table lookup learning scheme is
used to generate rules from these inputoutput data pairs.
The method has been detailed in [9] and [13] and so will
only be briefly reviewed here, with particular reference to the
prediction algorithm. The method consists of the following
steps.
Step ADividing the Input and Output into Fuzzy Regions:
In this initialization step, which is performed only once before
the algorithm is run, the range or intervals of the input and
output variable domains are defined. In this case, the input
and output domains are the previous values and future values,
respectively, of the flux linkage and angle. Each domain is
then divided up into fuzzy regions. Finally, each fuzzy regionis assigned a fuzzy membership function.
Step BFuzzy Rule Adaptation from InputOutput Data
Pairs: Once the fuzzy membership functions in the input and
output domains have been defined as in Step A, data can be
used to determine fuzzy rules and create the fuzzy rule base.
To determine a fuzzy rule from each inputoutput data pair,
the first step is to determine the degree of each crisp data
point in every membership region of its corresponding fuzzy
domain. The crisp data points are then all assigned to the fuzzy
region with maximum degree. Then, these fuzzy regions are
combined to form a fuzzy rule relating the input values to
the output values. Thus, each new inputoutput data pair will
produce a fuzzy rule.As an example, consider an inputoutput data pair
After assigning the data points
to the fuzzy region in the inputoutput domain with the highest
degree, the following fuzzy rule can be formed:
(12)
where is the fuzzy region of highest
degree assigned to data values
respectively.
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Step CAssigning Rule Degrees: In order to choose be-
tween data sets that produce the same antecedents but different
consequences, a rule degree or truth is assigned to the rule.
Then, conflicting rules are resolved by choosing the conflicting
rule with the highest degree. In the developed method, a degree
is assigned which is the product of the membership degree of
each variable in its respective region. For example, the rule in
(12) would have degree
(13)
where is the membership degree of crisp data point
in fuzzy set
Step DAdaptive Rule Base Modification: Every time a
new measurement is made, a new inputoutput pair consisting
of the previous and the present values is made and, thus, a
new rule can be formed relating previous values to future
values. Each new fuzzy rule is stored in the fuzzy rule base,
unless there is a conflicting rule already existing which has
a higher degree of truth. In this manner, the predicting fuzzy
rule base is adaptive in nature and will change during the
actual operation according to the data input values.Step EPrediction from Rule Base: The adaptive fuzzy
predicting rule base is then used to predict a future data value
from the previous data points. Here, the value
is a chosen integer that represents the value of at
the data point in the future (where each data point is
separated in time by one computation period of the sensorless
algorithm). Essentially, the predicting fuzzy rule base is used
as the nonlinear mapping between the previous data points
and
To make a prediction, the previous values
are used as the crisp input to the
fuzzy predictor. The inputs will trigger rules in the fuzzy
predicting rule base, and this will give an aggregated fuzzyoutput. This output is then defuzzified to give the crisp
prediction of The operation of the fuzzy predictors
with the predicting fuzzy rule base uses maxmin implication
and center average defuzzification. These methods use simple
algorithms and, thus, have the advantage of fast computation.
In this application, values of 1 and 4 were used
for the flux linkage predictor, and 1 and 2 and
4 were chosen for the angle predictor (where and are
the parameters defined above). Therefore, for any iteration
the four previous and present values of flux linkage,
, are used to predict the next value
of flux linkageSimilarly, the previous four values of angle are used to
predict the next two values in time of angle and
Two values are predicted because the next value
of angle can be used to compare the predicted and
estimated value, and the next value in time after this angle
can also be used by the motor controller.
In each iteration, both training of the fuzzy rule base (Steps
B, C, and D) and prediction from the rule base (Step E) occur.
Specifically, when a new value of flux linkage or rotor
position is estimated, it is used with the previous values
to first modify the rule base by creating a new rule that maps
Fig. 3. Fuzzy membership functions for decision block.
TABLE IIIFUZZY RULE BASE FOR CONFIDENCE
past to present values. The updated rule base is then used for
prediction.
The second part of the fuzzy predictive filters, which is the
FL-based heuristic decision block, will be detailed in the next
section.
B. Weighting of Predicted and Estimated Values
Using Heuristic RulesAs can be seen in the block diagram of Fig. 1, the predicted
values of rotor position (from the angle predictor) and
flux linkage (from the flux linkage predictor) are used
in conjunction with the estimated values of flux linkage
(from integration) and rotor position (from the fuzzy
model output). In the ideal case, the predicted and estimated
values should be exactly the same. However, as mentioned
above, these may differ due to errors. In this case, either the
predicted values or the estimated values may be used, and a
decision must be made as to which value should be chosen in
order to increase the accuracy of the fuzzy predictive filter. In
this system, a knowledge-based heuristic decision maker was
implemented. This decision-making algorithm was termed adecision block. From Fig. 1, it can be seen that the decision
blocks of the flux linkage and angle produce final weighted
values and respectively.
The principle purpose of these decision blocks is to imple-
ment human intuition in selecting a good weighting between
the estimated and predicted values of flux linkage and angle.
For instance, it can be said that under steady-state speeds, the
rotor-position and flux-linkage trajectories will be regular and
periodic functions. Under this condition, the fuzzy predictors
will be able to forecast with good accuracy [8], [9]. Therefore,
if the predicted and estimated values differ under steady
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TABLE IVPUBLISHED EXPERIMENTAL RESULTS
speeds, then this would more likely be from errors in the
estimated values and, thus, more weighting can be placed on
the predicted value.
However, during transients, the fuzzy predictors may not
perform as well, due to the learning period always required
with new events. In this case, if there is a difference betweenthe estimated and predicted values, then the predicted value
would more likely be in error and, thus, more weighting will
be placed on the estimated value.
Thus, under steady speeds and conditions, it can be intu-
itively said that the confidence in predicted values will be high,
whereas under transient speeds and conditions, this confidence
will be low. In addition, it can be said that the confidence in
the predicted values will be higherfor low acceleration values
than for high acceleration values.
From the above discussion, it may seem that some con-
ventional mathematical function relating confidence in the
predicted values to the actual motor acceleration can easily
be defined. However, some practical considerations make theuse of a fuzzy system advantageous.
Firstly, it can be seen from the above discussion that
high, low, and steady are linguistic terms that contain a
certain amount of fuzziness. With conventional mathematical
logic functions, it is difficult to adequately represent heuristic
knowledge directly. However, fuzzy systems can deal with
situations where sharp distinctions between the boundaries of
application of rules do not occur.
Another advantage of using a fuzzy system in this case is
that it allows flexibility to easily fine tune the relationship
between acceleration and confidence by modifying the fuzzy
sets and rules. During tuning, the general heuristic rules can
remain unchanged.Furthermore, a major advantage of using a fuzzy system is
that it can cope with inherent uncertainty in the input signals,
unlike traditional mathematical logic techniques which would
require accurate inputs for accuracy in the outputs. In this
system, the input variable is acceleration. The acceleration
cannot be directly measured by a mechanical sensor in this
application because the system is sensorless. Another method
is to calculate acceleration from speed values. Successful tech-
niques have been recently developed to estimate acceleration
by using predictive polynomial differentiators [16], [17] or
model-based state observation [18]. However, in this case, no
direct measurement of position or speed is possible. If the
position estimates are used instead, the errors in the estimates
may be too high for calculation of acceleration.
Therefore, a fuzzy system was developed to relate prediction
confidence to acceleration which eliminates the need for
accurate inputs and can use heuristic knowledge. The fuzzysystem only requires the acceleration feedback to be accurate
enough to determine which predefined fuzzy domain the
acceleration belongs to. Thus, only imprecise knowledge is
required about the motor acceleration.
Instead of acceleration, an acceleration factoris used, which
gives an approximation of the actual acceleration. As discussed
above, this approximation can be used in this application
because only the relative acceleration is important (e.g., high
or low), and not the actual numeric value. Therefore, an
acceleration factor is defined as
(14)
Here, is the rotor angle at step and is the time
between each iteration, and and were chosen to both
equal five. It should be noted that this factor is an imprecise
representation of acceleration and contains a delay of
between the first measurement being available and when
it applies.
The decision block uses this fuzzy system and gives the
predicted values of flux linkage and position a
confidence value based on the linguistic knowledge described
above. It is a single-inputsingle-output (SISO) fuzzy system
where the input fuzzy domain is the acceleration factor,
while the output domain is the confidence. The membership
functions of the variables acceleration factor and confidencefor this decision block are shown in Fig. 3. For simplicity, both
fuzzy domains have been normalized to vary from 0 to 100.
The fuzzy rule base that was used is shown in Table III. The
rules in this table are created using the general heuristic knowl-
edge discussed above. This demonstrates the ease in which FL
can encapsulate human intuition expressed in linguistic terms
to create a knowledge-based algorithm [19].
V. EXPERIMENTAL RESULTS
To test the new scheme, an SR motor drive system was
designed and constructed. The drive consists of the following
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(a)
(b)
Fig. 4. Error elimination ability of FL-based predictors. (a) Flux linkage. (b) Rotor position. The points with arrows highlight the iterations where thepredicted value can be used instead of the estimated angle to lessen the effect of switching noise.
components as described in detail in [9]: four-phase SR
motor (415 V, 4 kW, 9 A, 1500 r/min), insulated gate
bipolar transistor (IGBT) inverter, digital signal processor
(DSP) control board (ADSP21020), A/D converter board, andan interface board. Many experiments were performed to prove
the performance and reliability of the method. Although, due
to space limitations, only some selected results are presented
here, a wide range of other results has been published, as
mentioned in Table IV. In this paper, two important tests are
given: performance with high amplitude impulsive noise and
Gaussian noise.
A. Fuzzy Predictive Filters with Non-Gaussian Noise
To demonstrate the effectiveness of the fuzzy predictive
filters, a test is shown for the case when the feedback sig-
nals are imposed with high-amplitude impulsive noise. As
mentioned above, the practical SR motor drive often has
the problem of high-amplitude impulse-type noise caused by
switching or commutation of high-amplitude currents in theinverter circuit. The commutated current waveforms have
short rise and fall times and, hence, these waveforms contain
significant amounts of energy at high frequencies (such as
radio frequency or RF region). This radiated energy can
be transmitted through parasitic stray capacitances to the
control, interface, and measurement circuitry. Some parasitic
capacitances will always exist between the high-power inverter
circuits, the high- and low-voltage sides of the opto-isolation
circuits, the low- and high-voltage sides of the current and
voltage measuring circuits, and the low-voltage control and
A/D converter circuits.
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(a) (b)
Fig. 5. SR motor phase current. (a) With added noise (10% of maximum). (b) Expanded comparison of current waveforms, with and without noise.
(a) (b)
Fig. 6. SR motor phase voltage. (a) With added noise (10% of maximum). (b) Expanded comparison of voltage waveforms, with and without noise.
The characteristic feature of this generated noise is that it
can have high amplitude during the switching of a power
device. However, this noise is only seen during the switch-
ing instant. Therefore, the coupled noise in the control and
current and voltage measurement circuits may have high
amplitude, but be transient in nature. This type of high-
amplitude impulsive-type noise is defined as non-Gaussian
noise and presents problems for practical systems because it
is difficult to model mathematically and suppress efficiently.However, the fuzzy predictive filters of flux linkage and angle
as described above were developed to lower the effect of non-
Gaussian noise for the practical operation of the sensorless
position estimation scheme.
In Fig. 4, a demonstration of the fuzzy predictive filters
ability is shown. This figures shows estimated flux linkage and
angle derived from experimentally measured waveforms of
current and voltage using the previously described motor drive
running at 670 r/min. It can be seen in the figure that high-
amplitude error pulses occur in both the estimated flux-linkage
waveform and the estimated rotor-position waveform. In order
to obtain experimental consistency, these random pulses were
added into the estimated signals.
In Fig. 4(a), the waveforms of the flux linkage estimated
from the measured current and voltages are shown, with a
triangle representing each point where the flux is estimated
from the current and voltage measurements. In the figure,
a flux-linkage waveform with high noise error can also be
seen. In this test, the estimated flux-linkage waveform with
error is input to the flux-linkage predictive filter instead ofthe actual estimated flux. When this waveform is input to the
flux-linkage predictive filter, it can be seen that the points with
high-level noise have effectively been replaced by predicted
values. It should be noted that, if the filter could not remove
the erroneous value, then due to the operation of integration,
all future values of the estimated flux linkage would carry this
error.
In Fig. 4(b), the waveforms are shown of the measured
encoder angle and the estimated angle with impulsive-type
noise (at different test times, but with the same conditions as
the flux linkage test). In the results, a triangular point shows
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(a)
(b)
Fig. 7. (a) Measured rotor position. (b) Estimated angle from angle estimation scheme.
the measured encoder positions at each sample time. In this
test, the estimated angle that has been corrupted with high-
amplitude noise pulses is input to the angle predictive filter. It
can be seen that the noise in the estimated angle is effectively
removed in the filtered angle value. The filtered value can,thus, be used instead of the estimated value to reduce the
effect of switching noise.
The very high error pulses would normally lead to a
controller error every time the error pulse occurred (due to
a high rotor-position error). This could cause the controller
to change the switching patterns of the motor phases and,
thus, change the switching state of the inverter power switches.
Hence, this would lead to erroneous switching of the motor
voltage that may cause greater harmonics in the motor wave-
forms, increased torque ripple, and audible noise. In addition,
there would be higher losses due to the motor phases being
unnecessarily commutated, due to inverter losses and heating
from the power devices being switched in error.
The results above have shown that when the FL-based
predictive filters of flux linkage and angle are used, the
high error pulses from sources such as switching noise areeffectively eliminated, which leads to a more robust and stable
motor drive operation.
B. Gaussian-Type Noise
A further examination of the usefulness of the fuzzy pre-
dictive filters in the sensorless SR drive is shown in this
section. The results in this test demonstrate the robustness of
the scheme under high levels of Gaussian-type feedback signal
noise. Note that the essential difference between the previous
impulsive noise results and the following tests is that, in these
results, there is a lower peak amplitude, but higher average
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914 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 5, OCTOBER 1999
(a) (b)
(c) (d)
Fig. 8. 20% of maximum amplitude noise. (a) SR motor phase current. (b) Expanded comparison of current waveforms, with and without noise. (c) Phasevoltage. (d) Expanded comparison of voltage waveforms, with and without noise.
level of feedback signal noise. In the previous tests, there was a
high-level, but short-duration, impulsive feedback signal noise.
Therefore, these conditions provide a more difficult test of the
fuzzy predictive filters performance. This can be explained by
considering that, in the case of Gaussian-type random noise,
the previous input values to both the flux-linkage and rotor-
position fuzzy predictors will have a high average error. This
will lead to high average errors in the predicted values of theflux and angle predictors [21], which will, in turn, decrease the
accuracy of the filtered feedback signals and the resulting angle
estimation. Therefore, the performance of the fuzzy predictive
filters is lower in this case. However, as will be shown below,
even under such conditions, the fuzzy predictive filters offer
a measured decrease in the level of error seen in the resultant
output of the system (the angle estimation) as compared to
the level of noise in the input feedback signals (flux linkage
and current).
In Figs. 5 and 6, the experimentally measured waveforms
of current and voltage for one phase of the SR motor are
shown for the case when the motor is operating in single-pulse
mode at a steady speed of 660 r/min. Although the measured
currents and voltages are affected by noise and measurement
inaccuracy, Gaussian noise was deliberately added to the
signals after digitization by the A/D converters. This is in order
to definitely observe the performance of the fuzzy predictive
filter under difficult conditions.
In the first set of results, a noise error of up to 10% of themaximum level of the measured signals is added. It should
be noted that the original signal always contains some initial
error.
An expanded view of the current and voltage in Figs. 5(c)
and 6(c) clearly shows that the voltage and current with
noise deviates significantly at various points in time from
the measured values without added noise. The measured and
indirectly estimated rotor angle for this test is shown in Fig. 7.
The average amplitude of the error between the measured
and estimated angle in this test is 1.24 , while the maximum
amplitude of error is 3.97 . The average error represents 2.1%,
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CHEOK AND ERTUGRUL: HIGH ROBUSTNESS OF AN SR MOTOR ANGLE ESTIMATION ALGORITHM 915
Fig. 9. Estimated angle, 20% of maximum amplitude input noise.
while the maximum angle estimation error represents 6.6% of
one electrical cycle of 60 , which is less than the maximum
10% input signal error. The error in the estimated angle is nothigh relative to the input error, and successful operation of the
motor is possible.
Further experiments were carried out to test the scheme at
higher noise levels and to see the operational limits of the
filters. The level of noise imposed on the motor waveforms
of current and voltage was increased to 20% of the input
measured signals maximum level. In this set of results, the
noise has a significant component and provides a difficult
test for the fuzzy predictive filters. The added noise can be
clearly seen in the expanded waveforms in Fig. 8. In Fig. 9,
the estimated angle from the angle estimation algorithm is
shown for this experiment (the measured angle was shown
in Fig. 7). It can be seen that the general trajectory of therotor angle has been retained in this test, even for the high
level of noise. At no point in this test has the large deviation
of the input current and voltage data caused a breakdown of
the algorithm. The average angle estimation error is 2.80 , or
4.7% of one electrical cycle, while the peak error is 9.92 , or
16.5% of the electrical angle cycle of 60 , which is still lower
than the maximum 20% input signal error amplitude.
Hence, it can be seen that fuzzy predictive filters can be used
to add robustness to the sensorless algorithm, even under the
presence of high levels of feedback signal noise. It has been
shown that the peak estimation error has a lower percentage
value than the peak input error. In addition, the average angle
estimation error is sufficiently low.
VI. CONCLUSION
In most applications where motor drives are used, the
reliability of the drive is of utmost concern. This is particularly
the case for some applications of the SR motor drive, such
as in aerospace applications [22], where the reliability and
robustness (such as the ability to operate when one or more
phases fail) are the main reasons for the choice of the motor
drive. Hence, if a drive system using a position-detection
algorithm does not have a very high robustness and reliability,
it will not be advantageous over those using position sensors
and will, in fact, degrade the system reliability.
Feedback signal noise and error can affect the reliability ofthe position detection algorithm. To improve the robustness of
the angle estimation against this noise, some form of filtering
may be used. However, conventional filters do introduce some
delay and, in addition, may not be able to suppress non-
Gaussian-type noise.
In this paper, a new fuzzy predictive filtering method was
shown, which used time-series prediction of both the estimated
flux linkage and angle. In addition, a heuristic rule-based
decision block was implemented to detect and discard noise
in the feedback signals. As the scheme is predictive in nature,
there is no inherent delay or phase shift introduced into
the feedback. Furthermore, the fuzzy predictive filter does
not require any mathematical modeling of the noise and,therefore, can also be used effectively to filter non-Gaussian
impulsive noise. It was shown experimentally that the FL-
based angle estimation with predictive filters could cope with
the difficult operating conditions that are found in motor drive
environments.
Additional results showed the ability of the fuzzy predictive
filters to improve the performance of the scheme under high
levels of Gaussian-type feedback signal noise. Hence, it was
demonstrated that, by using fuzzy predictive filters, the scheme
can successfully estimate the rotor position under high error
and noise conditions in practical SR drives, as well as being
potentially suitable for other sensorless drives.
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Adrian D. Cheok (S93M98) received the B.Eng.
(Hons. First) and Ph.D. degrees from the Universityof Adelaide, Adelaide, Australia, in 1993 and 1998,respectively.
From 1996 to 1998, he was with Transmissionand Distribution, Transportation Systems Center,Mitsubishi Electric Corporation, Amagasaki, Japan.Since 1998, he has been an Assistant Professor inthe Department of Electrical Engineering, NationalUniversity of Singapore, Singapore. His researchinterests include power electronics and motor drives,
fuzzy logic and soft computing, nonlinear modeling and control, noise andEMI, embedded systems, and digital signal processing.
Nesimi Ertugrul (M95) received the B.Sc. de-
gree in electrical engineering and the M.Sc. degreein electronic and communication engineering fromIstanbul Technical University, Istanbul, Turkey, in1985 and 1989, respectively, and the Ph.D. degreefrom the University of Newcastle, Newcastle uponTyne, U.K., in 1993.
He joined the University of Adelaide, Adelaide,Australia, in 1994. His research interests includerotor-position sensorless operation of brushless per-manent magnet and switched reluctance motors,
real-time control of electrical machine drives, electric vehicles, and powerelectronics utility systems. He is currently engaged in research in the field ofinteractive computer-based teaching and learning systems involving object-oriented programming and data acquisition.
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