High Robustness of an SR Motor Angle Estimation Algorithm using fuzzy predictive filters and...

7/30/2019 High Robustness of an SR Motor Angle Estimation Algorithm using fuzzy predictive filters and Heuristic knowledge

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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.

02780046/99$10.00 1999 IEEE


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CHEOK AND ERTUGRUL: HIGH ROBUSTNESS OF AN SR MOTOR ANGLE ESTIMATION ALGORITHM 905

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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(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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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.

REFERENCES

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[7] B. Kosko, Fuzzy Engineering. Englewood Cliffs, NJ: Prentice-Hall,1997.

[8] A. D. Cheok and N. Ertugrul, A model free fuzzy logic based rotorposition sensorless switched reluctance motor drive, in Conf. Rec.

IEEE-IAS Annu. Meeting, San Diego, CA, 1996, pp. 7683.[9] N. Ertugrul and A. D. Cheok, Indirect angle estimation in switched

reluctance motor drives using fuzzy logic based predictor/corrector, inProc. IEEE PESC98, Fukuoka, Japan, 1998, pp. 845851.

[10] T. Williams and R. Carter, Measurement of machine inductances usingan operational amplifier integrator, Int. J. Elect. Eng. Educ., vol. 10,pp. 177181, 1972/1973.

[11] A. D. Cheok and N. Ertugrul, High robustness and reliability of a fuzzylogic based angle estimation algorithm for practical switched reluctancemotor drives, in Proc. IEEE PESC98, Fukuoka, Japan, 1998, pp.13021308.

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efficient implementation for motion control applications, in Proc. IEEEInstrumentation and Measurement Technol. Conf., St. Paul, MN, 1998,pp. 881886.

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[18] P. R. Belanger, Estimation of angular velocity and acceleration fromshaft encoder measurements, in Proc. 1992 IEEE Int. Conf. Roboticsand Automation, Nice, France, 1992, pp. 585592.

[19] R. F. Sutton, Modeling Human Operators. New York: Wiley, 1991.[20] A. D. Cheok and N. Ertugrul, Use of fuzzy logic for modeling,

estimation, and prediction in switched reluctance motors, IEEE Trans.Ind. Electron., to be published.

[21] A. D. Cheok, A new fuzzy logic based sensorless rotor positionestimation algorithm for switched reluctance motor drives, Ph.D.

dissertation, Dep. Elect. Electron. Eng., Univ. Adelaide, Adelaide,Australia, 1998.

[22] A. V. Radun, C. A. Ferreira, and E. Richter, Two-channel switchedreluctance starter/generator results, IEEE Trans. Ind. Applicat., vol. 34,pp. 10261034, Sept./Oct. 1998.

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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