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IMTC 2003 -Instrumentation and MeasurementTechnology ConferenceVail, CO, USA, 20-22 May 2003

Sensorless Speed Detection Based on STFT of Series Excited MotorShi Jingzhuo, Xu Dianguo, Liu BaotingDept. of Electrical Engineering, Harhin Institute of TechnologyHarbin, 150001, P.R. ChinaEmail: shijz@hit,edu.cn,xudiang@public.hr.hl.cn

A m This paper studies on the sensorless rotating speeddetection methods for the single-phase A C series-mcited (SACS)motor. The method to solve thisproblem based on S T F T s workedout a n d the experiments show that, th e results with high precisioncan be obtained within IS seconds. The comparison between themethods using ST FT an d wavelet is also given OU Thecomparison shows that the method using ST FT is bener than thatusing wavelet both in calculation time andprecision.

I . I N T R O D U C T I O NThe single-phase AC series-excited (SACS) motor is widelyused in electrical tools and home appliances because of itssimple StNCNre and ability to be used under either AC or DCpower supply.In general, the SACS motor is tested using the traditional

torque testing systems. In these systems, encoder is commonlyused to detect the rotating speed of motor. The usage of encoderin the testing system has some disadvantages:

I ) Increase cost;2 Make the testing system more complex and not easy to be3) Easy to be fail to function.To avoid these disadvantages, sensorless methods have beenused to detect motors rotating speed. Th e rotating speed can he

acquired from the motors winding current andor voltagewaveforms based on Digital Signal Processing @SPtechnology.

There are commutator and commutator segments in theseries-excited m otor. The voltage comm utation will result in thespikes in the winding current waveform. The amplitude of thesespikes is depended on the amplitude of the commutation forceand current. The frequency of these spikes is depend on therotating sDeed of th e rotor,

installed;

for SA CS motor. The next part will analyze the spee d (detectionmethod in detail. The detected results are also given oiit in thispart. The comparison with different methods (STFT vs. Wavelet)will be analyzed in part Ill. Some conclusions are described inpart IV.

11. S P E E D D E T E C T IO N OF S A C S MOTOR.Fig.1 shows the sketch map of the test system. HP-61113A is aprogrammable AC power source and the GPIB card i s used tocontrol it. AD card and the pre-processing card are used to

acquire original data.

Fig.1 Sketch m ap of the testing systemsstructureFig.2 is the actual waveform of motor winding current andterminal voltage acquired using an oscilloscope. The ratedvoltage is A C I IOV and the whole testing time is 2 seconds. Thewinding cument rises quickly to the maximum value, afier that, itdeclined slowly to the stable value.

_ . Fig.2 Actual waveform of t he starting process1)c x K x p60 =-. nwher e, is rotating speed in rpm; K is the number ofcommutator segments; p is the number of motors pole pairs;c is a constant, c = 2 while K is odd, and c = 1w h i l e K iseven.

Thus i t can be seen, the rotating speed can be detected from theanalysis of the motor winding current waveform.This paper focuses on the sensorless speed detection method

Fig.3 is a tested waveform o f the armature current on a motor(We Call it example A below) and the frequency spectrum that isobtained by the real-time FFT. In the figure, the distortioncaused by the phase commutation is obvious, and the highfrequency components concerned with the rotational speed ofthe appeared. ~ i ~ . 4s the waveform of the armaturecurrent of another motor (we call it example B below). Thedistortion of the current resulted from the commutation exists

0-7803-7705-2/03/ 17.00 02 00 3 IEEE 1322

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hut not very obviously. From the FFT spectrum in Fig.3 and 4,we c an Observe the relatively obvious harmonic compo nents (theparts have been drawn by red circles) concemed with therotational speed o f the motor.

Fig.3Winding current waveform and its FFT result3Winding current waveform and its FFT result

Fig.4 Winding current waveform and its FFT resultDur ing the process of the motors starting from zero to stablespeed, the harmonic component concem ed with the speed of themotor in the waveform of the current increases from OHz o thestable value, covering a wide range, especially including thefrequencj. hand around 50160Hz. Moreover, the amplitude andthe form of the distortion of the current waveform due to thecommutation is different for different motor .All these haveadde d the difficulties of the detection of the motors speed.From the view of digital signal processing theory, the signal

of the arm ature current during the process of motor starting is akind of unsteady signal: Its amplitude and phase varyun-periodically with the time, and eventually tend to h e stablesignal (refer to Fig.2). And the useful signal superimposed thecurrent signal which we care about (the harmonic componentswhich reflect the information of the speed) is even an unsteadysignal whose amplitude, phase and frequency varyun-periodically with the time. As the signal of the armaturecurrent tends to be stable eventually, the useful signal also getsto be stable signal. But its amplitude and phase still varyperiodically with the time. This is because the useful signalresults from the process of commutation of motor is concernedwith the amplitude of excited current and physical structure ofindividual commutator segments. Therefore, the signal we careabo ut is a kind of complicated unstable signal. On the other hand,the power source of the motor is AC power, which adds thedifficulty of disposal.In order to obtain the information ,of the speed, the usefulsignal should firstly be extracted, which is also a process to filternoises. Then, the useful signal extracted will he disposed to

obtain the information of the instantaneous frequency concernedwith the rotational speed of the motor. Only from the view ofobtaining the information of the speed, the two steps above canhe brought together. That is, we can dispose directly upon thesignal acquired from the sampling in order to obtain theinformation of the speed. Reasonable design of the hardwarecircuit can make a reduction in the level o f the noise to a degreethat may he neglected comparing to the useful signal discussedabove. If the hardware cannot do this, then it will be difficult tofilter the noise and to retain the unsteady useful signal. To do so,every order of the statistic of the noise and the useful signalsneed to he analyzed carefully, especially when a general usedfilter is tried to design. It is certain that we want to not onlyobtain the information of the speed but also do some othernecessary signal processing to benefit the identification of theparameters of the motor. But at this time, the useful signalsuperimposed upon the signal of current has become uselesssignal which should also he filtered. Then the design o f the filterwill become relatively easy.Through the analysis above, it is concluded that we shoulduse the time-frequency analysis method o r the united analysis inthe multi-scale domain to get the speed information.STFT (Short Time Fourier Transformation, whose quickalgorithm is called S TFFT) is derived from the method of soundspectrogram method that is brought forward respectively in theyear 1946 and 1947 by Koenig and Potter. It supposed that theunsteady signal is steady (approximately steady) in a shorttime interval which is chosen by th e analyzing window function.The window is moved smoothly to obtain some different timeintervals. The unsteady signal snippets cu t by these windows a redifferent and are supposed to be fictitious steady signal in thedefinite width of time. Then, upon the assumption o f the steady,the power spectrum in different time intervals can he figured outbased on the traditional Fourier Transformation. There is thecorresponding quick algorithm - STFFT, which can be used inthe calculation to shorten the elapsed time greatly. This method,STFT, is also a kind of time-frequency united analysis methodand can he used to analyze the distribution of the unsteady signalin the time-frequency united d omain.

The essential expression of the continuous STFT is:S T F T f , f )= -_[s u)g* u t ) ~ - J z d u 2)

here, s U) is the disposed signal and g(u- , is the windowfunction moving smoo thly in the time domain. The choice of thewindow function is considered to be compromised between thewidth of the main lobe and that of the side lobe. Kaiser windowis used here.Fig.5 is the starting signal of winding current of example Awithout any load. For the purpose of clarity, the scale of time hasbeen stretched and only a small part of the whole startingwaveform is given. From the figure, ,we can observe thevariation of amplitude, phase and frequency of the useful signal.The total sampling time is 2 seconds and the data size is onemillion points.Fig.6 is the result of calculation through S TFFT. The width o fthe window in the transformation is 10000.points and thecontiguous windows overlapped 5000 points. From Fig.6, wecan see clearly the changing course o f the .frequency of the

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useful signal superimposed upon the current signal, which is alsothe changing course of the motors rotating speed. In this figure,there are several obviously curves. This is because the basisfunction of the S T M is sinusoid function between which and thewaveform of the useful signal there always exists difference.Therefore the frequency components that have a relationship ofunit fraction or integral multiple with the actual component areemerged. The power (or energy) of these frequency componentsis smaller than the actual one.. .

. . . . . . . . . . . . . . . .. .. . . . . . . . . . . . . .. . . . . .

Fig.7 gives another form of the result in which the referenceframe is accordant with the traditional Fourier Transformation.In the figure, only the result in a short time segm ent i given outto make the figure visible. It can be concluded in this figure thatthe real frequency components reflecting the speed have thehighest amplitude among all of the high frequency harmonics,thus they can be extracted easily. F ig 8 gives out a comparisonof the speed betw een the calculated result and the actual testingresult. They are consistent with each other.The calculation mentioned above was done on an industrialcomputer with PI11 886 processor with 128MB SFAM. Theelapsed time of calculation is less than 10 seconds.

I I

. . .. . . .

Fig.5 Actual winding current w aveform

Fig.6 STFFT calculation resuit. . . . . . .

I .8I6

m 1.4s 1.29 0.8{ 0 6re 0.4

0 200 2 4 6 8 IO 12 14 16

E l.-.

Frequency, kHzFig.7 STFFT calculation result

0 -D 0 1 2 0 3 0 4 6 6Time, sFig.8 Detected spe ed comparison

0 0 5 1 1.5Fig.9 STFFT calculation result

-1 0 2 0 3 4 1 5 1T1me.s

Fig.10 Detected s pee d comparison

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Fig.9 and 10 is the result through STFFT of example B andthe comparison between the actual and the calculated speedvalues. We can see that the same satisfying results can be gotthrough STFFT for the motor sample with not obvious distortionin the current waveform.Fig. 11 is the result based on STFFT of another motor sample.The error between the actual speed and detected values areshow n in Table I.

I

0 00 10 20 30 40 50 60 70 80 91 01 11 2l 31 41 5l 6Time, sFig.11 Detected speed comparison

I I I I I IE rror (% )] 1.19 0.67 I 1 1 5 I 0.65 -0.17 -0.75 -1.26111. C O M P A R I S O N B E T W E E N S T F T A N D W A V E LE TThe wavelet analyzing method is also used to calculate thespeed of motor sample A and B. The calculation result isrespectively shown in Fig.8 rind 10 for comparison. For sample

A the results by the two ways are nearly uniform while forsample B, the wavelet analyzing result have a bigger deviationwhile the STFT result is closer to the actual value. During thecalculation, the db5 wavelet packages which have the best effectare taken to decompose the cum nt s ignal and get 2N coefficientpackages, then the speed of the motor can be obtained. Becausethe data size is large, the time of calculation using the waveletanalysis is over twenty minutes.Therefore, we can see that, the method using db5 waveletspends more t ime on calculating and the effect is not satisfyingin the problems o f speed d etection discussed in this article.Wavelet is a kind of processing method that can analyzesunsteady signals in two dimensions with multi-resolution, thepulpose of analyzing is to see both the forest (the summary of asignal) and the trees (the details of the signal). Multi-resolutionof the traditional wavelet analysis is high resolution to thecomponents of low frequency and low one to the components ofhigh frequency, which is consistent with the human visual senseand hearing but not certain to fit other signals. Multi-layerwavelet packages developed later can choose differentresolutions for different frequency segments, which reach thesame goal by different routes comparing to STFT [SI.

Mann and Mihovilovic brought the chirplet and chirplettransform into the area of digital signal processing in 1992.Thesignal of armature cument of the motor in the state of startingwithout any load may be looked as a kind of special signal oflinear frequency modulation. As opposed to th e signal of l inearfrequency modulation in the general meaning, the useful signalhere is the changing high-frequency component superimposedupon the current signal of low-frequency. The author has beenconsidering whether we can use the basic concepts of chirplettransform and the similari ty of the disposed signal to design afeasible method so that we can raise the accuracy and therapidity further during the course of calculation.I V - C O N C L U S I O N SThis paper discusses the speed detection of single-phase ACseries-excited motor without sensor and gives out the method tosolve the problem using STFT. From the experiment results, theeffect is satisfying. As a kind of united analysis in both of thet ime domain and frequency domain to be applied in thesensorless speed detection for the motor detection, it has someadvantages as follows:I Because STFT is a method based on FFT, it has fastalgorithm which is r ipe and easy to be program med, usedand modified;

2 The analysis result is directly corresponding to the timedomain and frequency domain, so no extra transform isneeded. It is easy to be understood and applied;3 It has good adaptive ability.As a method of united analysis in the time-frequencydomain, i t is the same as other methods that , STFT also has thecontradiction between the resolution of time and frequency,which is described by the Heisenberg inequality (uncertaintyprinciple). It is shown in the problem discussed in this paper thatthe signal is steady in a short time which is delimitated by theanalysis window. We can obtain a value of speed throughcalculating which is considered as the average value of thevariational speed during the given time segment. And obviouslythe speed changes continuously. In terms of the uncertaintyprinciple, the frequency resolution in the result of calculation

(speed resolution in this paper) will surely decreased if the widthof the analysis window is decreased (that is to decrease thelength of time segment and to increase the resolution of time).Suitable comprom ising should be found betw een them when theunited analysis method existed now is applied to the realproblems.The other aspect of this problem is that when the speed ofthe motor is low, the error of the calculation result will be biggerbecause there is probable no or little spike brought about by thecommutation in an analysis time window. This problem is donewith by the combination of the specific points identification andextrapolation method in our work.With the progress of the times, the requirements for thenew method and techniques of motor testing in the motorindustry are increasing unceasingly. The authors have made

some attempts in the application of digital signal processing inmotor testing area and want to discuss in this area with otherresearchers. It is certain that with the further applying of thedigital-signal-processing technique in motor testing area, thelevel of the mo tor testing technique will be raised unceasingly.

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REFERENCES[I]. hrisco, R.M.. Automated, Full Load Motor Testing At ProductionSpeeds. Electtical Insulation Confercnce, 1997, and ElectticalManufacturing Coil Winding Conference. Procecdings: 337 -343[Z].Jugan, I Advanced Methods Of Motor Testing. Electrical ElectronicsInsulation Confer ence and Electrical Man ufactur ing Coil WindingConference, 1993. Proceedings, Chicago 93 EEICIICWA Exposition,

287 -290[3]. Kevin D. Hunt, Thomas G. Habetler. A Comparison of SpeClNmEstimation Techniques for Sensorless Speed Detection in InductionMachines. IEEE Transactions on Industry Applications, 33(4): 898-90514). M. Aiello, A . Cataliotti, S Nuccio. A Comparison of SpeClNmEstimation Techniques for Periodic Not Stationary Signals. Proceedingof IEEE Instrumentation and Measurement Technology Conference,2001,Hungary. 1130-1134[ 5 ] A.V.Oppenheim, R.W.Schafer, ' I.R.Buck. Discrete-Time SignalProcessing. 2 Edition. Pre itice- Hall Inc. 1999

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