speed sensor less control of ac machines using direct flux control scheme

8/14/2019 Speed Sensor Less Control of AC Machines Using Direct Flux Control Scheme

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Speed Sensorless controlof AC machines usingDirect Flux Control Scheme

Anshuman Tripathi, Student member IEEE,Ashwin M Khambadkone*, Member IEEE, Sanjib K

Panda, Member IEEE

Abstract-Due to incorrect estimatio n of stato r flux vectoraround zero speeds, the performance of m ethods for speedsensorless control of induction motors, is very poor. Wepropose a simple method to accurately estimate the statorflux vector and demon strate it's functioning for operationat very small angular velocities. Estimation of average syn-chronous angular velocity in every sampling period is doneby using th e stator flux error vector. Using th e Direct FluxControl (DFC) method we show how to get the rotor an-gular velocity at and around zero value. Test results arepresented for dynamic torque operation at and around zerospeed. The advantage of this method is that, it uses theavailable information of the DFC method for achieving sen-sorless operation without complicating th e original controlscheme. Given the fact that most sensorless induction mo-

tor drive applications do no t require a servo performance atzero speeds, the proposed scheme is shown to give a reason-able accuracy.

I. IXTRODUCTION

Sensorless speed control makes a drive sys tem economi-cal. But how close is the speed and torque control perfor-mance to t he one tha t uses a speed sensor? Th e importantfactor that influences the performance of a sensorless driveopera tion using conventional met hods is, estimati on of t hestator flw vector. Common methods of sta tor flux vec-tor estimation are those using voltage model or the currentmodel. For robust torque an d flux vector control schemes,voltage model is used because it involves only the statorresistance. In this meth od th e induced voltage vector is in-tegrated to obtain th e stator AUK linkage vector. However,a pure integrator has drift and initial value problems [I],[2]. These problems a re solved by using a low pass filter in-stead of a pure integrator but thi s results into a magnitudeand phase angle error in the esti mated flux vector. Furthe r,th e problem of dc-bias necessitates high pass filtering. Ahigh pass filter cascaded with an integrator, is equivalent t oa low pass filter that once again results into a magnitudeas well as phase angle error in the estimated flux vector[3]. Faithful estimation is guaranteed for operating fre-quencies higher than a few Hz, but around zero speed, thismethod fails to properly estimate the IIUK ector becausethe magnitude of dc offset and other disturbances becomemore pronounced than the induced emf. This deteriorates

the zero speed, steady state and dynamic performance ofschemes like Direct Torque Control (DTC) [4], as it leadsto incorrect voltage vector selection. Moreover, closed loopspeed sensorless control is not possible, if wrong st ato r flux

Authors are wi t h the department of Electrical Engineering, N ational University of Singapore, Engineering drive-3, Singapore,117S76. *Corresponding author (phone no.(0065)6874515i email:eleamkQnus.edu.sg)

estima te is used. Th e focus of this paper is to develop atechnique th at helps to improve the estimation of the s tato rflux vector and rotor angular velocity, for values down tozero. We will also show th e speed and torque dynamic nearand at zero speed. Th e metho d proposed here is differentfrom the approaches taken in [5 ] , GIand uses conventionaltechnique of speed estima tion whereby th e stat or flux esti-mate is used to d etermine the synchronous angular velocityand slip velocity is used to get the rotor angular velocity.The sensorless scheme presented here, is not intended forservo applications. Hence opera tion at zero speed with fulltorque is not the main thrust. Direct Flux Control (DFC)

171 scheme is used for analysis and experimental verifica-tion. In the next section, we will highlight the problemduring sta tor flux estimation and give a simple method ofcorrecting it.

11. ESTIMATION F STATOR LU X SING M ODIFIED

High performance torque control requires accurate esti-mation of stator flux vector for all operating rotor angularvelocities. Different methods ar e proposed to elimina te th eeffect of dc offset tha t is always present in th e sensed cur-rents, resulting into saturation of th e integrator. A methodof limiting the magnitudes of cy and 0 omponents, 111 cansolve th e problem of saturation b ut results into a variable

phase angle error specially at speeds around zero. Thismakes the system unstable at operating frequencies be-low 3 Hz. Most of the other methods like (21 are basedupon the modified flux estimation model of Fig. 1 . Thismethod attempts to compensates for the magnitude andphase angle error brought about by using a low pass filter.Compe nsati on in the magni tude and angle of flux is done

VOLTAGE MODEL

LO w Pass Filter compensation compensation

Fig. 1. Modified voltage model for flux estimation

after low pass filtering. This method is good at discardinghigh frequency noise but the dc-offset still appears at theoutput of the filter, specially at very low operating veloc-ities. Moreover, the closed loop steady st at e and dynamicperformance of a speed sensorless drive system at speedsaround zero will depend upon th e parameter k which needsto be tuned by trial and error [2]. Reference [3 ] improves

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upon the estimation of this compensation by having a cas-caded assembly of a complex compensating gain, a highpass filter and an integrator. This cascade combination ef-fectively is a compensated low pass filter. Following equa-tion (using normalized quan titie s) is used for stat or Huxestimation,

T+Js = /{(I - j X S & l ( l d , ) ) ( U , - s & ) - XU,$,,}dT (1)

here, W. is the synchronous angular velocity and X is a tun-ing parameter. Th e poles of the resulting low pass filterwill be self adjusted corresponding to the operating angu-lar velocity. Thi s model will work well only if th e followingtwo conditions are satisfied. (a ) amo unt of dc-offset is samefor the sensed currents an d (b) analog gains provided bythe an ti noiselaliasing filters are exact ly equal. Implemen-tatio n of the modified voltage model helps to deal withthe problems of noise and drift. However, th e calculatedflux still exhibits a dc offset bias at operating frequenciesaround the zero value. Besides this, th ere is no stand ardway to fix the factor A. In order to help with the devel-opment of an ad aptiv e algorithm or t o cancel off the offsetdirectly, an offset detection/correction algorithm needs tobe developed. Ideally, it should be able to detect th e valueof the dc bias at a faster rat e than t he frequency of the sta-tor flux, and it should not be computationally intensive, soas to maximize the sampling frequency as the executionof the control algorithm is limited by the processor speed.Fig. 2 provides a view of the algorithm used to detect thebias. In this figure, the problem due to dc-bias is shown

4

between any two points with respect to the "displaced cen-ter" of th e stat or Hux vector locus is same . Once thesepoints are located on the locus of the flux vector, linesjoining the points YO), ( ~ 2 ~ ~ 2 )nd ( ~ I , Y I ) , ~ 3 ~ ~ 3 )can be dramn. Po ints pl and p2 divide these lines into twoequal parts and the co-ordinates of these points are givenas, z 2 + ~ 0 ) / 2 , ( y 2 + ~ 1 0 ) / 2 and (z1+z3)/2, Y 1 + 2 / 3 ) / 2 . Th elines joining p l an d ( z ~ , y t ) nd pa and ( 2 2 , ~ ~ )ntersecteach other at a point (zc, c). This point is the "displacedcenter" due t o biasing. The average value of this bias istaken for one cycle and this is used t o obta in th e value ofX of eqn. ( 1 ) to get a correct esti mate of t he Hux vector.Therefore, this me thod of correction of the dc-bias is selfregulating. After a few cycles of bias correction the valueof X stabilizes and can be used directly to e stimat e the Huxvector. A flow chart showing the steps of bias estiniation

for flux linkage

Update samples(x, Yo b..

Ncalculate bias

(X. I Y.)

Increment biasupdate counter

reset bias updatecounter

to bias control

Fig. 3. Flow Chart far bias correction

Fig. 2. Algorithm for flux estimation

and an approach to tackle th e same is illustrated. (zn, SO) ., - - - ,.( z ~ , y ~ ) ,z2,yz) and ( z 3 , y3) are the Hux vector estimates . \ ,for consecutive sampling insta nts. The angular difference the stator flu vector locus is shown to exhibit a constant

and correction is shown in the Fig. 3 . The effect of hiascompensation can be seen from the plots of Figs. 4 and 6 .A small step change of 0.1 Hz, in the synchronous angularvelocity U, of the stator Hux vector is given at standstill.For a n ar bitrar ilv fixed value of X in eon. (1 ) the center of

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offset. Under similar conditions, the bias compensation al-gorithm results into t he corrected locus of Fig. 5. Fig. 6 shows the locus of th e stator flux vector at a rotor angularvelocity of 0.05 H z . As the operating frequency increasesbeyond 10% of the rated value the modified voltage modelas given in eqn. 1 gives faithful estimate of the st ator fluxvector. Thus the bias detection and correction algorithm

may no longer be used. Th e next section gives a new

St.OP ; .... .;.

.+.I_ ...-,. _--,:I,, ...-.-,-. i f . .C/ ...... -... -2 :.

. ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. . . . . . . . I

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

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

. .. :. .

.. .

i : . :. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .. .. i :. . A

Fig. 6 . Stator flux vector locus a t 0.05 H i , without (left) and with(right) bias correction algorithm

Re

Fig. 7 . Principle of torque control

During steady sta te conditions, t he synchronous angularvelocities of the stator Hux vector at two consecutive sam-pling inst ants are same. Thus the angular displacement v ssbetween any two samples will be equal. This condition isshown in the vector diagram. Depending upon the op erat-ing an gular velocity, the Hux error vector Allt, decides theduty cycles of the switching states.

A step command in torque, generates a slip angular ve-locity th at defines a new position of th e reference flux vec-tor. This results into an angular displacement p d y n tha twill be much larger tha n th e stead y state value.

Fig. 8 gives the block diagram of the control structure.Output of the torque controller is slip angular velocity thatis added with the rotor angular velocity to give the syn-chronous angular velocity of the reference stator flux vec-tor. During a step change in torque command, there isa ste p change in the position of th e reference flux vector.Dynamic of the estimated stator Hux vector is decided bythe predictive dead-beat flu)( controller, which forms theinner loop of the block diagram of Fig. 8.

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PFig. 8. Block diagram for sensorle~s ynamic torque control using th e DFC scheme

B. Predictive stator flu control and estimation of sy m the actual flux vector and the predicted reference will be2wsTs. Hence, if th e predicted reference vector an d thehronous angular velocity

Stator flux vector control is done in stator coordinates.To mitigate phase erro r, predictive control becomes neces-sary. In reference [8] it hils been explained how predictiveflux vector control compensates for the phase error. Be-fore deriving the synchronous angular velocity let us definethe reference flux vector a nd t he predicted flux vector insta tor co-ordinates. In discrete ti me system we will choosethe sampling period as 2T, where T, will be called a th esub-cycle. Therefore the predicted st ato r flux reference is

^ ^

estimated flus ector ar e available, t he error vector A + , ( k )will directly define th e switching state s th at will make thiserror zero after every sampling period. This is done inthe following manner, (a ) A Q S ( k ) s mapped in the samespace diagram as th e voltage vectors of the inverter and ( b)switching of th e adja cent voltage vectors is done such thatthe t otal volt-seconds obtained is equal to the volt-secondsof A~,b~(k). his method of obtaining the inverter dutycycle is called st ato r flux vector based PWM. Magnitude ofthe flus error vector, l A ~ - ( k ) I ecides the rat e at which the..glvc'l aaflux vector can b e moved. Hence it should give the average

+;s ( k ) = I+; 1eAd!4+4dk+112~s) (2 ) angular velocity of stator flux vector in a sampling period.Thus, besides defining the switching state vectors, A+,(k)+* ( k ) = +: (k )eh (k +f ' )2 Tscan be used to extr act t he synchronous annular velocity ofS ( 3 ) -the stator flux vector. .4t a sampling instant k as shown

in Fig.9, +,(k) makes an angle E with the reference a-axis.A + , , ( k ) is the flux error vector. Th e angular displacement

In steady state, the predicted reference flux +&moves ata stator frequency of U s rad/s, as shown in Fig. 9. In

-

tP

a-

of the er ror vector is p. From the figure, we can say that

This gives,

Conventionally, th e synchronous angular velocity is ob-tained by differentiating the stator flux vector angle. Thismethod has problems during the machine star t up. Usingthe proposed method we can find out the average angularvelocity in a sample for al l operating frequencies includ-ing zero. The adva ntages of the DFC method over conven-tiorial methods are th at it is more robust, achieves constantswitching frequency operatio n an d can operate in overmod-ulation ensuring th e best torque dvnaniic at all operating- ~ .

Fig. 9. Predictive dead beat control of stator flux velocities. In th e next section we show how to obta in th erotor angular velocity and thereafter present experimentalresults for the speed sensorless operation.ne sampling period 2T,, the a ngular displacement between

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W I . W w = 5 v CKpOan"........ oc q ... . . . . . . c.a:, ......... De,:, .

C. Estimation of rotor angular velocity

Using eqn. ( G ) ,angular velocity of th e sta tor flux vectorcan be estim ated. To estimate rotor angular velocity, theslip velocity a s defined by the output of torque controllerFig. 8 ; is made use of. Thu s th e difference of these veloci-ties gives the rotor angular velocity under both stead y sta te

and dynamic conditions. Th e slip as given by the torquecontroller does not depend upon the rotor time constantan d as such is more robust to te mperatu re variations. Es-timated rotor angular velocity is filtered using a a low passfilter. Results of dynamic control using estimate d rotor an-gular velocity are shown in Figs. 10 an d 11. Both figuresshow a reversal in the rotor angular velocity. Fig. 10 isplotted by putting an un-tuned value of X in eqn. (1). Theestimated speed is controlled b ut t he a n error in the phaseangle of the flux components is evident. This will givetorque oscillations. Fig. 11 is plotted with a t uned value ofX using the bias estimation algorithm. Th e estimated fluxis shown to be having no phase angle error.

.:v

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

- = " :. . . . . . ..oc.r,. .....................

I I

Fig. 10. Speed control using the DFC scheme: ste p change from -50R P M to +50 RPhI with phase angle error and without biascorrection

vY

-4

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

'i

I I

. . . -Y

i4 :

Fig. 12. A step of 500 R P M from standstill, rising estimated rotorangular velocity for closed loop drive operation

Fig. 13. Rated Torque step with zero reference speed

torque step a t a rotor angular velocity of 0.2 p u . Dur-ing torque transients, the slip angular velocity changes, re-sulting into a transient in the estimated angular velocity.However, the steady s tat e estimate is same as the encodervalue. Th is can be seen in Fig. 14. Th e drive system usesan inverter of 2 kW and a 0.75 k W induction motor. Theswitching frequency selected is 5 kHz.

IV. CONCLUSION

A simple method of estimation of rotor angular veloc-ity has been explained. Conventional metho d of speed es-timation is used, that necessitates accurate estimation ofthe stator flux vector at all operat ing frequencies speciallythose near zero. Modified voltage model is effectively em-ployed along with a bias detection algorithm, to accurately

Fig. 11. Speed control using the DFC scheme: st ep change from -20and +s,B are alsoPM to +20 RPIW with bias correction,

shown.

estimate the stator flux vector at frequencies approachingzero. Test results show a reasonable dynamic performanceusing the DFC scheme.

Fig. 12 shows the dynamic torque control for a rotorangular velocity step of 0.7 pu . The estimated rotor ve-locity is eqnal to the angular velocity obtained froni theencoder. A step change in the torque conimand at a rotorangular velocity of zero value is shown in Fig. 13, Thisfigure demonstrates that dynamic contro l of torque can beachieved even at zero speed. Similarly, Fig. 14 shows th e

REFERENCES[I ] J .Hu. and B.Wu, "New integration algorithms for estimat ing mo-

to r flux over a wide speed range," I E E E transactions on Power

[2] Shin M. H . , Hyun D. S., and Chae S. Y . , "A n improved stator flux13, no, 5, pp, 694-700, 1998.

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Fig. 14. Rated Torque step at B reference speed of 0.2 p u

estimation for speed sensorless stator flux orientation control ofinduction motors," in IEEE Transactions on Po wer Electronics,march 2000, vol. 15, pp. 312 -318.

"Modified integrator for voltagemodel flux estimation of induction motors," in Ind ust ed Elec-

tronics Society, I E C O N '01. The Wth Annual Conference of theIEEE, sept-oct 2001, vol. 2, pp. 1339 -1343.141 Idris N.R.N.and Yatim A.H.M., "A n improved ~ t a t o r lux estim a

tiori in stead y state operation for direct torque control of inductionmachines," IE EE tmnsoetions on Industry Applications, vol. 38,no. 1, 2002.

(51 Wolbank T.M., Woehrnschimmel R., and J.L. Machl. "Zero speedsensorless control signals of induction motors with closed rotorslots,li in Poruer Electronics Specialists Confmnce, 2002, vol. 2,

[6 ] Holtz J . an d Juirtao Quan. "Sensorless vector control of inductionmotors at very low speed using a nonlinear inverter model andparameter identification." in Indnst nj Apptications Conference,Thirty-Sizth I A S Annual M eeting, sept-oct 2001. vol. 4, pp. 2614-2641.

[ i ] . Tripathi, A . M. hambadkone, and S. K. Panda, "Predictivedead-beat stator flux control with overmodulation and dynamictorque control at constant.switching frequency in ac - drives." inIEEE IndwtTy Applzcation Conference, 37'h I A S annual meet-ing, Oc t 2002 , pp. 208&-2085.

[8] Anshuman Tripathi, A. M. Khambadkone, and S . K . Panda,"Space-vector based, constant frequency, direct tor que controland dead beat sta tor flux control of ac machines," IEEE Interna-tzonal Conference o n Industrial Electronics, Control, Instrumen-tation and Automation, IECON, vol. 2, Nov. 2001.

[3] Hinkkanen M. and Luomi J . ,

pp. 99 7 -1002.

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speed sensor less control of ac machines using direct flux control scheme

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