Sensor Less Control of IM With Simultaneous on-Line Estimation of Rotor Resistance and Speed Based on the Feed Forward Torque Control Scheme

8/14/2019 Sensor Less Control of IM With Simultaneous on-Line Estimation of Rotor Resistance and Speed Based on the Fee

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Sensorless Control of Induction Motors with Simultaneous On-line Estimation ofRotor Resistance and Speed Based on the Feedforward Torque Control SchemeS. K. Jeong', Z. G . Lee', H. A. Toliya?, P.Niazi'

'Division of Mechanical E ngineering, F'ukyong National U niversity, Pusan, KoreaE-mail : [email protected].!uDepartment of Electrical Engineering, Texas A&M University, College Station, TX 77843-3128E-mail :[email protected]

Abstract - In tbis paper, a new speed sensorless inductionmotor scheme which can work at any speed including the lemspeed is presented. The proposed method is robust to rotorresistance variations. Simultaneouson-lineestimations of speedand rotor resistance are realized based on a feedforward typetorque control scheme. The rotor flux with a low frequencysinusoidal waveform is used to help the estimation. The controlscheme has no current minor loop to determine voltagereferences. Since the proposed estimation does not depend onany derivative term of currents and stator voltages, itcontributes to speed sensorless with good performance at verylow speed repion. Furthermore, the proposed control b simplyusing motor parameters and stator curreuts withoutdetermining any PI gains for current feedback and any signalinjection for the rotor resistance estimation. Simulations resultssnpported by experiments are given to show the effectiveness ofthis method.

I. INTRODUCTIONA number of sensorless induction motor drives have beendeveloped in the past [1-51. However, the performances ofthese sensorless drives are not sufficient when compared tothe sensored ones. A major drawback of these drives is due tothe difficulty of control at low stator frequency. During this

region of opmtiou, the signal-to-noise ratio of the statorcurrent is decreased significantly and the effect of statorresistance voltage drop isnot neg ligible. Another difficulty isto ensure the robustness of drives against parametervariations, especially rotor resistance. Also, it is well knownthat simultaneous estimation of speed and rotor resistance ishardly obtained in the vector control induction motor driveswith constantrotor flux [3].To solve these problems, we suggest a novel speedsensorless scheme based on a feedfonvard torque controltechnique [6] .The control scheme has some different featurescompared with the classical vector controls. First, it controlsrotor flux as a sinusoidal waveform in the d,q referenczh m e without affecting the torque control performance. It ispossible to estimate on-line both speed and rotor resistanceusing the rotor flux. econd, it does not have any current feedback loops. Thus, we do not need to consider any phasecompensations based on the delay between stator voltagesand stator currents. Since control voltage can be determinedusing t h is feedfonvard technique, we can excludecomplicated process in order to design PI gains in c m t

regulators. Third, the electromagnetic torque is controlledvery fast and independent of the rotor flux without inducingspike in the cu rrents because the co ntrol voltage was derivedtheoretically from the steady state currents values. Sincespeed and rotor resistance estimations do not depend on thestator resistances, stator voltages, and any oth er derivatives ofcurrents, it is possible to achieve speed sensorless with goodperformance even during low speed region. Especially, we donot inject any high frequency signal to estimate the rotorresistance, thus we expect less current ripples and we do notneed to design a high band-pass filter to reject them out.Hence, we can reduce the burden of hardware to inject highfrequency signals and also software to detect these highfiequency signals.In th is paper, at 6rsf the feedfonvard type orque control isdescribed in detail using the machine equivalent circuiteqnations. Then, he estimationeqnationsfo r speed and rotorresistance are derived from stator currents in d, q referenceframe. Atter that, the speed sensorless based on the torquecontrol scheme is des crii ed- Finally, through severalsimulation results using a PWM voltage-source inverter andexperiments based on a DSP control system, the validity ofthe proposed method is verified.D. THEMOTOR MODEL ANDTI33 FEEDFORWARD TORQUE

CONTORI.Suppose hat the stator current isx,, he rotorcurrent is x2 ,

and the control input stator voltage is U,, then he dynamicequations of induction motor(I.M) are given as ollow:[;I=[ M i D -I + Wd e ) R2 +h (D -D jde)p'].2 (1)

where R , , L, , ( i 42 tatcu and mtor) are thei nduct? ncedI * i n~qres pedi v e l y . . A l s o , M isthemutualinduclance,8, istheeleceical rmgularpositios m d D istheMetmtialope"(4~3).t is n o t e d h e bat xI, ,, and U,me o o m p h variables which have two "pmds a and B , mthestaticmaxyrefermceftame.I b e instaataneouS e lech"gne6c tcque of LM using thevariable5x,andx, isgivenby

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T = N M l m [ x l ?,I (2)Where N is the pole pair number. The symbol Imrqmsents the imaginary part of the variables and thehorizontal bar -means con jugate complex variable.Generally, the rotor flux and the rotor current can bedefined as rotating vectors which have am plitudes and phasesgiven by(3) and (4).

In (3) and (4), the f 1) an d g(t) represent phase angles ofthe rotor flux and the rotor current, respectively. T hey will beabbreviated as f and g hereafter to simplify the equations.Since the e lectrical torque of LM can be defined as a vectorproduct of the rotor current and the rotor flux such asT =N;krsin(-g), a new expression for x2 is obtained from(4).

Substituting (3) and (5 ) in the rotor side of the inductionmotor equation (l ), we can drive (6).

From the real part of (9, he inverse tangent of g is writtenas.(7)

Then, the rotor current is described by (8) which is obtainedby substituting(7) in (5).

The stator current x1 is also rewritten by substituting for4 nd the newly obtained x, in (3).

From (8) and (9), it is noted that there are no m s i e n tterms about time t. Thus, it is obvious from (2) that

theoretically we can co ntrol the instantan eous torque withouthaving any transient torque.The command voltage as a con trol input which can realizevery quick torque response is derived from the stator side ofthe induction motor equation (1) using these xI nd x l .

m. PEED SENSOWSS CONTROLALGORTHMThe rotor speed can be estimated using ( I 1) taking the

imaginary part o f (6) and replacing the torque term by thestator current according to (9).

It is noted that the second term of the right hand side in(11) m e a slip f requency. As a result, the speed can becalculated very simply using the motor parameters, statorfrequency, the rotor f l u , and the stator current. From (ll),the estimated speed is closely related to the motor parameters.Particularly, it is well known hat the rotor resistance variesduring motor operation due to the increase of temperame inthe rotor winding.Therefore, we need to estimate its value.From the real part of (9), the rotor resistance can bedescribed as (12).

It is noted here again that the rotor flux has to becommanded as a sinusoidal waveform to estimate the rotorresistance, since the deferential value of rotor flux isnecess;uy in the dq reference fiame. Another i m p t pointis that the rotor resistancehas a possibility of diversion if th edenominator of (12) is near zero. To overcome this problem,the rotor resistance is calculated by integrating the statorcurrent and the rotor flux a t every quarter cycle such as (13).

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Fig. 1 illustrates the suggested speed sensorless controlsystem The system is consisted of four major parts, speedcontroller, torqne controller, speed estimator, and rotorresistance estimator.In th is control scheme, there is no current feedback loopand also the current information is not used for producing thevoltage commandN. UMERICALIMvLAnoN

To verify the proposed sensorless control scheme, threeseparate simulationsare performed using the P W M oltage-source inverter and an 1.M whose parameters are listed inTable I. The carrier fkquency is set at 4 kHz and thesampling times for speed calculation and current integrationof 1.M model are set at 1 ms, and 1 11s respectively. At lirst,the simulation results for feedfomard torque controlperformancesare investigatedbased on Fig. 1.

PR I.S[!dq N 2uR 220/380[P7 x R 6.6/3.8[,4]RI 3 . 7 I [ Q ] R, 2.79[Q]L, 236.79 [ mH ] L, 236.79[ mH ]M 220 . 42[m H ] J o . 0 O 2 1 N m ~ s 2 / r ~ d 1

Fig. Z(a) shows the torque response when the torquereference is changed abmptly step wise f N.m to 5 N.mat time equal 50 milliseconds. Fig. 2@)also shows the torquercsponse to the commanded torque, M, whicb is more

complicated than he previous stepwise command.Motor speed is set at 15 rpm and IS0rpm, espectively.The rotor flux is commanded to be a consfant value in Fig.Z(a). However, in Fig. 2@), it varies with time which is givenby 1,=O.SZ5{l+O.lsin(lOf)} Weber.

Fig. Z(a) and Fig. Z@) are consisted of three and fourpieces of figures, respectively. The tirst one represents torqueresponses according to the step and M torque references,respectively. They sho-w that the torque responses accuratelyfollow their respected commanded values. The second oneexpresses voltage comm ands to achieve the torque eferences.When the toque reference is changed abruptly, a very highvoltage is added to the steady state value to eliminate thetraosient torque response based o n th e f e e d f m d torquecontrol. The third one represents the stator currents responsesunder the voltage commands. Th e last one in Fig. Z(b) depictsthe variable rotor flux. These results show that the torquecontroller performs correctly even though the rotor flux iscommanded tobe sinusoidal.Fig. 3 shows the estimation results of the speed and rotorresistance. Among them, the first one depiqs the estimationspeed and rotor resistance, respectively. These results showthat the estimated values well coincide with their actualvalues. The rotor flux waveform was given as1 =0.525(1 tO.lsin(f)) Weber. The initial value of the rotorresistance in Fig. 3@) was given appropriately to confirmthe co nvergence characteristic of it to its actual value.

V. EXPEIUMENTALREsULTFig.4 shows the experim ental hardware set up based o nDSP system The dead time of inverter was 5 f is and thecarrier ftequency was &t at 2.5 kHz, nd the sam pliig time

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Fig.4. DSP -based h d w n e sctup for theexpnimCnt

was 1 ms. Also the A/D converter to calculate the current had12 bits resolution and 3.2 ps conversion time. The rotor fluxwas givenas .I,=0.6(1+0.1sin(t)) Weberduringexperiment.

Fig. 5 represents experimental results of estimating thespeed and the rotor resistance using the hardware hown inFig. 4. The motor parametem are shown m Table I. Fig. 5(a)shows, the reference speed, actual speed from an encoder,and the estimated speed, under steady state at 3 rpm. Th eestimated speed shows good agreement with the actual speed.Fig. 5@ ) shows an estimated rotor resistance using (12).Actually there are somedisagreementsbetween the real valueand the estimated one. However, the filtered estimated valuefollowed the a d alue very c losely after a few seconds.

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U .. J.0

Fig. 5(c) and Fig. S(d) illustrate the stator currents in d, qaxes and the mtor flux, respectively. They were used forestimating the rotor speed and rotor resistance. The ermrbetween the rotor flux reference and the response in Fig. S(d)is the reason of imprecise estim ation of the rotor resistance.Fig. 6 shows an experimental result of speed sensorlesscontro l. Since low speed operation was of interest, speed wascommanded from 0 rpm to 3 rpm under no-load.

g 0.4I2 03

0.0 5.0 10 I3 20time 11dm 1Fig. 6 .ExpCrimental result of the speed remorless conml.

Itis sbownthatiheresultofspdsensorlessm m l ollowsfbeactualspeed closely.

VI CONCLUSIONIn th is paper, a novel speed sensorless control schemebased on the feedfonvard torque control was proposed.Especially, the method aimed at the simultaneous estimationof the rotor speed and the rotor resistance on-line. Throughsimulation results, the validity of the proposed sensorlesscontrol scheme was initially verified. The experimentalresults for sensorless control with variable rotor fluxreference also showed good agreement with the theory even

at very low speed such as a few of rpmREFERENCES

[ I ] S. SwaaLauin and S. Sangwongwanicb, A Spad-Smnorlcss IMDrive With 0ecaupli.g Contml and Stability Analysis of SpedE h a t i o n , IEEE Dm. I d . Applimf,,vol. 49,2002, no. 2, pp. 444-455.121 Y. Kinpara andM. oyama,Speed SennorlessV m ontrol Methodof Induction Mo ta IncludingB Low Speed Region, JIEE,vol. IZOD,2oW, p. 223.229.K Akam a d A. Kawmura, Sensorl.nn V q aw and Zero SpeedEnimatiau with Oa-Line Secanday Re&sJtanee Estimation of[3]

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Induction Mom Without Adding Any Signal:' B E E T ? m . 1 4+. 1999,pp. 187-193.[4] 1.1. Ha and S.K SUI, "Sasmleas Ficld-OrientatiOn Cmtml of 811Industion Mashine bv Hi&-Frequency Signal In1ectiols"EEE Trow.. - . . . .,MA&., 1999, vol. 35, no. I, pp. 45-51.LKubora andK. MataLse, "Sped Senrmless Field-Onmted Cmml

of lndustionM m a witb Rotor Rerisla~ceAdqWion,'' IEEE Trow.MA&-., ol. 30,no.5, l994,pp. 1219-1224.T. Hayashi, Y. Fujii m d T. Sekiguchi, "Sfudy on an AnalyticalSolution for h s "w tm Torque h t m l of an Induction Motor:'. h d&$ c fEE , vol. 4,1989, pp. 323-324.[7] K. Ohnishi, N.Ma&, and Y. Hori, "Estimation, dcatification, andS-les Contml in Motion Conwol System," proceedings of =,

vol. 82.m. 8 , A u p s t 1994,pp. 1253-1265.

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Sensor Less Control of IM With Simultaneous on-Line Estimation of Rotor Resistance and Speed Based on the Feed Forward Torque Control Scheme