sensor less speed control of an induction motor

8/6/2019 Sensor Less Speed Control of an Induction Motor

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Sensorless Speed Control of an Induction Motorwith No Influence of Resistance VariationToshiyuki Kanmachi Isao Takahashi

Sm da i National College of Technology1, Kii:ahara, Aoba-ku, Send ai 989-3 1, JAPAN

Nagaoka University of Technology1603-1, Kam itomioka, Nagaoka, 940-21, JAPAN

Phone: +81-22-392-4761Fax: +8 1-22-392-3359

E-mail: kanma chi@cc endai-ct. c pAbstract - M m y speed sensorless vector control

systems of induction motors have been developed. However,the speed control characteris t ics are affected by machinetemp eratu re variat ions , because these methods use theprim ary and the secondary res is tance value to es t imate therotor speed.

This paper describes method of the primary and thesecondary resistance estim ation fo r speed sensorless controlsystems. The primary resistance estimation uses thesecondary flux which is calculated by the instantaneousreactive power. 011 the other hands , the secondaryresistance is directly calculated by the line voltage and thecurrent without speed sensors. This method makes possibleon th e PWM inverter fed induction motor. By combiningthese two methods, the speed control characteristic is robustto the m achine tem pera ture variat ions. The feasibi li ty ofthese methods was verified by some simulation andexperimental results. In the tested system, the com pensationof the prim ary a nd th e secondary res istance mismatching isachieved.

I. INTRODUCTION

The speed sensorless vector control systems of a ninduction motor have been developed and applied in theindustrial drives. 1 [2][3] These systems, w hich haveeconomic advantage: and high performance, are requiredin several applications. However, there are two problemsin the perform ance of the speed sensorless vector contro lsystems. First, the estimation of the primary and thesecondary flux are difficult in the low speed region.[4]The performance of the torque an d the speed are affectedby this problem. Th e second, the accuracy of speed controlis influenced by mismatched motor parameters, used inthe speed estimation, the primary and the secondaryresistance. 5]Some identification methods of the secondaryresistance without speed sensors have been

Phone: +81-258-47-95 15Fax: +81-258-47-9500

E-mail: [email protected].[6][7] In these methods based on the adaptiveidentification system, the secondary resistance in thecontroller can be converged to the correct value w ith longtime constant. We already had proposed a directlyidentification method of the secondary resistance.[8] 9] Inthis method, the secondary resistance is calculated quicklyby only using the instantaneous terminal voltage and theline current without speed sensors.

On the other hand, the sensorless vector control systemwith no influence of the primary resistance had beenproposed.[101 In this system, the rotor speed is estimatedby using the reactive power, and it is robust to the prima ryresistance.

In this paper, the primary resistance identificationmethod using the reactive power is proposed.[ll] Thismethod can be applied to existing speed sensorless controlsystem. AdQtionally, by combining to the abovesecondary resistance calculation method, the sensorlessspeed control system will be free from the machinetemperature variations.

11.PRIMARY RESISTANCE IDENTIFICATIONFig.1 illustrates the equivalent circuit of an induction

motor. Base on this circuit, the characteristics equationsare expressed as (1).

"

Fig.1. Equivalent circuit of nduction motor

O-78O3-3823-5t9.7l~10.000 997 EEE 91 PCC-Nagaoka 97Authorized licensed use limited to: Sree Chitra Thirunal College of Engineering. Downloaded on July 01,2010 at 09:01:15 UTC from IEEE Xplore. Restrictions apply.
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where RI an d R2 are the primary and the secondaryresistance; L I an d Lz are the primary and the secondaryself-inductance;A4 is the mutual inductance; wm is therotor speed; p represents d/dt; a is equal to M/Lz ; C isequal to L l - aM . The secondary flux a q h d , areobtained to solve the first and the second lows of (1) as

These equations mean that the secondary flux can bedirectly calculated from the primary voltage and theprimary current with considering of the voltage drop at R ,and the leakage flux. The accuracy of these equations areaffected by RIvariations.

On the other hand, the reactive power q , which iscalculated by (4), means the energy on the mutualinductance and the leakage inductance.

The exciting current of the secondary flux lo s calculatedusing q as

q / ( w o a A , f ) - P I f l ( a A 4 ) (5)

where w0 s the angular speed of the secondary flux vector.On the steady state, woapproximates to the angular speedof the primary current col, herefore the amplitude of thesecondary flux is estimated as follows;

Fig.2. Adaptive identification system of primary resistance

Since (6) does not involve R I , he accuracy is robust to RIvariation.

Fig.2 illustrates the adaptive identification algorithm ofE,, where (6) is the reference model and (3) is theadjustable model. The error between the secondary flux ofthese model is used to drive the PI adaption mechanismwhich generatesRI for the adjustable model.

Fig.3 sh e w the simulation results of the proposedidentification method. The nominal value of the primaryresistance is equal to 0.53(R), and the initial value of R^,in the adjustable model is 50(%) of the nominal value.The secondary flux of (3) converges to the value of (6)within 2 (sec). The primary resistance adjustment fromthe initial value to the co rrect one is verified from fig.3.

Fig.4 shows El identification errors of the proposedmethod with the mismatching of the mutual inductanceaM. The accuracy of the secondary flux calculation of (6)is affected directly by a M mismatching. Therefore, themismatch of aM will be a serious problem for this method."7dentification start0

0.8 r I

Time (s)Fig.3. Simulation resu lt of primary resistance identification.

100Load torque (Yo

Fig.4. Primary resistance identification errorfor mutual inductance mismatching.

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hAs can be seen in Fig.4, the minimum R , identificationerror at the rated load is k 17(%) with k lo(%)mismatching of aM .

Fig.5. shows the: identification errors of 2, ithmismatched the leakage inductance &. The leakage flux isenough smaller than the secondary flux. Then, theinfluence of the leakage inductance mismatching to theproposed method can be ignored. The maximumidentification error ai: rated load is f .4(%) for ?z lo(%)mismatching o f & .

111. SECON DARY RESISTANCE ESTIMATIONSolving respectively the third and the fourth low of ( l) ,

the secondary resistaiice is obtained as (7).

These equations demand the value of the rotor speed w,which is not able to detect on the speed sensorless drives.Therefore. we cari not calculate these equationsindependently. By considering (7) are sirnultaiieousequations, the secontiary resistance can be calculated as(8) to eliminate CO,,,;

This equation means that the secondary resistance iscalculated by the inlier product of aty,. i, and dividing

A& - (Yo)

Load torque (Yo) 100

A& 1O(%)t/Fig.5. Primary resistancc ideatlficatlon s17'01'

fo r leaka iy inductancz mismatching.

p(laty,l') by iz q z .When the secondary flux is represented by theamplitude and the phase angle 8, as (9), thedifferential vector of the secondary flux pry, is calculatedas (10).

If the secondary flus has no ripples, the second term of(10) is equal to zero, and the phase angle between thevectors 9, nd pq, becomes to d 2 . Therefore, thenumerator of (8) goes to zero. Additionally, thedenominator of (8 ) which is expressed by the differentialvalue of the secondary flux amplitude is equal to zero.Then , it is impossible to calculate the secondary resistance.However, the PWM inverter makes the flux ripples andassures the possibility of the 3,calculation.Fig.6 shows the simulation results of the secondaryresistance estimation. The induction motor, R , is equal tol(Q), is fed by the PW M inverter and the rotor speed iskept at 1500(r pni) under ra ted load. It illustrates that thenumerator and the denominator are not always equal tozero and the Rr estimation is possible. However, there aremomentary zero cross points in the denominator and theiiumerator which m akes impossible to divide. Therefore,the estimation of RZmust be avoided near these zero crosspoints.

Fig.7 illustrated the R, stimation block diagram. It cancalculate R , directly and instantly from the instantaneousprimary voltage and current. However, when the value ofdenominator is small at neighboring the zero cross points,there is possibility that the calculation error of divisionbecome increase. The calculated R2 is averaged by a LP Fto suppress the calculation error at n eighboring zero cross

(a.) Numerator of@)5 0. 3

ru (b.) Denoniinator of (8)Y

Time(iiic) 20" " ' " '4 08m (c.) Estimated secondary resistance.Fig.6. Sirnulation results of secondary resistance estimation.

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points. The time constant of the LPF, which removes theripple frequency components, is enou gh shorter than thetime constant of R2 variation. Therefore, the influence ofthe LPF to R", estimation's dynamics is small, and therotor speed estimation is almost not affected.

Fig.8 shows the & estimation errors with themismatching of uM. The mismatching of uM makeserror in the secondary current calculation of (8). However,the numerator of (8 ) is not affected by aM mismatching,then the R, estimation error is small. The maxim um erroris equal to -4(%) a t lo(%) mismatching in aM .

Fig.9 shows the E2 estimation errors of (8) withmismatching of L? The secondary flux ripples, which areused in the secondary resistance estimation, depends ongreatly the leakage inductance. Therefore,R2estimation ishighly sensitive to the mismatching of 1 As shown inFig.9, the maximum R2estimation error is f 4O(%)withk o(%) mismatching in e.

)r

h

Iv. SYS TEM CONFIGURATION

Fig.10 illustrates the sensorle ss speed contro l system ofan induction motor based on DSP(TMS32OC25). n l l r d . : d e n o m i n a t o r

" Id7(v,,-R,i ,,)dt I "ey2d , n . : n u m e r a t o rI 1 I + 1 1 -

? i 3-4 AaM- 1 O(Yo)

Fig.8. Secondary resistance estimation errorfor mutua l inductancc mismatching.

applying the proposed El nd E, identification methods.On the steady state, assuming coo is equal to the inverterfrequency reference wl*, the rotor speed &, s estimated as

where T s the generated torque, which can be calculatedbY

The estimated speed is fed back and compared with thespeed reference U,,,*.he error between these value isused to drive the PI controller which g enerate the inverterfrequency reference col*. The sign of col* gives directionof the rotation (F B) , and the amplitude makes Ru dS top(FUS) command which decides the voltage and the

A&(?- dl c15 0 1Aa - l o (%)c

Load torque (Yo) 10 0__._____.___.--._.__A P - 5(%)t

50 A h - lo(%)Fig.9. Secondary resistance estimation eil-or

for leakage inductance mismatching.

I -DSP(TMS320C25) AFig.10. Configuration of speed control system

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frequency of the PWTVI inverter. T he PW M inverter driv esthe induction m otor with hexagon al primary flux locus toproduce large flux ripples. The secondary resistancecalculation will be assured by these flux ripples.

To estimate3,R"., and the rotor speed d.he primaryvoltage and the primary cu rrent must be detected. In thissystem, the primary flux in (2) and the reactive power in(4) are calculated by some analogue circuits.

Fig. 11 illustrated the calculation c ircuits of the p rimaryflux and the re ad ve power q . The primary flux iscalcu lated by the integra tion circuits using the ultra-lowoffset voltage amp lifiers, and in (2) can be varied toestimated value in Ijig.2 by the 8bits multiplying D/Aconverters. The reactive power is calculated by theanalogue multipliers and averaged by LPF. By using theanalogue circuits, the error due to the sampling cycles andthe quantization is reduced.

The calculated V I . q and the primary current aredetected by 1 2bitsA/D converters, and used to estimateE land in Fig.2 and Fig.7. By using these estimated valuesof zl nd R",. the rotor speed estimation in (11) is notaffected by the variations of RI an d Rr. The speedestimation and control with the compen sation of R I an d R ,are carried out on IXP. The calculation time is about105(ps), and the sampling frequency is fixed at4.88(kHz).

converges to the nominal value w ithin 3(s), and the speedcontrol error is reduced to l(rpm ). The identification errorof R", is -2(%). The dynamics of convergence whichdepends on the PI adaptation mechanism is enough tocompensate the machine temperature variations.

Fig. 13 shows the secondary estimation result. Thespeed reference is 200(rpm ) and the load torque is ratedvalue. The primary resistance is fixed at nominal value.The estimated converges from initial value, which is30(%) of the nominal value, to the correct one. Theconverging time which is caused by the LPF is about1.5(s). It is enoug h shorter than the time constant of themachine temp erature variations. The speed control erroris reduced from 74(rpm) to 4(rpm ). The calculation errorof r?, is about 5(%).

Figure 14 shows the speed control characteristics withboth com pensations of the primary and the secondaryresistance. The initial values of each resistance are 50(%)of the nominal values. When the induction motor iscontrolled without and estimation on the ratedtorque, the speed control error is 63(rpm). Afterbeginning the estimation of E l an d E 2 , each valuesconverge to the suitable value within 3(s). It reduces thespeed control error from 63(rpm) to l(rpm). Theestimation errors of each resistance are und er 3(%). Thisresult shows that the simultaneous estimations of R I ,E,an d &,,, are possible on the speed sensorless drive system.v. EXPERIMENTALESULTS

VI. CONCLUSIONSTable 1 shows the rating and motor parameters of the

induction motor using in the experiments. The testedmachine is coupled to a 2(kW) dc mach ine

Fig. 12 shows the primary resistance identificationresult which is indelpendent of the secondary resistancecalculation. The induction motor is driven under the ratedload torque and the speed reference is 200(rpm). Theinitial value of the eistimated A I is 50(%) of the n ominalvalue, and the speed control error which is caused by themismatching of E, is 24(rpni). The estimated AI

v ,2.W I d In this paper, the primary and the secondary resistanceestimation methods of an induction motor are described.They can use for speed sensorless control and compen satethe machine temperature variation. The conclusions aresumm arized as follows:1)By using the reactive power, the p r im ly resistance isestimated on the adaptive identification system within2(%) error.2)By using the flux ripples, the secondary resistanceestimation without speed sensors is possible. Th e accuracyTable. 1. Parameters of induction motor.

1.5kW Induction motorI200V, 55Hz , 4poles

Primary resistance R I 0 53 QSecondary resistance R2 0 51 LZMutual inductance a M 54 3 nlHLeakage inductance I' 3 19 mH

Fig.1 1. Block diagram of analog circuit.

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h Identification start9, .81 Z 0 .49E.*$ 5 0 Time(s) IOhg 20 0v-29 10 08r Time(s) IO

Fig. 12. Experimental result of primary resistance compensation.

h

Time(s) 10

Fig. 13. Experimental result of secondary resistance compensationof the secondary resistance calculation is obtained within5(%).3)In this paper, proposed estimation methods of R , an d R,are combined and applied to the simple speed sensorlessdrive. The mismatching of R , an d & are c ompensated bythese m ethods, and the speed control error caused by themismatching is reduced from 63(rpm) to l(rpm).4)The accuracy of the proposed primary resistanceestimation method is affected by the mismatching of themutual inductance, and the secondary resistanceestimation is highly sensitive to the leakage inductance.5)By using the analogue circuits to calculate the primaryflux and the reactive power, the detection error caused bythe sampling cycles is reduced.

A

ACKNOWLEDGMENTThe authors would like to express their ap preciation to

Mr. I. Miyashita of Toyo Electric Co. Ltd. and PowerElectronics Laboratory members of Nagaoka University of

Fig. 14. Primary and secondary resistance com pensation.REFERENCES

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sensor less speed control of an induction motor

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