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Current commands for high-eff ciency torquecontrol of DC shunt motorS. Funabiki, PhDT. Fukushima, MSc

I n dexin g t e r m : M otor s , Magn e ti c dev ices and properties

Abstract: The current commands for a high-efficiency torque control of a DC shunt motor isdescribed. In the proposed control method, theeffect of a magnetic saturation and an armaturereaction are taken into account by representingthe coefficients of an electromotive force and atorque as a function of the field current, the arma-ture current and the revolving speed. The currentcommands at which the loss of the motor drivesystem becomes a minimum are calculated as anoptimal problem. The proposed control techniqueof a motor is implemented on the microprocessor-based control system. The effect of the consider-ation of the magnetic saturation and the armaturereaction on the produced torque and the mini-misation of the loss are discussed analytically andexperimentally.

List o f symbolsE lEO = an electromotive forceI a = an armature current1, = a field current0K A I, , )kel, k,, ,ke3 and k, = constantsKA Z, , )Tfz,I ,, I , , w )T,,,,(I,, o)Kgl , , I , , o)k,,, k,, ,k,,, k and kF = constantsPl OSS = a motor lossk,,, k,, and k, = constantsC O S S = a loss of motor drive systemkal(m,), ka2(m,),k, ,(m,) and kft (m, ) = coefficientsma and m, =time ratios in armature chopper andfield chopperRa, R, = resistances of armature and fieldv, = a voltage drop of brushv,l, v,, =voltage drops of diodes in armature

= a battery (24 V)

= a revolving speed of motor= a coefficient of electromotive force

z = a produced torque= a coefficient of torque= a torque due to iron loss, mechanicalloss and stray-load loss= a torque due to iron loss= a torque due to mechanical loss and= a coefficient of output torquestray-load loss

chopper and field chopperPaper 8103B (Pl ), first received 20th April 1990 and in revised form18th March 1991The authors are with the Department of Electrical and ElectronicEngineering, Faculty of Engineering, Okayama University, 3-1-1Tsushima-naka,Okayama700JapanI E E P R O C E E D I N G S - B , Vol .138, N O .5 , S E P T E M B E R 1991

RFET1, RFET, = resistances of FETs in armaturechopper and field chopperv,, K, = voltage coefficients corresponding toswitching loss of armature and fieldchopperk1(1, I , ) , k,(Ia, If), k, ,.k,, k#,), kdl,), k,, k, and k,= coefficients1: = a command of armature currentIf = a command of field currentI , mx and If mx = maximum values of armature and fieldN = the number of revolutionPG = a pulse generatorCT = a current transformerE, = a DC supply voltageRI = a load resistanceu(k) = an output of digital PI controller at kthd( t ) = an incremental output of digital PIK , and K i

current

periodcontroller

= gains of digital PI controller= an output of controller in kth control= a reference of controller in kth controlperiodperiod

f ik)r(k)T* = a torque command1 IntroductionIn an application of the DC motor to the drive system, itis desirable to operate the motor drive system at high-efficiency in addition to the control of the revolving speedand the torque. This proposition can be achieved by con-trolling both the armature current and the field currentso that the efficiency becomes maximum at every oper-ating point [11.The microcomputer-based control systemare proposed to regulate the ratio of the armaturecurrent to the field current to minimise the loss of motor[2, 31. The control method is proposed based on theoptimal regulator theory with an evaluating function ofthe efficiency and the system response [4].The produced torque of the motor is in proportion tothe product of the armature current and the magneticflux. The magnetic saturation and the armature reactionaffect the magnetic flux in the motor. Therefore, the rela-tion between the field current and the magnetic flux isnonlinear. Then, the relation between the torque, thearmature current and the field current also has nonlinearcharacteristics. In this case, the deviation exists betweenthe torque command and the produced torque. Conse-quently, it is impossible to operate the motor at high effi-ciency without consideration of these effects [SI.In this paper, the current commands for the high-efficiency torque control of a DC shunt motor, taking

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account of the magnetic saturation and the armaturereaction [ 6 ] , is described. The produced torque and theloss of the motor drive system are expressed as a functionof the armature current, the field current and therevolving speed of the motor. The effect of the magneticsaturation and the armature reaction are taken intoaccount by representing the coefficients of the electro-motive force and the torque as a function of the fieldcurrent, the armature current and the revolving speed.Then, the current commands at which the loss of themotor drive system becomes a minimum can be solved asa solution of an optimal problem. The proposed controlof the motor is implemented on the microprocessor-based control system. The effects of the consideration ofthe magnetic saturation and the armature reaction on theproduced torque and the minimisation of the loss are dis-cussed by the calculation and the experiment.2 Motor drive circuitFig.1 shows the drive circuit of a DC shunt motor. Fig. 2shows the configuration of the chopper circuit. The drive

chopperE1a3@hopperFig. 1 DC shunt m otor drive circuitcircuit is composed of a battery ( E , = 24 V) and twochopper circuits with a MOSFET and a diode shown inFig. 2. The armature current and the field current areoutput

Fig.2 Conjguration of chopper circuit

regulated by two chopper circuits, respectively. Thecircuit for a regeneration is omitted in this Figurebecause the power running is dealt with in this paper.The tested motor in this paper has the ratings of theoutput 250 W and the revolving speed 1800 RPM .3 Consideration of magnetic saturation andarmature reaction3.1 Electromotive forceA magnetic flux in a DC motor is affected by a magneticsaturation (MS) and an armature reaction (AR). There-fore, it is desirable to take them into account for a high-efficiency motor drive. Then, the electromotive force ofthe motor is expressed by

E , = K . d I f 9 I a b (1)The effect of MS and AR in eqn. 1 can be considered bythe coefficient of the electromotive force. The circles228

shown in Fig. 3 shows the no-load characteristic curve ofthe tested motor gained by experiment. The coefficient ofthe electromotive force of the tested motor is indicated bycurve a in Fig. 3. Then, this curve is approximated by thenext expression taking account of AR .

O l o r / *

L l I I I0 0 2 O L . 0 6

field current I f , AFig. 3 Coefficient of electromotiveforce0 measured

KAIf > 1,) = kel I ; + ke , 1, + ke3 - a 1, (2)The term of k , I , in eqn. 2 represents AR . The lines b andline c are for the coefficients without consideration of M Sand AR. The line c is the straight one drawn through therated value and the origin. The line b is selected to beapproximately a line tangent to the curve a with almostthe same slope as the line c . The residual flux offset k, , isset to zero in the case of line c. The two curves b and care used for the comparison of the proposed controlmethod taking account of MS and AR with the controlmethod without consideration of them.

3.2 TorqueAs the torque produced by the motor is denoted as thetorque transmitted t o the load, it is expressed by [7]

(3)Namely, the torque transmitted to the load is defined asthe electrically produced torque minus the torque due tothe iron loss, the mechanical loss and the stray-load loss.Then, the torque for these losses is expressed by

The torque due to the iron loss is expressed as a functionof the field current and the revolving speed because thehysteresis loss is in proportion to the product of the fre-quency and the square of flux, and the eddy current lossis in proportion to the product of the square of frequencyand the square of flux. The torque due to the mechanicalloss and the stray-load loss is as a function of the arma-ture current and the revolving speed because the mech-anical loss is a function of the revolving speed and the

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stray-load loss is in proportion to the product of therevolving speed and the square of armature current. Theyare, thus, expressed as follows :

The second bracketed term of the zf i equation representsflux, the coefficients being found by curve-fitting to themeasured magnetic curve, and the I, term allows for theslight reduction in net flux that occurs with armaturereaction.4 Minimisation of loss and current commands4.1 Loss of motor drive systemThe motor loss is composed of the copper loss, the brushloss, the iron loss, the mechanical loss and the stray-loadloss. The last three losses are the product of the revolvingspeed and the torque z, nd z . They are expressed byusing the state variables, that is the armature current, thefield current and the revolving speed.

PI o s s = ka11: + ka2 I a + kf1I; + kf 2 I ,+ (k , ,w2 + kN2 oXk e1l ; + ke2 1,+ k, , o + k , 1 : 0 2+ ke3 - a I , ) , + k , , 0 3 + kM 2o2

( 6 )The iron, mechanical and stray loss terms correspond tothe relevant torque terms discussed in Section 3.2, multi-plied by o. n eqn. 6, the term of (kalZ: + k,,Z, + kflZ:)expresses the copper loss in the armature circuit and thefield circuit, and the brush loss. The terms of ( k , , 0 2+ k, , oXkelZ: + k, , I s + ke 3 - ,I,) and ( k , , 0 2+ k , ,w) show the iron loss and the mechanical loss,respectively. k , Z:02 indicates the stray-load loss.

Fig. 4 shows the loss of the motor with I, = 0.6 and0.4 A. The k values in eqn. 6 and Table 1 are chosen byTable 1 : Coeff ic ient of loss expression

a b C d2.75 x l o - 3.85 x l o - 3.74 x 101.75 x 10-22.503.36 x 10-4-1.43 x l o - 2.02 x 10 - 1.05 x 1 0-24.20 x 1 O- 3.90 x 10-58.93 x 10-7

2.75 x l o - 2.75 x lo- 2.75 x l o - 3.85 x lo - 3 .85 x lo - 3 .85 x l o - 3.74 x 10 3.74 x 10 3.74 x 101 . 6 8 ~ 1 0 - ~. 3 2 ~ 1 0 - ~ . 7 8 ~ 1 0 - ~2.46 1.72 2.220 0 0- 1 . 4 3 ~ 1 0 - 0 02.02 x lo - 1 .28 x l o - 1.33 x l o - 1.05 x lo- 1 .89 x 04.20 x 3.97 x 3.95 x lo - 8.22 x 1 0 - 7 1.73 x 1 0 - 6 2.57 x 1 0-63.90 x 10-5 6.20 x 10-5 8.00 x 10-5

curve fitting to the experimental results. The coefficientsin eqn. 6 are shown in the (a)column in Table 1.

Table 1 lists the k values used later for performanceand loss predictions. The k values in the first twocolumns of the Table correspond to the analysis incorpo-rating MS (line a on Fig. 3)with and without AR takeninto account, respectively. The 3rd and 4th columns cor-respond to lines b and c, respectively, of Fig. 3 whichneglect AR and M S.In a practical motor drive system, the loss due to thepower convertors for regulating the armature current andthe field current must be taken into account. Then, eqn. 6is rewritten by the next expression.I E E P R O C E E D I N G S - B , Vol . 138, N o . 5 , S E P T E M B E R 1991

FI I I

0 5 10 15a r m a t u r e c u r r e n t I , , Aa

loo/I

0 5 10 1 5a r m a t u r e c u r r e n t 1 , Ab

Fig. 4 Loss of motora I , = 0.6 Ab If = 0.4 A0A

N = 1800 RP M (measured)N = 1400 RP M (measured)229

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When a MOSFET and a diode are conducting, aMOSFET is assumed to be at a constant resistance and adiode ha.s a characteristic of constant voltage drop. Onthe other hand, they have an infinite resistance in theperiod of nonconduction. Furthermore, the switching loss

rttI 5 t

0 50 100torque c o m m a n d I * , mFig. 5 Current command in proposed control method~ N = 1728 R PM

N = 960 RP M~~-

1 5 -t o--C? -7 -

0 1 1 1 1 1 1 1 1 1 1 1 1 1torque c o m m a n d T * , m

0 50 100Fig. 6

~ a with AR- -- - - - a without ARb without AR

c without AR

Comparison of current command

~~~~

of the switches can be contained in the coefficients K,(m, )and k;,(m,) because it is expressed as a function of eachcurrent .230

The coefficients K l ( m , ) and kb,(m,) are expressed as afunction of time ratio of the armature chopper. Then, mais a function of armature current, field current andrevolving speed. The coefficients k,,(m,) and kf,(m,) areexpressed as a function of time ratio of the field chopper.Then, m, is a function of field current. Therefore, thesecoefficients vary with the operating state of the drivesystem.4.2 Current commandsThe total loss of the motor and the drive system isexpressed by using the armature current, the field currentand the revolving speed in eqn. 7. It is unfortunately notpossible to formulate a general expression for the currentcommands to minimise the total loss given by eqn. 7.However, it is possible to use eqn. 7 to evaluate P;,,, for aset of speed and current values for a specific scheme, andthen to search for the pair of current values that minimiseP;,,, at each speed. The controllable loss with the con-stant revolving speed is expressed by

PLss = kI(Ia 9 , ) I ; + k z ( I a I f Y a+ k , I: + k , I ; + k5(I,)Z;+ k 6 ( I , ) I , + k , I , I : + k , I , I , + k , (8)

Further, the armature current and the field current mustsatisfy the following requirement0 d , d ,, ,0 d , d , , , (9)Therefore, the maximum efficiency drive of the DC shunt

motor is regarded as the optimal problem to solve a setof current command to satisfy the requirements expressedby eqns. 3 and 9 and then minimise the loss expressed byeqn. 8. Then, the solution in the optimal problem is a setof the current commands, I,* and I / * for a set of therevolving speed and the torque command. For the testedmotor, the torque is divided by 1 gm and the revolvingspeed is divided by 128 RPM. The evaluation of optimalcurrent commands is carried out by searching theminimum value in the losses which are calculated underthe restriction of eqns. 9 and 3. In the experiment, V,, =V,, = 1.0V and RFETl = R,,,, = 0.05 Q in eqn. 7.Fig. 5 shows the obtained current command againstthe torque command at N = 960 and 1728 RPM. As thetorque command becomes larger, the commands of thearmature current and the field current increase. The fieldcurrent command is limited to the maximum value of thefield current in the torque command greater thant* = 95 gm. As the revolving speed becomes larger, thefield current command becomes smaller so as not toincrease the iron loss. That is because the variable lossequals the no-load loss at the maximum efficiency.

Fig. 6 shows the current commands corresponding toTable 1 at N = 1728 RPM. For the curves b and c , thefield current command becomes the limit value in thesmall value of the torque command. The armaturecurrent command for the curve b is smaller than thoseof the others in the range of the large torque command.5 Experimental system5.1 Experimental circuitFig. 7shows the experimental system. The control circuitis composed of a C P U board, an A/D convertor boardand a counter board. They are connected through themultibus.

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A 16 bit microprocessor 8086, a ROM, a RA M and aserial interface RS-232C are installed on the CPU board.The development of the program is carried out on thepersonal computer NEC PC-9801.

m ul t i b u se5PU boardFig. 7 Experimental systemPG = pulse generator

The torque command, the revolving speed, the arma-ture current and the field current are detected and con-verted into the digital values on the A /D convertorboard. The resolution of the A/D convertor is 12 bits andthe converting time is 5 ps.

The counter board has a 16 bit counter (8253) andgenerates the pulses according to the chopper period andthe on-time of the chopper. The clock frequency of thecounter is 2 MHz.5.2 Control methodFig. 8 shows the control block diagram. The currentcommand for the minimum loss is calculated in advance

m i c r o c o m p u t e rI--------- 1

I I .* I I - I n

r i I 1

Fig. 8 Block diagram o DC motor controland arranged in tabular form in the RAM. In the execu-tion of this control, the current command correspondingto the torque command and the detected revolving speedis looked up from the table in the RAM. Then, the arma-ture current and the field current are regulated by thecorresponding digital PI controller, respectively.The output of the digital PI controller is expressed by

u(k)= ~ ( k 1)+ d(k) (10)( 1 1 )

d(k) in eqn. 10 is calculated as followsd(k) = K p { y ( k - ) - ( k ) } Ki{r (k )- Y ( ~ ) I

Therefore, the PI control is implemented by executingeqns. 10 and 1 1 for the armature current and the fieldcurrent, respectively. The gains of the PI controller forthe armature current and the field current are decidedfrom the response and stability viewpoints by the simula-tion. The control period is 500ps .I EE PROCEEDI NGS -B, V o l . 138,N o . 5 , S EPTEMBER 1991

The memory used for the main program and the tableof the current commands are 0.73 and 8. 3 kB, respec-tively.6 Experimental results6.1 Output torqueThe effect of the consideration of M S and AR on thetorque control of the motor is discussed in this Section.Fig. 9 shows the characteristics of the produced torque

0 50 100t o r q u e command l *,mFi g. 9 Characteristics o torque0 a with AR

U without ARA b without AR0 c without AR

against the torque command at the revolving speed of1800 RPM. The solid line in this Figure indicates thetheoretical value.The measured net torque produced when the currentcommand decision-making was done on the basis of lineb analysis becomes significantly smaller than the demandtorque. That is because the coefficient of electromotiveforce is estimated larger than the actual value when thefield current is large. Then, the current command is cal-culated as a smaller value than the required one toproduce the torque demanded.The measured net torque produced when the currentcommand decision-making was done on the basis of linec analysis becomes larger than the demand torque in thesmall torque command. The produced torque by usingthe coefficient of electromotive force of the line c is largerthan the theoretical value when the torque command issmall. Then, the produced torque is smaller than thetheoretical value when the torque command is large.That is because the produced torque is reduced by thearmature reaction when the torque command is largeand the coefficient of electromotive force is estimatedsmaller than the actual value when the torque commandis small.

The produced torque in the case of the line a withoutAR agrees with the theoretical value in the range of thesmall torque command. However, the torque is smallerthan the theoretical value in the range of the large torquecommand. That is because the current command is esti-mated smaller due to the neglect of the armature reactionas shown in Fig. 6and the increase in resistance becauseof the temperature change.

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On the other hand, the produced torque by the pro-posed control method with the line a with AR agrees wellwith the theoretical torque in all of the range. Therefore,the consideration both of MS and AR in the torquecontrol of motor is proved an important matter.

100

3 -a- V I

VII2 5 0 -

6.2 Effect on loss reductionFig. 10shows the loss of the motor drive system in theproposed method and the conventional control methodwith a constant field current. From this Figure, areduction of loss in the motor drive system is achieved,especially in the range of the small torque command. O n

-

69

01 3 4 1 , a I a 1 1 I0 50 10 0torque command 7, m

Fig. 10and proposed controlCalculated__ proposed_ _ - - constant field current I , = 0.6 AMeasured

Loss of motor drive system with constant Jield current control

0 pr o po d+ constant field current I , = 0.6 A

t1 1 1 1 1 1 1 1 1 1 10 50 100

torque 7 , g mLoss of motor drive system against output torqueig. 11+ w i t h AR

-+ c without AR232

the other hand, the losses of the motor drive system inthe two control methods are the same in the range of thelarge torque command because the field currentcommand in the proposed method is equal to thecommand in the constant field current control. The devi-ation between the calculated values and the experimentalvalues is mainly due to the copper loss in the wiring, etc.

Fig. 11shows the measured loss of the motor drivesystem with the coefficients of electromotive forceexpressed by the line a with AR and the line c withoutAR. In this Figure, the horizontal axis indicates the pro-duced torque. From this Figure, it is proved that the con-sideration of MS and AR is effective in the reduction ofloss in the motor drive system, especially in the range ofthe small torque. Fo r example, the reduction of loss is3.1% at the torque of 50gm and 5.7% at the torque of33gm. n the other hand, the loss with the line a at thetorque of 90gm is almost the same as the loss with theline c. That is because the current command with the linec becomes equal to that with the line a as the torquebecomes larger. Meanwhile, the loss of the motor drivesystem for the line b without AR is only a little largecompared with the loss for the proposed control method.That is because the current command for the line bwithout AR is near to those for the proposed controlmethod in the range of the small torque and almost thesame in the range of the large torque.

7 ConclusionsThe current command for the high-efficient torquecontrol of DC shunt motor taking account of the mag-netic saturation and the armature reaction is described.The effect of the magnetic saturation and the armaturereaction are taken into account by representing the coef-ficients of the electromotive force and the torque as afunction of the field current, the armature current and therevolving speed. The loss of the motor drive system in theproposed method becomes smaller than the loss in theconstant field current control, especially in the range ofthe small torque command. The effect of the consider-ation of the M S and the AR on the torque control andthe reduction of loss of the motor drive system are dis-cussed experimentally. It is found that the considerationof the magnetic saturation and the armature reaction iseffective in the torque control and the reduction of loss.8 References1 KUSKO, A., and CALLER, D. : Control means for minimization oflosses in AC and DC motor drives, IEEE Trans. , 1983, IA-19, pp.2 OHMAE. T.. MARUMOTO. K.. and NAITO. S. : Microorocessor561-570 , . , ,~~~ ~based efficiency optimized speed control for DC shunt motor, Tr an s .S I CE, 1982,18, pp. 628-634 (in Japanese)HONG, S.C., and PARK, M.H.: Microprocessor-based high-efficiency drive of a DC motor, I EEE Tr an s . , 1987, IE-34, pp.

433440EGAMI, T., WANG, J., and TSUCHIYA, T.: Efiiciency-optimizedspeed control system synthesis method based on improved optimalregulator theory - pplication to separately excited DC motorsystem,I EEE Tr an s . , 1985, IE-32, pp. 372-380FUNABIKI, S., FUKUSHIMA, T., and HIMEI, T .: An effect ofmagnetic saturation on efficiency-optimized torque control of a DCshunt motor. IEE of Japan, 1987, IAS National Conversion, pp.423 428 (in Japanese)FUNABIKI, S. , and FUKUSHIMA, T.: High-efficient torquecontrol of DC shunt motor taking account of magnetic saturationand armature reaction. Int. PCIM, 1988,1, pp. 62-70OKITSU, H., SUZUKI, S. , and KIUCHI, Y .: A Measurement offriction torque,J . S I C E , 1970,9, pp. 35-40 (in Japanese)

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