mechanism for detecting super low rotating speed utilizing square hysteresis loop cores

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS ANDCONTROL INSTRUMENTATION, VOL. IECI- 24, No. 2, MAY 1977

MECHANISM FOR DETECTING SUPER LOW ROTATING SPEED

UTILIZING SQUARE HYSTERESIS LOOP CORES

Takao Ouchi and Teruhiko Ohtomo

ABSTRACT circuit, is difficult to synchronize with the commercialfrequency voltage source. This super low rotating speed

Many problems concerning highly sensitive detection detector solves these difficult problems. The square hys-of low rotating speed remain unsolved. A square hyster- teresis loop core used in this detector is able to per-esis loop core has excellent merits. It is able to per- form the function of pulse counting, DA conversion andform both DA conversion and power amplification simultane-power amplification simultaneously, since it has stableously because it has the functions of integral operation saturation characteristics and the functions of integraland memory. operation and memory [11 [2]. As a result, the thyristor

Based on this viewpoint, the authors have already circuit and the magnetic amplifier can be controlled byreported a photoelectric type rotating speed detector, the output of this detector easily. Moreover, variousin which the average output current varies in proportion circuit constructions may be carried out without troubleto the variation of rotating speed. because magnetic cores are capable of isolating the input

Thereafter, the authors proposed a new mechanism and output circuits, and having many isolated outputs.for detecting super low rotating speed which can obtain The lower limit of the detectable low rotating speed cana highly sensitive detection of lower rotating speed that be decreased in inverse proportion to the reset period,heretofore has been difficult to detect and which can be that is, the number of the cores.operated by the commercial frequency. This paper investi- Up to date, the authors have already reported thegates the precision of DA conversion and the linearity photoelectric type rotating speed detector with whichof control characteristics of this detector, and clarifies low rotating speed can be detected sensitively [3].the lower limit of the detectable low rotating speed. It Thereafter, the authors proposed the new mechanism forhas been proved that the lower limit of this detector can detecting super low rotating speed which can providebe varied in inverse proportion to the reset intervals highly sensitive detection of lower rotating speeds withand that the limit can be decreased in proportion to the the output synchronized with the commercial frequencynumber of cores used because the reset interval varies [4]. This paper investigates the mechanism for detectingin proportion to the number of cores, the super low rotating speed, the accuracy of DA con-

version and the linearity of control characteristics inINTRODUCTION this detector, and clarifies the lower limit of the

detectable low rotating speed. The transient responseIt is required that the rotating speed of the rotary characteristics of this detector is investigated, based

kiln in a process for cement manufacture be variable over on the viewpoint of control systems, because it is subjectthe range of 1 r.p.m to 1/3 r.p.m and that its speed be to frequent use as the element of control systems. Thisconstant of any control setting beyond 3 percent to 5 per- detector was applied to rotating speed control of a DCcent. It is required that the rotating speed of calender servomotor and this practicality was confirmed [5]. Itroll in a process for rubber manufacture be variable over appears that this detector may be useful for low rotatingthe range of 3 r.p.m to 12 r.p.m1 and speed be constant speed control in cement and rubber manufacture.at any control setting in order to prevent the generationof the inequality. The DC Ward-Leonard system and thestatic Leonard system have been adopted as the methods of MECHANISM FOR SPEED DETECTION AND PRINCIPLE OF OPERATIONdriving the motor. Now, magnetic amplifier and thyristorcircuits have been widely used to control the motor speed. Fig.l shows the full-wave output type circuits forTheise hamplifiersbeen uslyued dircntrolyw themtortpe. detecting the super low rotating speed with a number ofThese amplifiers are usually fed directly with the output the cores of Cn= 8. All the transistors act as switches.of tachometers ( generator type ). However, many problems the coreshapin =i8-uAllwth tra rsteresis loopconcerning low speed control remain unsolved, because The pulse shaping circuit with square hysteresis loopthere is a limit in the sensitivity for detecting low ro- and is operated by the triger pulse generated by photo-tating speed.

thaingsevconswhe]tro:is na urthartheTheirecesuit

197(

neezYonE

Recently, the digital tachometer has been used, so electric devices. Every core in Fig.l is reset by thet these difficult points have been overcome and rotat- output voltage of pulse shaping circuit. Fig.2 shows thespeed has been measured with a high accuracy. But, time chart for driving the switching transistor connectederal mechanisms for conversion of pulse counting, DA on the reset and gate circuit respectively, Fig.l. Theversion, power amplification and so on become necessary period c in Fia.2 equals the half-cycle period 10 m sen the digital tachometer is used as an element of con- of the commercial frequency f All reset period SWL system. This is especially true when rotating speed gR8 equal Tr = 7T and all gate periods SWG, '-- SWG8measured by counting the number of pulses generated in equal g = T = 10 m sec. The transistor Tc1 of core I innit time ( this unit time has to be made fairly longer Fig.l conducts only in the reset period of SWRl ( thatn the half-cycle period of commercial frequency for is, 0 -'- 7T period ) of Ch.1 in Fig.2, and core I is resetpurpose of measuring super low rotating speed ). by the shaped pulse voltage. In the next gate period ofrefore, DA conversion, which has been used until SWG1 ( this is, 77 -io 8T period ) in Fig.2, the transistorently to convert into an analog signal that may be Tgl of core I in Fig.l conducts, and then the core I isted to control the magnetic amplifier or the thyristor gated, and the output is obtained on the load Rl at the

same time as core I is saturated. The voltage waveformM induced across the control winding N1 in this operatingManuscript received July 6, 1976; revised December 28, condition is illustrated in Fig.4 and the B-H

characteristics in this condition is shown in Fig.3(a).The authors are with the Department of Electric Engi- In the same manner, the transistor Tc2 in core II conductsring, Faculty of Engineering, Yamagata University, only in the reset period SWR2 ( that is, 7 r" 87 periodBzawa, Japan. of Ch.2 in Fig.2, and core II is reset by the shaped

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI- 24, No. 2, MAY 1977

ICORE I

Fig.l. Circuit for detecting super-low rotatingspeed

pulse voltage. In the next gate period of SWG2 ( that is,8T~,v 9T period ), core II is gated and the output is ob-tained on the load RL. Next, the mechanism for detectingof the full-wave output circuit will be described asfollows.

Each transistor Tcl,.., and Tc8 in Fig.1 conductsin the reset period SWR1,.., and SWR8 in Fig.2 re-spectively and each core I rv VIII is reset by the shapedpulse voltage which its repeating frequency is in pro-portion to the rotating speed. The gate period SWG1,..,and SWG8 of each core I'-.' VIII in Fig.2 equal to thehalf-cycle period of the commercial frequency 50 Hzthat is, Tg = T = 10 m sec. ), each transistor Tgl,..,and TqB in Fig.1 conducts in this gate period re-spectively and each core is gated. As a result, the full-wave output can he obtained.

Generally, in case of the full-wave output typewith a number of cores, Cn. = m + 1, there are the follow-ing relations between the reset period Tr, the gate peri-od and the number of coresCn

T =mT Tr +T (m +l1)Tg g g

C m + 1 ), however, M = 1,2,3,4,...

Here, assuming that the number of shaped pulses in the

reset period Tr is n and that the amount of reset flux

becomes maximum when n equals to N , assuming that the

number of shaped pulses generated per one revolution of

the photoelectric devices is P, the detectable range of

the rotating speed is decided by N and P. It seems to be

quite all right to decide the detectable range 4fromthe rotating speed when the number of shaped pulses in-

cluded in the reset period become 1 to the rotating speedwhen the amount of reset flux becomes maximum with n =NGenerally, in case the number of cores Cn- is m + 1, the

lower limit of the detectable rotating speed is decided

by the upper limit of the number of pulses generated per

revolution and n = 1. Assuming that the rotating speed

per minute is nr and the repeating frequency of the

INPUT

Ch.

f- VI

-J= STEP STATE INPUT ----

- SWRI,~ LSWGI

0: T - SWR3Ch.4 f-

Oh.!

Oh.'Oh.

OUT-PU'

71IZZl/ VZZLZZ7I7VVAZL1~2 VAI"VLZV,-2iV4T 0 " , FPtV/VV/ T vzv,v,vvv/.v7I v,vZv,:~v,v,vII/1/l////l W I' 1111,11 /V GV/AAATt I~~L~&V~

ITI '3T-

5T 17T -~-TIME t!IT

=0

FIg. 2. Transient response of super-low rotatingspeed detector

shaped pulse is fp , the following formula is given.

nr=60n/I( PTr ) (r.p.m)

f1 /Tr=npr

nr= 60 f /P (r.p.n)p

( 2)

( 3)

( 4)

The lower limit of the detectable rotating speed in thiscircuit is decided respectively by substituting Tr ofeq. (1), n = 1 and P = 6000 ( as the maximum value of Pis 6000 on the market ) into eq. (2). It is proved thatthis lower limit decreases in inverse proportion to thereset period Tr as shown by eq. (2), that is, the numberof core.

Next, the operating principle of full-wave outputtype circuit in Fig.1 will be described respectively asfollows. We manage and analyze the system in Fig.2 asthe sampled- data control system that has the samplingperiod of Tr + Tg = 8Tg = TM . Assuming that the instantrotatinig speed is C(t) and that q is a positive integer,tjoutput corresponding to the integral sampled- reset fluxin 0',7T period is obtained in 7Tv, 8T period. Gener-ally, if the period of o--8T in Fig.2 is regarded asthe q-th sampling period and the period of 8T -'.'16T isregarded as the ( q + 1 )-th sampling period, the averagevalue of the number of shaped pulses n8(qTm) containingin the reset period SWRl = Tr = 7Tm /8 ( that is, 0 ,7T period) is represented as follows.

q-18) T7T~ m

n (qT; ) = P. I. t ) dt

8 7T5

where q =l, 2, 3, 4......

Assuming that the height of the shaped pulse voltageacross control winding Nl is Er and that the shapedpulse width is T the flux amouint Mr(qTm) which is

reset in the q-th sampling period of 0-,.'-7T is given as

follows.

E T

A4'r (qT~) = P. ~n(qT )

N1( 6)

Assuming that the resistance reflected on the terminal of

204

(5 )

oll 2T5 m m m

-1 --V/V/1/./V,/V-/V-/I/Zl Vllllvzlllv777VA I

CZ .0: 3T m i


the gate winding of core I is Rso , and that Te is thefiring angle in the gate period ((7Tm /8)^. Tm),

T0 (qTm) = 2 A D(qT~)a ~~E

5 / `7 N

II (qT ) = -* 0Es T0(qT )

E -s TT

qthe average output current IlSqT ) in the gate period((7Tm /8) v Tm) is given approximately from eq.(6) andeq.(7)

1N2IE T P (q-1/8)T \

R f1 - 2ErTpe mI(TY = E - C(t) dt (8)

Rso N¢iTg , ( q-lYT I9 ~m -

As the sampling period of core II is Tm /8 lagging thesampling period of core I, the output corresponding to theintegral sampled-reset flux in T?8T period is obtainedin 8Te- 9T period. Generally, the average output current

I(qTSm + Tm/8) in the period ( TM '.i9Tm /8) of core II isgiven approximately as follows

1 0 N2 Nr*TpCP ¶

I1(qT~ + rTm/8) --E- N CTjMq78 dtm)

mThe sampling period of core VIII is 7T /8 lagging thesampling period of core I, the average output currentIZ ( qTm + 7Tm /8) in the period ( 1-1/8)STm ev(1+6/8)Tmis given approximatelly as follows

(p(q+6/8) T

(qT +7r /8)E - CM d (10so lg

(q-1/8)T

This system in Fig.l can be represented by the multi-rate sampled-data control system with the sampling peri-od Tm ( = 8T = 8Tg ). It is proved that the outputsynchronized with the commercial frequency is obtainedand the control characteristics shown in Fig.3(b) areobtained.

Next, in case of Cn = 8, the half-wave output canbe obtained without difficulty under conditions of a resetperiod Tr of 150 m sec., of the gate period Tq of 10 msec., and of the time intervals between the beginning ofreset period in core I and at the same period in the coreII, between the beginning of reset period in the core IIand at the same period in the core III,....of 20 m sec.In case of the half-wave output type, there are thefollowing relations between Tr3 Tg and Cn

T = ( 2m + 1 )T , T + T = ( 2m + 2 )Tr g r g g

C = ( 2m + 2 ) / 2 = m + 1, however, m = 1,2,3,4,..n( 11)

LINEARITY OF CONTROL CHARACTERISTICS AND ACCURACY

OF DETECTION

The various causes which give an effect on thelinearity of control characteristics are investigated in

this section. The causes of the deviation from this linearline may be divided into two broad classes. One resultsfrom the square hysteresis loop core itself and the otherresults from the circuit construction. And, the causesresulting from the circuit constrution may be divided intotwo classes too. One results from the difference of thenumber of the shaped pulse included in each reset period,the other results from the irregularity of the controlcharacteristics of the parallel-connected magnetic circuits.

(a) Results from Nonlinearity of Square HysteresisLoop CoreResulting from the existence of different amount

of return flux A¢Dh on each flux level, the nonlinearvariation of the average value of exciting current forthe shaped pulse with Ipn by each flux level, and theexistence of the amount of flux in the saturation region.

(a

s wim\i~~fn~

NI 3

-A-c(offr 0 N

NO. OF PULSEI) (b)

Fig. 3. (a) Actual B-H curve. (b) Control characteristics

GATE PERIODTfTr-

- Tfp- RESET PERIOD

TbTp

Fig. 4. Induced voltage of N1 winding.

(b) Difference in Number of Shaped Pulses Included inReset Period

Fig.4 shows the waveform of the induced voltage onthe reset winding Ml of a core I. Assuming that Tp is theshaped pulse width in seconds, Tb is the time intervalsof the return voltage, Tf = 1/ fp is the pulse intervalin seconds of the repeating frequency fp of the shapedpulse, To is the firing time in seconds in gate period,and that Er is the height of the shaped pulse induced on

the reset winding N1 . The number of shaped pulse includedin each reset period equals n, respectively, in case thatTr / Tfp is integer. The following relation is given ifthe repeating frequency of shaped pulse is varied by Af-more than this state

n + An =T (f f+f)r p- p

n=r-A fp = nO+q 0o-n<nO = 1, 2,t 3, 4,.

( 12 )

In case of 0 n < 1, the number of shaped pulse of n n0

and n ± no + 1 will be contained reciprocally in eachreset period. The difference of this number causes thedeviation in the average output current of this detector.But these deviations are reduced by increasing the numberof the shaped pulses N and by making the voltage-timeintegral of the shaped pulse smaller.

(c) Irregularity of Control Characteristics in EachMagnetic Circuit

The degrees of the agreement of the average gate

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T9 -

T


current characteristics T1 to I8 in the parallel-connectedmagnetic circuitsis represented in percentage by dividingthe maximum value amoung the deviation of the other fromthe 1, characteristics of the core I by the maximum aver-age gate current of 1,. In order to decrease these devi-ations. it becomes possible by adjusting slightly thereset or gate circuit resistance and the number of resetor gate winding, and by connecting the high resistanceparallel with the gate winding. Fig.3(a) shows the B-Hcurve of the core being reset by the shaped pulse. Assum-ing that Atfr is the amount of flux which is varied bythe return voltage generated after resetting by the lastshaped pulse, and the amount of flux which is caused bythe circuit condition will be contained in this Ajr.Assuming that Atr is the amount of the effective resetflux and At is the amount of the gate flux. There is thefollowing relation among the amount of flux.

tr + AOgs = g + Atfr (13)Assuming that ero and e80 is equivalent counter electro-motive force of each transistor connected with the resetcircuit and the gate one, rc and r8 is equivalent re-sistance of each transistor of these circuits respectivelyRr is the sum of rc and the reset circuit resistance, R.is the sum of r8, the gate circuit resistance and loadresistance, Is is the average exciting current over thegate period ,T, and E. is the voltage source of outputcircuit, the iollowing formula is given

-it - IT-R -er) T - AOf J+ AtN( pn r °) P fn} 9b8

=+.(Es - I8-Rs - eO) -T0 + Atf (14)N2

Assuming that AOF is the average value of the amount ofreturn flux AO n from n = 1 to n = N, and Ip is the aver-age value of r from n = 1 to N, the following formulais defined

^Odfn = Atfn - FtFI = Idpn - pn - I

p

Therefore, Te is given from eq.(14) approximately byomitting the iteam more than secondary one and it iseq. (Ap .1) in Appendix(I). Then, the average outputcurrent I1 for the gate period Tq is given by

Iz -_*(1~-)~=ZmI kd n -LI( 16)s g

where 1Zm is the maximum average output current in caseof n = 0

E

im =

Rs

2 N I R + e2 s s so-_~~ AO 1 +

R-T gs ES g S /

2 Es N2 I*-Rs+e IAACM?M= .1+ S S0~

E8 '-R.T E g .

Fig.3(b) shows the average output current characteristicsas shown in eq. (16) where Ito is the minimum average outcurrent in n = N, Idmn in eq. (16) indicates the devi-ation of this control characteristics from linear line.

Assuming that the maximum value of AIdyn for the numberof pulse n is represented by [ AIdm ]max , the deviationof the control characteristics from linear line is definedas follows

AI = cAId 1mx 1 / ( I n Ilo )Ec nnll max. .1011( 17 )

The accuracy of DA conversion from the shaped pulse Q isdefined by

( 18 )Q = ( 'im - Z,). 100 / N

AId,n has an effect on the linearity, but, these effectsbecome more complex since AIdfn ' , Is andIS fr containing in this AIdim undergo a non-linear change by theflux level. There are the following methods in order toreduce these effects; it is to make the value of I and.pnIs smaller by winding adequately the coil which its re-sistance is small, and it is to make the circuit re-sistance smaller as much as possible without connectingthe elements of transistor and diode on the reset andgate circuits, and it is to make the time interval of thereturn voltage Tb smaller as much as possible by meansof making the amount of the return flux reduce, and itis to select the cores which the control magnetizationcurves are uniform and APgs - A'fr is small.

DIFFERENTIAL OUTPUT TYPE CIRCUIT FOR DETECTION

Principle of OperationIt has been mentioned on the circuit in Fig.l so

that the average output current reduces linearly with theincrease of the repeating frequency of shaped pulse. butit is mentioned in this section on the circuit constructicso that the above-mentioned current increases linearlywith the increase of this repeating frequency. Thiscircuit is shown in Fig.5 [5]. The time relations betweenthe reset and the gate of this circuit are the same, Fig.;This circuit is to detect the difference in the voltageacross the dividing resistance Rdl and Rd , so that theaverage output current corresponding to the gate pulsewidth is obtained. Therefore, the transistors Tql and Ticonduct simultaneously in the gate period of T" = SW1g,the transistors Tg2 and T-'2 conduct simultaneously in thegate period of SWG2 .

Transient CharacteristicsThe circuit of core I in Fig.5 is called channel 1

and is represented by [ Ch.l ], the circuit of core IIis called channel 2, that is, [ Ch.2 ] and so on. In thedifferential full-wave output circuit with Cn = 8 and Tr= 70 m sec. The last waveform in Fig.2 shows the outputtransient response after the application of the shapedpulse with the repeating frequency fp in a step state atthe beginning of reset period in core I ( t = 0 ). Intime interval of 0 to T, the output corresponding to theinterval of Tg /7is obtained on Ch.3 in the interval ofT to 2T since the core III is reset only for the interval!of Tr /7.Then, the output corresponding to the intervalof 2Tg /7is obtained on Ch.4 in the interval of 2T to3T. Similarly, in the interval of 7T to 8T, the finalsteady-state output is obtained on Ch.l at first. Gener-ally, in case of the number of the used core Cn = f + 1,it is obtained at first in the interval of mT to C m +1 ).T after the application of the step input. The transient characteristics of the differential full-wave outputtype detecting circuit is investigated, in case of thenumber of the used core Cn = m + 1 and the reset periodof Tr = mTf = mT ( here, T = T = 10 m sec. ). Assumingthat C(t) is an instanteneous rotating speed and C(S) isthe Laplace transform of this speed. Here, Tg + Tr =( m + 1 )T = Tm in eq.(l) is regarded as the samplingperiod of this circuit, and_q is a positive integer.The average output voltage Ez(qTM) on Ch.l for the peri-od Tg of mTm /(m + 1) to Tm is given approximately asshown in Appendix(II)

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI- 24, No. 2, MAY; 1977

@Di

Fig. 5. Detecting circuit of differetial output type.

q - 1/l(m+l)) TmE (qT ) = KDJ\ C(t) dt + AT'

(q - 1) Tm

Where, KD = E .Kd'P*RL / Tg ( R + dl

AT E AT Rr / T - ( Rr + Rd,)dmn ' 9q = 1, 2, 3, 4. . . . .

The average output voltages Ez(qT, + Tm,E1(qTm + 2Tm /( m + 1 )), . , and EZ(qTmon Ch.2, Ch.3, . . . and Ch.( m + 1 ) foiod are shown in Appendix III . This circielement is represented by the block diagirate sampled-data control system with thEof Tm shown in Fig.6.Here, kd is the ratio of the average outsthe gate period to the average value of tspeed for the reset period. The relationK is given byDkd = KD mm/ ( m + I

The Laplace transform B(s) of the outputto the Laplace transform of the average cT7(s) and B(z) is the Z-transform of B(s)transient response of this detector afte.of step state input at the beginning ofcore I is represented by the Z-transformthe sampling period Tm as shown in Fig.6

B(z) = ---d z m f 1 + 2m (Z- 1)

m- 1zm+1Z +

1

+m Z +m + ( m - 1 ) z

m - 1%m +

T i2 in eq.(21) equals e m- , but replacingit is evident that Z = ( Za )m+ltherefore eq.(21) can be rewritten by

m+l k-"d(l -B( Z + 2 Z + 3 Z-a a7' a a3

+ ( m - 1 )z-(m-l) + m Z -m+ m -(m4a a a

Eq.(22) shows the transient response to tFig.2 shows the response in case of m = 7

( 19 )

C(s) ~1mS ' Ch.,2 81s1m'~TiSeTm+ 0 PTt kdL~~~ ~ e }

Ch.IP

m= 1.2;3a / T3 Tm '(m+l)Tm: 1,2,3 1 Ch.mI 1

Fig. 6. Sampled-data control system of differetialfull-wave output circuit.

the number of the used core Cn = 8. It was made sure ofbeing able to represent equivalently by the sampled-data.control system with the sampling period of T = Tm /(m+l).This equivalent block diagram is shown in Fig.7.

C(s) -mTS T Bskd

mTSs

m = 1,2,3,4-'-'T = Tm/(m+l)

/(m + 1)),+ mTm /( m + 1))

r the gate peri-uit as the controlram of the multi-e sampling period

Fig. 7. Sampled-data control system equivalent to Fig.6

EXPERIMENTAL RESULTS

Fig.8 illustrates the characteristics of the aver-put voltage for' age output current It ( dashed line )_of the detectingthe rotating circuit and the average gate current 1-( dashed linebetween kd and of core I in case that the amount of-reset flux becomes

maximum, when the number of shaped pulse n containing for20 ) the reset period of Tr = 150 m sec. is 36 and 48 in the

t in Fig.6 equals half-wave output circuit with Cn = 8, and it illustrates,)utput voltage in addition, the characteristics of It ( solid line-)).Here, the and Il ( solid line ) of core I in case that the abover the application condition for the reset period of Tr = 70 m sec. is 37

reset period in and 49 in the full-wave output circuit with Cn = 8.equation with In case of the characteristics with n = 36 as aparameter in the half-wavg output circuit in Fig.8, the

low rotating speed over the range of 0.067 to 2.4 r.p.mcan be detected highly sensitively with an accuracy ofDA conversion Q = 2.75 percent-if the photoelectric pick-up' with the number of pulse per one revolution of P =

*. . . . . 6006 is used. Then, the deviation of the average output

current characteristics Iz from the linear line is 0.71 percent. The degrees of the agreement of every charac-+ 1 + teristics of each average gate current bf I, to I8 in

each core I to VIII becomes 1.2 percent. And in case ofthe characteristics with n =48 as a parameter in thehalf-wave output circuit, the low rotating speed over therange of 0.067 to 3.2 r.p.m can be detected highly sensi-tively with an accuracy of DA conversion Q = 2.1 percent

Za by e Tos if the photoelectric pick-up of P--6000 is used. The de-Za by e viation of I7 characteristics from linear line is 0.47

percent. The_degrees of the agreement of each character-istics from I, to-8 is o.75 percent if it is set on thebasis of Il characteristics. Thus, if the number of the

+ shaped pulses Nl which makes the amount of the reset flux+ s * ' maximum is selected larger, the accuracy of DA conversion

Q is reduced but the detectable rotating speed becomes-1) + . 22) larger.

In case of the curve with n =37 as a parameter inthe full-wave output circuit, the low rotating speed over

:he step input, the range of 0.14 to 5.3 r.p.m can be detected highly7 in eq. 22 and sensitively with an accuracy of DA conversion of Q = 2.7

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Table. 1. Detectable range of rotating speed

20 10I _-

- zwor.:iEo

8>

<s

4 uJ3 (l.L - l<l

4w10 - 5H

D0.H

w

345 1

-J2

._

O0 -0C

characteristics of super-lowrotating speed

Fig.9 illustrated the average output current char-acteristics and the average gate current characteristicsIdl in case of Cn = 4 ( at that time, Tr = 30 m sec. )and Cn = 8 ( Tr = 70 m sec. ) in the differential full-wave output circuit. Table*1 shows the range of the rotating speed and the various constant in case of N =40 andP = 6000 as an example from the practical viewpoint.Fig. 10 illustrates to compare the characteristics of therotating speed detector ( Cn = 2 ) [31 with one of thesuper low rotating speed detector (Cn =4 ,8) [4]. Thoughthe lower limit of the detectable rotating speed can bevaried in inverse proportion to the reset period of Tit can be decreased in inversed proportion to the numberof the used cores since the reset period varies in pro-portion to the number of the used cores.

25 30 35 40ROTATING SPEED nf, (r.p.m)

Tr- 70rms fp (kp.p.s)

Fig. 9. Control characteristics of differrentialoutput type detector.

percent. The deviation of characteristics from linearline is 0.7 percent. The deg'rees of the agreement of eachcharacteristics Il to I8 is 1.5 percent. In case of thecurve with n = 49 as a parameter in the full-wave outputcircuit, the low rotating speed over the range of 0.14to 7 r.p.m can be detected highly sensitively with anaccuracy of DA conversion of Q = 2 percent, if the photo-electric pick-up of P = 6000 is used. The deviation of IZcharacteristics from the linear line is 0.46 percent.

Fig.10. Rotating speed characteristics of varioustype detector

APPLICATION OF DC SERVOMOTOR TO LOW ROTATING SPEEDCONTROL

Applications of this super low rotating speed de.-tector for control of a DC servomotor will be investi-gated analytically and the practicality of this detectorwill be ascertained. Fig.ll illustrates.the block diagramof this low rotating speed control system. The DC servo-motor is driven by the full-wave bridge type magneticamplifier which operates on commercial frequency and ro-tating speed is reduced one hundredth by the use of gearswith the ratio of 1 to 100, and the photoelectric devicewith P = 6000 is connected directly to the output axis.The output of the super low rotating speed detector isfedback.negatively to the input of this magnetic ampli-fier. The feedback loops of the rotating speed is repre-

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DETECTABLE 014 0.33 0.067 0.14 0.043 0.091RANGE (r. p.m) 5.71 3. 33 2.67 5.71 74 3.63

PULSE 6000 6000 6000 6000 6000 6000ACCURACY OF 2.5 2.5 2.5 2.5 2.5 2.5AD CONy. %RESET PERIOD 70 30 150 70 230 I10

Tr (ImS)NO. OF PULSE I I- i I- I

IN Tr n 40 40 40 40 40 40OUTPUT HALF FULL HALF FULL HALF FULLWAVEFORM WAVE WAVE WAVE WAVE WAVE WAVE

SED CORE 4 4 8 8 12 12REPEATINGFREQfp(p.s)571.4 1333.3 266.7 571.4 173.9 363$

Fig. 8. Control

E

30z

iUcrIcr

DI.

20LO

cr-w>


GEAR,MAGNETiC f nA_ AMPLIFIER v

Sup. Low Rot. f.II>6: ng-~SPEED DE:T.

Fig. 11. Block diagrain of low rotating speed controlsystem

NQ OF- ~~~~~CORE 20

,,,-^2_/ CORE 24

_,,> ~~~CORE 12 Trw 0

CORE 8 a X 90KC X 1.41

Km 38Kd = 2.

I

0Orn A,

1.4

02

- .2

<i6

i: 0.4

Q2

;eVv 400

SHEDLINEOil165).9

8i8x 1045)36

SOLIDLINE

0.01Q 1931000.9174.02xI :S2.036I2I036

(seco

( sec)( se% v)

(r/od )

600TIME (ins)

Fig.12. Sampled-data control system of low rotatingspeed

sented by the multirate sampled-data control system withthe sampling period of T = Tm / ( m + 1 ). Therefore,this system is represented by the sampled- data controlsystems with the sampling period of T as shown in Fig.12.Where Go(s) is the Laplace transform of integration sampl-ing of the magnetic amplifier input vjoltage for the resetperiod, G1(s) is the transfer function of the averageoutput voltage to the average input voltage of magneticamplifier, G2(s) is the transfer function of the rotatingspeed to the armature voltage of DC servomotor. The Z-transform of transient response speed to the step inputis given by

K =Kc m

C(Z) = XT ( Z - 1) (Z - e-aT) ( Z - e Tmo) +MO

Fig. 13. Calculated value of step response of used core

It was shown that the maximum average output voltage doesnot change when Cn varies and the highly sensitive de-tection of low rotating speed becomes possible since kdincreases with the increase of Cn

SOLID LINE: EXPERIMENTAL VALUEDASHED UNE: THEORETICAL VALUEo 1.2

I.C

b0.E

g:0.4

0.2

*

Cn r 8Kd '4.76Kc '2.617Km a 3.56xid4T *0.01a x45.4Tm :0.1-25

_0 100

Cn z 42.092.6173. 56xld0.0145.40.125

(V/rad )

4t rad/Soc )

( sec.)(seci

I I I I I I i I I I1 1 I I1200 300 400 500

TIME (ms)

*KcKkd (l - e/mo)Z (l - z m)

m T

where = K K k (1-e MO) / m-c m d

KKK / T (24)c m MO

If the number of shaped pulse N which the amount of maxi-mum reset flux is obtained for the reset period isconstant, the value of eq.(24) becomes constant approxi-mately provided that the number of the used cores Cnvaries. In case of Cn = 4 ( that is, m = 3 ) in this de-tector, Fig.13 illustrates the experimental value andthe theoritical value of the transient response in casethat its final steady state is 5 r.p.m after the appli-cation of the step input to the speed control system ofDC servomotor which rotates on 3 r.p.m [51, and, in ad-dition, it illustrates those in case that the speed ofthis motor is varied from 2 r.p.m to 4 r.p.m after theapplication of the step input.

If the number of shaped pulses N, by which the a-mount of the maximum reset flux is obtained, is set at40 in the differential full-wave output type detector,the range of the detectable rotating speed is given asfollows from eq. (2),0.33 to 13.3 r.p.m with Cn = 4, 0.14 to 5.71 r.p.m withCn = 8, 0.091 to 3.64 r.p.m with Cn = 12, 0.067 to 2.67r.p.m with Cn = 16, 0.053 to 2.11 r.p.m with C. = 20.

Fig. 14. Comparison of theoretical value withexperimental value of step response

Fig.14 illustrates the transient response of speed controlsystems of DC servomotor to the step-input with Cn as aparameter, and illustrates, in addition, the transientresponse to the step input with Cn as a parameter in casethat K, was reduced to some degree. The step responsebecomes oscillatory if Cn increases, but this oscillationis reduced if KQ decreases.

CONCLUSION

It has been shown that accurate digital instrumen-tation of rotating speed becomes possible by making useof the square hysteresis loop core as an element of DAconversion with noticing the function of integral oper-ation and memory of this core, and also shown that ahighly sensitive detection of lower rotating speed whichhas been difficult to detect becomes possible. And, more,a thyristor circuit can be driven from a full-wave recti-fied voltage source if DC voltage source Es of the outputcircuit is exchanged for the full-wave rectified voltagesource. The mechanism for detecting, which is able toperform simultaneously the function of pulse counting,DA conversion and power amplification and the control ofthe thyristor circuit or the magnetic amplifier, wereproposed. Though the lower limit of this detector can bevaried in inverse proportion to the reset period, it canbe decreased in inverse proportion to the number of thecores used since the reset period varies in proportion.Thus, if the number of shaped pulses N needed to make the

------

I Il1


amount of reset flux maximum is increased, it is possible ,(q+/(m±i))Tto make the accuracy of DA conversion Q better, but thedetected rotating speed becomes larger. This detector E1(qT + 2T /(mn+l)) = -K 2 C(t) dt + AT I A .6concept makes it possible to construct a circuit capable m Pof isolating the input and output circuits. The transient i (q--(m-l)/(m+l))Tcharacteristics of the differential full-wave output type mdetector were investigated and the low rotating speedcontrol of a DC servomotor with this detector was investi- (q+(m-1)1(m+l))Tgated analytically and the practicality of this detector mwas established. E(T -'mT /(m+l)) = K (t)da+A'T A .71E,<-'a mT ' "")d'-''AE \> > TLL7

APPENDIX ( I )

= <d.n + AT

where

K + -Igd +~

N1 Es

N2 N2 I Rr T\

s'Aby + 8As '1 Es

AT =

( Ap . 1 )

---T -p

constant

N I ,RrT NIRnT2 dpn rp1 2 s s p§~~+

N E NEls 1 s

N /T/IRs + eS\

E Egs f E

APPENDIX ( II

The average value of the number of shaped pulse forreset period Tr = [ (q l)Tm '- (q l/(m+l) )Tm] of Ch.lis given as follows

e(q-eq/1(m l) )T3,

Where q = 1, 2, 3, 4, . . . . . . .

REFERENCE

[1] J.Shida and T.Kikuchi, On the number of countingpulses of a multipulse magnetic-transistor counterJ.I.E.E. of Japan, vol. 84-12, no.915, pp. 1946-1956,1964.

[2] M.Sakao and E.Ohno, Partial switching character-istics of the square hysteresis core and its appli-cations , J.I.E.E. of Japan, vol.86-6, no.933,pp.987-995, 1966.

[3] T.Ouchi, On the circuit forms of magnetic amplifiercontrolled by the output of photoelectric rotatingspeed counter , J.I.E.E. of Japan, vol.85-5, no.920,pp.863-871,1965.

[4] T..Ouchi, T'.Ohtomo, N.Hagiwara and S.Jutoku, Mecha-nism fQr detecting super low rotating speedTohoku Joint Conf. of I.E.E. of Japan, no.2A7, Oct.,1974.

[5] T.Ouchi, T.Ohtomo, N.Hagiwara and S.Jutoku, Lowrotating speed cQntrol devices for DC servomotorTohoku Joint Conf. of I.E.E. of Japan, nQ.1D7,Oct., 1974'.

mqT~) T) 1 (q-l/(m+l)). Tm

+ m T pvlrWhere q = 1, 2, 3, 4 . . -Then, the output pulse width To (qTM) generated in the gaperiod of T is given as follows from eq.(A .1)

9 ~~~~~~~pT0(qTm) - Kd n(qTq) + ATd ( A .3

The average output voltage E1(qTm) for the gate periodT of mTm /(m + 1) to Tm on Ch.l is given approximatelyags follows

E .R T (qT)E (qT ) = A .4

R +R T pL dl g

From eq.(A .3) and eq.(A-.4), EZ (qTm) is represented ineq.(19) p p

APPENDIX ( III

rqTmE m(qT+ Tm /(m+1)) = Kg C(t) dt + AT (A.5)

(q-m/(m+l))Tm

TAKAO OUCHI was born in Fukushima, Japan on Feb. 13,1930. He received the B.E. and M.E. of Engineeringdegrees from the University of Tohoku in 1953 and 1956respectively, and received the Dr. from the Universityof Tohoku in 1975.

Since 1953 he has been with the Department of Elec-trical Engineering, Faculty of Engineering, University

tE of Yamagata. His work has been concerned with the mag-netic devices, pulse width modulation for nondestructivereadout and application to signal processing. Hiscurrent interests are in analog memory, control engi-neering and application of magnetic core to signalprocessing. Dr. Ouchi is a member of IEE of Japan,Society of Electrics and Comunication Engineering ofJapan and Society of Instrument and Control Engineeringof Japan.

TERUHIKO OHTOMO was born in Peking, China on July 29,1943. He received the B.E. and M.E. degrees in elec-trical engineering from the University of Yamagata,Japan, in 1969 and 1971, respectively.

Since 1971 he has been with the Department of Elec-trical Engineering, University of Yamagata, as a Re-search Assistant. He is now working on nonlinear mag-netic applications.

Mr. Ohtomo is a member of the Institute of Engineersof Japan and the Institute of Electrical CommunicationEngineers of Japan

N2T N2 (E - Es ) + (eso -ero)

mechanism for detecting super low rotating speed utilizing square hysteresis loop cores

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