TORQUE ― SPEED RIIGULAT10N OF DC MOTOR
BASED ON LOAD TORQUE ESTIMAT10N IIETHOD
Kiyoshi oHIS減 正,Kouhei OIINISHI
andKeio University

Kolhoku一 ktl, Yokollama, 223,

Kullio MIYACHIJapall―Abstract― As the output tOrque is reguユ ated thlough the speed rettuユ ator itl dc
motor driva system, the speed response delays by the lag of tit sPeed regula―
tor when the load torqlde is imposed. when thisユoad tt〕 Ique is directユ y EIQa一strad or indiractly estimated,additional torque resuユ atOr which ちyPasses thespeed reる ulatOr is POssible and the ■回prrpved speed rtsT)onse, such as the quickOl■ tPじ t tOrque resPonse and sIBall fldctuation Of the IBotor sPeed「wilユ becG□ ereali zed.
This Paper prOposas the torttue一 speed regulation tttiich is based on the op―と白回a■ control theory, in which tれ Q ObservQT is used to eこ t ttmと te the ■oca to士・―qu e, This stratagy also introduces the easy design Of the sPeed reguユ atOr ttn
dc moto̲W drive sysと e口 , as the desired system Performanc:e v主 ユl be takan into
acccunt in the proposed quadratic PerforttancQ index, PI schenaと ic design Pro―

cedure based on thェ s strateey and experimenta■ユ.

exttmp■ es are also shown.

INTRODUCT10N
t営

a尋ぷ
曇:i8:s 畳暑を言]:二 告岳:g圭。:と in i:lit督 8teを te8P,こ 品畳; 3[e8景 I
Pected tO have the ユarge pOtentiュ ユity to impFOVe the s),stem performance in thedrttve appユ ications, Moreover the design procedure is せisu al■ y simplifioa incan b魯 88品を 苦pli[d i:ythとthis modern controユ theory.
WhQn the ttodern control thecry is applied to the speed coiltrol ofとhesepar ateユ y excited dc motor, the plant system can be treated as a lillear ti■ le―illvariant syste□ . This means that the poユ e― zero assigrlment is nost importttnt
for the total system respOnse. llBut convQntional PI corttroユ ユer has ユoss free一
doIB in the contro■ design procedure than the regulator based on the moderncontrol thcory.

Besides various rQquiruHents to the system performance can beeas主 ユy taken ill the regulattOr design in the IBodren control thQory.

This paper‐ proposes the unified legulatOr design prOcedure based on thetheory, 主よ which the speed response to both the lo々 d torqueand the spe● d reference can be sPecified irldependently. For this purpose, thesuュ table quadratic perfo.肥 ance il■ dex ■s defined. As the result, concユ udedregulator based on this cost ゴunction can るe c■ assifよ ed into two subreguユ a̲tols. One is the sPeed regulator and thQ other is the tOrque reguユ ator. As
the augnented system, there is one series inte宮 ±4tor, which allov7S nO Steadystate offset. Thiも type of controユ ユer is exPected to Le ユess sensitive to thQ
CPt■ Inal contro■

system parametcr variations. In the speed regulator, the state feedback o=
the moasured qtlantity is necessary. In the torquQ ro3町 ator, the measured or
the ttStimated ユoad torque is efflュ ctive for the better regulattton. This ■oad
torque is defined as the uncontro■ la■ e but observable state variab■ e, so theobserver can be constructed to etstimate its value with the ar itrary estima丁tion tゴ ne cOnstant.
trhis lnetrlod is also imp■ emel■ ted and tested as sho珊 晩 in this paper,!■lPEO― Tokyo'83
1209/

2. LOAD T01QUE ESTIMAT10N

IThe ■mpact of the load torque to the dc moと or may g■ ve rュ se to the tcarmpo―
ヽ°・・
啓f督 者ゴ をとを最島北景呈豊二ititi:こ is i:i5:岳 苦;rtthを 書if:を r[1:e景 品ま:tespeed reference and the actual sPced. But the optina■ tOrque regulator, 恥オlich
can reduce this ttmpact drop, is Possib■ e lf the imposed ユoad torque is dttrect―
ly lneasured or indirectユ y estinated, This ntv torque regulator ■s required torespond very rapェ dユ y, sO とhe contro■ sisiaユ Cf the torque regulator ought tO

i3rtte岳 :暑品inを 3°g予

紺byPass the speed resulator.

As it isfor thetorque resulation tO rHoasure the 10ad
torque direcと 二y by the torquetteter,
the indirecと 口ことhod とO estimate theload torque shOu■a be adcPted.
This estimattton is made by the ob…

not econoEl■ Cal and practicaユserver as fol■ owo.
DC motor is a dynamical systβ mgoTerned by the following state equa―ttton,Fig.■ S impユ 主fied P■ ant modcユ
能I =Ax +B eaキy=cx

００１C１,と一﹁︱ ︱ ︱ ｌ ｄ１﹁︱ ︱ ︱ ︱ ヨ一Ｊ

１ 一Ｊ, E=０ｅ

B=Ｆ Ｉ

Ｒｌ門とｏ︺

Ｒ 一
Ｌ

6:告::ュ :]T:::::i号

ｒｒ ｌ ｌ ﹂, A

判唱……‐(2)

虫虫﹁引 ︱ ︱ 瑚xＴ一
ωＦＩ ＩＩ ＩＬ

whereof dc ttotor

E T load … '(・ )the dC motる r, Tload is COnsi古 :告 ed t。
by the zero― observer without steady:も :を :::::書 ::;:::::患

告::t°gned as f01lows,t[b工 a+ t c ―d ( s + a ) 〕ωr ]Us ing (4), the load torque ■s estinated as follows,Tュ。ad =台.。 adttTュ 。
ad―

(4)

―(5)

Therefore the 10ad torque ca■ be estimatad thrOugh the firsと order ユago T is
the tine constant and lllay be chosen as an arbitrary positive constant. The pa一
rameters a,b,c and d aFe determined uniquely by the estimation time constantてand ttotor paraIEeterS as follows,ｄＣ

一てＪ 一ＴｅこＪ 一ＴＫｂ≡

ュ 一Ｔａ一1210(6)It is recommended to s● ユect time constant て in re■ ation to tlle po■ es ofthe total systemo ln this PaPer, ィ 主s enough slnal■ to estimate the loaa tOrqueas conPared With the system time constant. The tota■ schematic b■ ock diagranThis points out that the Str,c―of the =mp■ emented observer is shown in Fig.2。
ture of this type of the observer is quite simp■ e for realization。

コ「ドＬＩT胡̲二 ̲̲̲̲Observar一 JFig。 2 Schematic structure of■oadtorque Observer

3, SPEED REGULAT10N・ BASED ON｀ OPTIMAL CONTROL TIIEORY

rn Order tO suppress the 士田paCt arOP, it is effectttve to use the addition―
which bypasses the sPaed regulator. The ■oad とortte is
unknown inPut, and also ュs treated as the obsdrvab■ e etate variab■ e in the dc
motor system, When the sPeed referellce and/o■ ■oad とo■ que are app主 主ea to thedc ttotor, equi■ ttbriun point of the state is changed atcording to the falue ofthe ■oad とorquP, The transient system perforlnancQ tts therefore represented asthe ■ocェ of the a■ ■ state variables frOn the initia■ state to the new eqllェ lib―
rium point, Thゃ se 10Ci are main■ y determined through the performarlce of thespeed regulator.
As the speed regulator can be independent fro輸 the tOrque regulator basca
on the observer, onユ y the coFltrOl po■ es, which govern the transient performance, are taken ェnto account in the design of the speed regulator. Des■ rablepo■ es are determined from the point of the total trade― off between the control
energy and thc system performance.
Moleover it is required that all COntrol―lab■ e state valttables settle down at the equi■ ibrium point in steady state.
Or.
For that purpose, the speed regu■ ator shouユ d have one ser■ es integr各 モThis integrator a■ so gives とhe better effect to the torque regulator because
the systeEl beCOmes iess sens■ tive to the parameter warュ ations. These requ■ re―田entS are reflected in the quadratic Performance index. This cOst funCtion isconstructed on the modified system, where one integrator is added as foユ ■OWS,3ユとOrque reg・dlator,

毒ｔ
一ｄ一Ｉｄ

五王 ■ 言v tt ETュ。ady=cI(7)

一(3)

―(9)

﹁００, B距︱工とX,C=E100ヨ１ｅ

Ｆ Ｉ Ｉ Ｉ Ｌω﹁ ｌｒ封 ■ どｒｉｌｌｌＬ

whEre―1211

Ke
R0ｄｅ
●
ユ二ｈｔPig,3 shows the block diagr 角rn Of― く9)

一L

二一

一Ａ

Ｅ一」

sys tFTn.

Fig.3 B■ 。ck dご agram of modifittd gystem

The quadratic PeFfOImance index is maこ と こc have suitable weightiIBg matrix
in which the sPecified variabユ es have strong ■reight. ・ The system may be de―Signed tO have =apid rise time ofコ Otor speed du字 とo the もpeed refarence chan―Virls
the fo■ lowing quaaratic:r暑 ::砲 ]l::k二:景si3,こ dihC inpact drop. So五旨岳E ―1子V) at中中,(10)︐０―ｆ︒

ｄａｈＴ・

７ｒ ｂｄｎ統的﹁︱︱出 ｔ０車

Ｑ(ユ エ)

Paralneters c and P wi■ ユ fix the control performance oftrhe sOlution to minim■ 2e Σ iS realized in the following・ｅ ｆｐＳ ｅｔｅ ａｈ ｔｔ一 Ｓvュ =TQ x +vT P

０ ０ ０ ｅ輸ねｆ
Ｏぱ ｏ ｓｕ縄Ｓ

ユｒｌ ｌ ｌ ﹂ ｅｄ ｃｅhere( 王を置―Kュ ω
2・ar
告K3 1 : tω . … ωrref )dとをと
itiC置 岳
:81:岳 n,feiliefe暑::岳Ciュ

8予 inS'【1' K2 and中中‐(12)K3 are conducted from the R主 一

Eq.(12) shOws that the speed regulaと or has one ser■ es ュntegfator as shownin Fig。 4.

1212

．
Ｆ ︲ヰ

確Ｆ― 十一 一キ ― ―￢1

￨1

￨

1一』

こαarrlatture
CuFrelRi senso伊凹↑

SDeedsensor
Pig,4 Schβ ttatic bユ ock こ工曇gram of speed regulator
based on state =ecdback
4. DESICN OF TORQUエ ー SPEE,i̲RFCULATo玉The ■oad torque functions as the ュn■ とia■ deviation from the equュ librュ unpo■ nt in thQ state sPace・
The とoど que reguユ aと or ■■とends to reduce this in■ tial
deviation so as to

主田prOVethe transient perforDanCe.

If the arIBature currentュs determュ ned

instantaneously, the cstimated ユoad torque csn compttnsate thecurrent in a molaent and the initia■ devttatiOn lllay be reduced sma■ ユ, So.it iseffective that the v。 ■tage co4Haland which drives the armature current corre―
sponding 、vith tlle estimated 10ad torqtle is added to the output vo■ tage commandof the sPecd re3u■ ator. This foと .uer vo■ tage colnmand 工s the output of the とor―que regulator.
This final voltaga col141land is represented as the suII1 0f both conIEands.

The additiOn of the torquc regulator gives no infユ uence on the response froIR
the speed reference to the actual speed if parameters are correcと ユy ad5ustQd
in the observer, The proPosed torqueゃ sPeed regulator is shown in Fttg.5,

op十 imct

speed ドQgutattor「:鉢 騰rFig.5 Torque一 sPeed regu■ ator bascd on ユoadtorque estimation method1213

Po■ es of thcr totai systern are determined siIIIPly only by the connectionsof the poles of contro■ led Plant and the po■ es of the cbserver, As the po■ esof the Observer ara dete■ Hlined arbitrarily and sufficient■ y distant, these ef―
fects are generaユ ly ttgnored.
In this time, the speed resPonse to the step load torque input is nearly
proPortiona■ to the second order differentiat工 on Of ωω
step(t)' Wheresと ep(t)is the sPeed response to tha step change of the speed reference. These charac―
teristttcs conduct the desien procedure using quadratic Performこ nce ttndex tA7hich
deter出 主nes the pole alユ ocation・ The weighting factor P nearly deteふ 四主nee thetrackttng perfo二 理ance to the sPeed reference and the other factor a nearly de―termines tile recovery tine of the impact droP, The desired po■ e assユ gnaent
コay bα arransed throush the coコ pro□ ise of these two fこ ctors. The poユ e ■oこ i by
P and α are shOwn in Fig,6.

Ittagincry

Inlこ gina,y(a)Pole 10ci to the change of PaxiS(b)POle loci tO the change of o■oc主 ■n relation to theweighting factor P and αFttg.6 Pcle

In actual scene, the Parameters can nOt be ■dentified correctユ y or will
be varied s■ owly with time.. The observer generates the offset according totllese paralneter variations｀ . But the series integFatOr in the speed regu■ ator
｀negates these steady state er■ ors. AccOrdillgly this type of ttDrque― speed re―gulator has no sensitivity of the steady state errOr.

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5. NUMERICAL AND EXPttRIMENTAL EXAMPLES
The proPOSed torquetspeed regu■ ator ュn Fig。 5 ■s ilrlp■ eIIlented and carr■ edout as sholfn ■ュ Fig.フ . The tFansュ るtorェ zed chopper is applied in this pOwer
converteI. The noコ inal Parameters of dc motor are shown in Tab■ e.■ . trhe es―
timation tine conatani T is deteと 」Ained as l田 SeC. The Elinimun time constantof tota■ system is aUout ten tines as large as T.

,o「 quein〔rttgutaloF

iuding obSeNar

W「Fig.7 Schematic diagram of tested systom
nuttber of poles

2■500

ratQd sPeed
L

44.3 1nH

J3.38 X 10 2
N・ m・ sec2/rad2
0:ユ X 10 5CP)
Tab le.ユ

0.75 1W

rated armaturQ current
RKe

7.5 ▲
2.25 Ω(α )O.58ユvesec/rad
ユ38Nomina■ paraIIleters and weighting factorsof tested dc moと or rdrive system

ig.8 shows the response of the rotor speeS to the singユ e and muユ tiple

岳岳とをモ
告忌 告「rpm

rated output::こ ini告:岳 :を :暑 :::告::l:モ I告岳号
どa:景;岳i::古 :告 ::者 : ::g〔 ::ibi骨::f i言:::岳 ::::告rotor speed can be reduced because of the torque regulator. The obServer also
wclユ esと imates the ユoad torque as shown in this figure. These resu■ t.s show
the au3mented torque― speed regulatOr is quite effective for the ttmPact dlop

1215

:ユ

and the welユ Speed I'egulaと ion,土Ｔ

6 rpm■20%辛■20%キ5A的牝 。ad■ 。ad↓I↑0.ア う sec

引0.3 卜Jトsec

0,75 secsecωr■ 。adi亀 。adIa￨(a)with oniy speed resulator
e・V2=° )(1・(b)with prOPosed torque― speedrettulator

Fig.8 Numer■ cal and experimentaユ examples of the response of
the roこ or speed to the sing■ e and IBultiple step loadtorque( up : measured , down : calculated )

1216

ｒｔ

ギ 0.3a6. CONCLuS10N
The proposed torque― speed reguユ ator is based on the modern conこ ro■ theory.
The design is diffせ .ent from とhe conventio■ al PI contro■ ler design. The speed
regulator based on the state Feedback with One integratOr and the torque regu―■ator based on the observer corlstitute the concluded total torque―
speed resu―
lator. The parameter seIIsitttvity ttn the steady state ユo zero because of theser■ es integrator of this spee4 reg準 ユaEOr,Tha total f̲ontro■ syst専 理 is・ s宝コple and it3 deSign is easy, whan it isbased on the stitab■ e PerloAttanCe ■nQox.
Nuコ ericaユ and experimentaユ resuユ ts show the vaユ エdity of this tyPe of theregulatOr. .

NOMENCLATURE
L : arIEature inductance貿rR : armature res■ sと ance

Kenr i COunter ●lectromotive force
ヽ」 : とoこ al inertia
ユ°ad torqueT■
oad :I a : armature current
ea : armature vOltage
lf : field current
的t° r speedrr°s : Laplace operator

REFERENCES

ef : rotor speed reference
oad : estimated ユoad torqueT : estimation time constant】 : quadratic Performance ■adex
P, α : weighting factor ■n the par―formallce ュndex°ことput signa■ of speed re宮 とユator
VユTユ:
V2 : :岩:put Signal of torque resula―
V3 : V° ltage ,ommand,(1) D.G.Luenberger, t'OBserving the state of a ■inear system,'l IEEEl・ Trans.
Miユ 。 Electron., vo■ .M工 L… 8, pp.フ 4‑80, Apr, 1964
(2) p.c,Luenberger,

1'observers fOr multivariable systems,いmaと 。 con tr., vol.AC― ■1, pp.190ャ ユ97, APrt ■966

IEEE Trans. Auto―(3) A.E.Bryson,Jr., and D,C.Luenberger, ・Ⅲ
The synthesis cf regulator ユogic
using state― variable concepts,・ ' PrOC. IEEE, vol,58, pp.■ 803… 1811, Ǹov,■970(4)B.ゃ 。Pinath, "On the control of linear muユ tiple inputtoutput systems,'1
Bell Syst. Tech. J., Mar. 197■

(5)D.C.Luenberger, 17An introduction tO observers,''
Contr., v。 1.AC‑16, NO.6, Dec. 197ユ

1217

IEEE Trans. Automat.

(6) 」.S.Meditch and G.H.Hostetter,accessible inputs,8,"Observers for systems with uiknowi atd in―
INT. J. COntrol, vol.■ 9, NO。 3, 473‑480. ■974・(7)T,Takeda and T.ritamori,tittal Jゼ racking sytttenSず t(8】ⅢA d● 6主d荷 ●t dd of ■illこ aを P.uユ ti― inPut― output 6p―

をSICE Trais.
v。 1114: N014b Aじ g。 1978 Ⅲ点.chiShi,【 .Ohnishi, aid K.Miyachi, 'tThe torquo ■ogulatbr using the obる こ■―
ver of dc motor,1' Report of IEE of Japa古 , RM382‑33, Flb. 1982!

1218