TORQUE ― SPEED RIIGULAT10N OF DC MOTOR BASED ON LOAD TORQUE ESTIMAT10N IIETHOD Kiyoshi oHIS減 正, Kouhei OIINISHI and Keio University Kolhoku一 ktl, Yokollama, 223, Kullio MIYACHI Japall ―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 the speed reる ulatOr is POssible and the ■回prrpved speed rtsT)onse, such as the quick Ol■ tPじ t tOrque resPonse and sIBall fldctuation Of the IBotor sPeed「 wilユ becG□ e reali 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 moto_W 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 the drttve appユ ications, Moreover the design procedure is せisu al■ y simplifioa in can 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he separ 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 modern control thcory. Besides various rQquiruHents to the system performance can be taken ill the regulattOr design in the IBodren control thQory. This paper‐ proposes the unified legulatOr design prOcedure based on the CPt■ Inal contro■ theory, 主よ which the speed response to both the lo々 d torque and the spe● d reference can be sPecified irldependently. For this purpose, the suュ table quadratic perfo.肥 ance il■ dex ■s defined. As the result, concユ uded regulator based on this cost ゴunction can るe c■ assifよ ed into two subreguユ a_ tols. 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 Steady state offset. Thiも type of controユ ユer is exPected to Le ユess sensitive to thQ 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 the observer 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, eas主 ユy !■ lPEO― Tokyo'83 1209 / 2. LOAD T01QUE ESTIMAT10N The ■mpact I of the load torque to the dc moと or may g■ ve rュ se to the tcarmpo― g予 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:te speed 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 to respond 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° 紺 byPass the speed resulator. As it is for the torque resulation tO rHoasure the 10ad torque direcと 二y by the torquetteter, the indirecと 口ことhod とO estimate the load 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 m goTerned by the following state equa― ttton, Fig.■ S impユ 主fied P■ ant modcユ 能 I =Ax +B eaキ y=cx と ０ １ C １ ０ , 一 ﹁︱ ︱ ︱ ｌ ｄ １ １ 一Ｊ 一 Ｊ ﹁︱ ︱ ︱ ︱ ヨ , E= ０ B= Ｆ Ｉ ｅ ｌ 門と ｏ ︺ Ｒ 一 Ｌ Ｒ 6:告 ::ュ :]T:::::i号 ｒｒ ｌ ｌ ﹂ , A 判唱 ……‐(2) 虫 虫 ﹁引 ︱ ︱ 瑚 x Ｔ一 ω ＦＩ ＩＩ ＩＬ where of 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 .。 ad = ttT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, 〓 ｄ 〓 Ｃ 一 て Ｊ 一Ｔ ｅ こ Ｊ 一Ｔ Ｋ ｂ ≡ ュ 一Ｔ ａ 一 1210 (6) It is recommended to s● ユect time constant て in re■ ation to tlle po■ es of the total systemo ln this PaPer, ィ 主s enough slnal■ to estimate the loaa tOrque as conPared With the system time constant. The tota■ schematic b■ ock diagran This 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 Ｌ Ｉ T胡 Fig。 _二 ____Observar一 J 2 Schematic structure of ■oad torque 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 the dc ttotor, equi■ ttbriun point of the state is changed atcording to the falue of the ■oad とorquP, The transient system perforlnancQ tts therefore represented as the ■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 the speed 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■ rable po■ 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 is constructed on the modified system, where one integrator is added as foユ ■OWS, 3ユ とOrque reg・dlator, 毒 ｔ 一 ｄ 一Ｉ ｄ 五王 ■ 言v tt ETュ 。ad y=cI 一 (3) ― (9) ︱ ０ ０ １ (7) ﹁ , B距 Ｆ Ｉ Ｉ Ｉ Ｌ ω 工 ｅ ﹁ ｌｒ封 ■ ど と X ｒｉｌｌｌＬ whEre ― ,C=E100ヨ 1211 “ Ke R 0 ｄ ｅ ● ユ Pig,3 shows the block diagr 角rn Of ― く9) ” 一 L 二 二一 ｈ ｔ 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) ， ― (ユ エ) ｆ ・ ７ ｒ ｂ ｄ 。 ｄ ａ ｔ ｎ統的 ﹁︱︱出 ０ Paralneters c and P wi■ ユ fix the control performance of trhe sOlution to minim■ 2e Σ iS realized in the following ・ = ０ ｅ ｆ ｈ 車 Ｔ ｐ Ｓ ｅ ｔ Ｑ ｅ ａ ｈ ｔ ｔ一 Ｓ vュ TQ x +vT P ０ ０ ０ ｅ 輸ねｆ Ｏぱ ｏ ｓ ｕ縄 Ｓ ユ ｒｌ ｌ ｌ ﹂ ｅｄ ｃ ｅ here ( 王 を 置 ―Kュ ω 2・a r 告 K3 1 : tω . を と itiC置 岳 :81:岳 n,feiliefe暑::岳 …ω rref )dと 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 shown in Fig。 4. 1212 ． Ｆ ︲ヰ 確Ｆ ― 十 一 一 キ ― ―￢ 1 ￨ 1 ￨ 1 一』 こα arrlatture CuFrelRi senso伊 凹↑ SDeed sensor Pig,4 Schβ ttatic bユ ock こ工曇gram of speed regulator based on state =ecdback 4. DESICN OF TORQUエ po■ nt ー SPEE,i_RFCULATo玉 The ■oad torque functions as the ュn■ とia■ deviation from the equュ librュ un 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prOVe the transient perforDanCe. If the arIBature current determュ ned instantaneously, the cstimated ユoad torque csn compttnsate the current in a molaent and the initia■ devttatiOn lllay be reduced sma■ ユ, So.it is ュs effective that the v。 ■tage co4Haland which drives the armature current corre― sponding 、vith tlle estimated 10ad torqtle is added to the output vo■ tage command of 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 r Fig.5 Torque一 sPeed regu■ ator bascd on torque estimation method 1213 ユoad Po■ es of thcr totai systern are determined siIIIPly only by the connections of the poles of contro■ led Plant and the po■ es of the cbserver, As the po■ es of 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 ω ω step(t)' Where s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 the trackttng 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 (a)Pole 10ci to the change of P gina,y axiS (b)POle loci tO the change of o ■oc主 ■n relation to the weighting factor P and α Fttg.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 to tllese 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. 1214 5. NUMERICAL AND EXPttRIMENTAL EXAMPLES The proPOSed torquetspeed regu■ ator ュn Fig。 5 ■s ilrlp■ eIIlented and carr■ ed out 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 constant of tota■ system is aUout ten tines as large as T. ,o「 in〔 que rttgutaloF iuding obSeNar W「 Fig.7 Schematic diagram of tested systom nuttber of poles 2 ■500 ratQd sPeed L 44.3 1nH J 3.38 X 10 2 N・ m・ sec2/rad2 0:ユ X 10 5 CP) Tab le.ユ 0.75 1W rated armaturQ current R Ke 7.5 ▲ 2.25 Ω (α ) O.58ユ vesec/rad ユ38 Nomina■ paraIIleters and weighting factors of 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 sec sec ω r ■ 。ad i 亀 。ad I a ￨ (a)with oniy speed resulator e・ V2=° ) (1・ (b)with prOPosed torque― speed rettulator Fig.8 Numer■ cal and experimentaユ examples of the response of the roこ or speed to the sing■ e and IBultiple step load torque ( up : measured , down : calculated ) 1216 ｒ ｔ ギ 0.3 a 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 the ser■ es integrator of this spee4 reg準 ユ aEOr, Tha total f_ontro■ syst専 理 is・ s宝コple and it3 deSign is easy, whan it is based 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 the regulatOr. . NOMENCLATURE L : arIEature inductance 貿r R : armature res■ sと ance Kenr i COunter ●lectromotive force ヽ 」 : とoこ al inertia ユ°ad torque T■ oad : I a : armature current ea : armature vOltage lf : field current 的 t° r speed r r° s : Laplace operator REFERENCES ef : rotor speed reference oad : estimated ユoad torque T : 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 pp.190ャ ユ97, APrt ■966 maと 。 con tr., vol.AC― ■1, 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, N`ov, ■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 (8】 Jゼ racking sytttenSず t Ⅲ A d● 6主 d荷 ●t“ dd of ■illこ aを P.uユ ti― inPut― output Ⅲ を SICE Trais. v。 1114: N014b Aじ g。 6p― 1978 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
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