and for the mechanical part of the system the torque equation is described as follows: 1 Js

Transcription

1 A dgn of th DC otor control crcut Abtract: Th ha conaton thod ald n th control yt dgn, th d of DC otor controlld by ung th fdback of both aratur currnt and tachotr voltag.. Modlng a DC otor Th ybol ud n th odlng dfnd a follow: L : aratur nductanc [H] a : aratur rtanc [Ω] : aratur currnt [A] : ald aratur voltag [V ] : back lctrootv forc contant [ c/ rad] V : torqu contant[ N / A ] J : rotor ontu of nrta[ kg ] ω : rotor d [rad / c] J : load ontu of nrta[ kg ] l f : dturbanc torqu [N]. B : vcou frcton coffcnt [ N / rad / c] l In th ca th lctrcal quaton gvn a d L + a ω (.) dt and for th chancal art of th yt th torqu quaton dcrbd a follow: dω ( J + J l ) + Blω f. (.) dt It oftn obl to nglct th on th dgn of a DC otor control yt, bcau th ffct of both th nductanc L of Eq. (.) and th vcou torqu B l ω of Eq. (.) vry lght. Th followng block dagra for th dgn of a DC otor control yt can b obtand. f J ω Fg. Th block dagra for th dgn of a DC otor control yt. Th tranfr functon to th otor d ω fro th ald aratur voltag n Fg. dcrbd a ω( ),(.) ( ) + T whr th t contant T T and th gan ar th followng forulaton: ( J + Jl ) a. (.4)

2 . Torqu control by an of aratur currnt fdback In ca of dtcton of th larg currnt, a ddy currnt nor oftn ud. It dtctd by nrtng th all rtanc n th aratur crcut, bcau th otor currnt not o larg n th yt. Hr, lt u u th ybol whn a th currnt rfrnc valu. Thn, G th tranfr functon of th currnt alfr. Morovr, th fdback rato of th otor currnt, th block dagra of th torqu control yt hown by th followng Fg.. G 0 f J ω Fg. Th block dagra of th torqu control yt.. Th contructon of th currnt alfr Th two tycal currnt alfr hown by th followng tranfr functon ar condrd: A) Alfr of th frt ordr dlay ty: G (.) + T B) Alfr of th ntgral ty: (+ T) G (.). Th ca of ung alfr of th frt ordr dlay ty Th tranfr functon to th otor d ω fro th currnt rfrnc valu ω( ) ( ) JT + ( J+ J whr J and ar gvn by th followng rlaton: + T ) + n Fg. dcrbd a, (.) J J + J l, a +. (.4) In addton, th block dagra of th torqu control yt n th condton that th rotor wa lockd hown by Fg.. + T f Fg. Th block dagra of th torqu control yt n th condton that th rotor wa lockd ( n th ca of ung alfr of th frt ordr dlay ty ).

3 Th tranfr functon to th aratur crcut currnt fro th currnt rfrnc valu ( ) ( ) + + T n Fg. dcrbd a,(.5) thn th tady tat aratur currnt gvn a. (.) +. Th ca of ung alfr of ntgral ty Th tranfr functon to th otor d ω fro th currnt rfrnc valu ω ( ) ( ) [( J + J (+ T) T ) + ( J + )] n Fg. dcrbd a ( + T), (.7) + T whr and T ar gvn a J T,T ( + ). (.8) J + J + At th t, f th dgnr lct th rlaton T T, thn th otor d ha th charactrtc of an ntgral lnt to th rfrnc valu. In addton, th block dagra of th torqu control yt n th condton that th rotor wa lockd hown by Fg. 4. T ( + ) f Fg. 4 Th block dagra of th torqu control yt n th condton that th rotor wa lockd Th tranfr functon to th aratur crcut currnt fro th currnt rfrnc valu n Fg. 4 dcrbd a ( ) (+ T), (.9) ( ) + ( T + ) thn th tady tat aratur currnt gvn a. (.0). Sd control by an of tacho-gnrator voltag fdback In ca of dtcton of th otor d, a tacho-gnrator vry oftn ud. On th othr hand, th otcal ncodr gnrally ud whn th oton control yt dgnd. Hr, lt u u th tacho-gnrator a th d nor. Thn, G v th tranfr functon of th d alfr. Morovr ω and S v ar th d rfrnc valu and th tacho-gnrator contant, rctvly. Th block dagra of th d control yt that th tacho-gnrator voltag fdbackd at th outr loo of th currnt fdback loo hown by th followng Fg. 5.

4 ω G v G 0 f J ω S v Fg. 5 Th block dagra of th d control yt. Th tranfr functon of a d alfr dgnd rctvly a th dffrnt for by an of thr th frt ordr dlay ty or th ntgral ty a th currnt alfr. In vry ca, th lag conator dgnd n ordr to ncra th gan argn n th low frquncy rang 4. Outln of otor controllr 4. Major contant of DC otor Th contant ud n th dgn of a otor controllr ar hown n th followng tabl. 4. Powr alfr of otor drvr Th owr alfr crcut of th otor drvr that contructd by cacadng of two owr oratonal alfr hown by Fg.. Tabl Th dgn contant (DC otor TYPE SS40E-E SAWAMUA DENI CO.LTD) Torqu contant [ N A] Back lctrootv forc contant 7. 0 [ V c rad ] Aratur rtanc a 4.[ Ω] otor ontu of nrta J [ kg ] Convron contant ω to v ω.8 0 [ V rad c] Powr alfr gan tanc for currnt dtcton 0.[ Ω] S v Convron xal of hycal unt Th ca of torqu contant gvn by otor cfcaton 0.7[ kgf c A] [ N A] : Th ca of back lctrootv forc contant gvn by otor cfcaton 7.5[ V r] : [ V c rad] π 000 Th ca of convron contant ω to gvn by F/V convrtr cfcaton 0[ Volt ] r00[ khz] : Pf 4 S v.8 0 [ V / rad/c], P 000[ ul/ rv], f 0 π 4

5 50kΩ 0.µF 0.µF +5V 0 50kΩ kω LM75 Ω Ω TG 0.µF 5 V M +5V 5V 50 k Ω 0.µF +5V 0.Ω INA 05 b 50kΩ kω LM75 ntruntatonal alfr 0.µF Ω Ω 5V 0.µF Fg. Powr alfr crcut by ung two owr oratonal alfr LM75 5

6 5. Dgn rocdur of controllr 5. Dgnng th currnt alfr of th frt ordr dlay ty Th outut voltag of th ntruntaton alfr(in05p) n th owr alfr crcut ( Fg.) ud a th currnt fdback gnal n torqu control. Th dgn cfcaton of th ty a follow:. Stady currnt to th currnt rfrnc valu 0. [volt] about 0.0 to 0.5[A].. Gan of currnt alfr cfd by th rang of 0 to 0 on th ca of th on ch ount.. T contant T lctd a about 0.00 to 0.0 n ordr to ov u th rng t of aratur currnt. Hr, th tady currnt to th currnt rfrnc valu 0. [volt] chon a 0.0[A] n condraton of th dgn cfcaton. Th dgn xal of ung both 0 and T dcrbd blow. Whn th contant ar ubttutd to Eq. (.), th fdback rato followng rlaton: obtand a. 5 by olvng th. (5.) Thrfor, th currnt alfr of th frt ordr dlay ty gvn by th followng tranfr functon: 0 G. (5.) Th crcut xal lntd by an of th oratonal alfr ar hown by Fg 7 and µF 50kΩ 0.00µF MΩ ω kω 5.5kΩ 5.kΩ kω 5 5 b 5.5kΩ 5 5kΩ 5 5kΩ 5kΩ 5kΩ o 5.kΩ 5V 5V Fg. 7 Th currnt alfr of frt ordr dlay ty. Fg. 8 Th currnt alfr of frt ordr dlay ty.

7 At th t, th cond ordr tr concrnng Lalac orator nglgbl, bcau th tr uffcntly all than th frt ordr tr. Thrfor, th tranfr functon to th otor d fro th currnt rfrnc valu can b lfd a ωv ( ) Sv Go ( ) JT + ( J + J + T ) + whr o and T ar gvn a r o, (5.) + T r Sv,T r J + J + T. (5.4) Furthror, th tranfr functon odl for th dgn drvd undr th otal load J. 5J, bcau thr ar fw ca a otor drvn wth a no-load. Whn ach contant dfnd bfor ubttutd to Eq. (5.4), th tranfr functon drvd by th followng quaton: o.7, (5.5) ( ) T r 0.5. (5.) Dgn of th d alfr Th outut voltag of th tacho-gnrator n th owr alfr crcut ( Fg.) ud a th fdback gnal n th d control. Th dgn cfcaton of th d alfr a follow:. Th d alfr nvolvd th ntgral charactrtc chon n ordr to rjct a tatonary dturbanc and t gvn by th followng tranfr functon : T T G (+ r ) + v. (5.7) + T. Th gan-croovr angular frquncy ω of th loo tranfr functon n th d control yt cfd by th rang 00 to 50.. Th ha argn θ of a d control yt lctd a about 0 to 5 dgr. At th t, th total gan 0 chon a 40 n ordr to t th gan-croovr angular frquncy ω. Du to 0. 7 n Eq. (5.5), th gan of th d alfr yld Whn th conator to fll th ha argn θ of 0 dgr drvd by ung th ha conaton thod, th gan-croovr angular frquncy ω yld 8 [rad/c] and th d alfr G v gvn by th followng tranfr functon: G 8.99( + 0.5) + / 40 v. /80 (5.8) 5. Dgnng th currnt alfr of th ntgral ty Th dgn cfcaton of th ty a follow:. Stady currnt to th currnt rfrnc valu 0. [volt] about 0.5[A].. Gan of currnt alfr cfd by th rang of 0 to 0 on th ca of th on ch ount.. T contant T lctd a T T o that th tranfr functon of to ω o th aroxat ntgral charactrtc. 7

8 µf 5kΩ 0kΩ ω 0kΩ 0kΩ 5 0kΩ 0kΩ 87kΩ 0.0µ F kΩ 00kΩ.kΩ Fg. 9 Th d alfr (n th ca of th currnt alfr of frt ordr dlay ty). 5. Dgnng th currnt alfr of th ntgral ty Th dgn cfcaton of th ty a follow:. Stady currnt to th currnt rfrnc valu 0. [volt] about 0.5[A].. Gan of currnt alfr cfd by th rang of 0 to 0 on th ca of th on ch ount. T contant T lctd a T T o that th tranfr functon of to ω o th aroxat ntgral charactrtc. Hr, th tady currnt to th currnt rfrnc valu 0. [volt] chon a 0.5[A] n condraton of th dgn cfcaton. Th dgn xal of ung 0 dcrbd blow. Whn th contant ar ubttutd to Eq. (.0), th fdback rato obtand a. 0 by olvng th followng rlaton: (5.9) 0. At th t, th tranfr functon G o to th otor d fro th currnt rfrnc valu can b gvn by a follow: G o ωv ( ) ( ) [( J+ J ( + T) S T ) + ( J 8 v + )] 0 (+ T) + T, (5.0) whr 0 and T ar gvn a Sv J( + T ) 0,T J + J +. (5.) Furthror, th tranfr functon odl for th dgn drvd undr th vald load J. 5J larly to th dgn aratr of cton 5.. Whn ach contant dfnd bfor ubttutd to 0 of Eq. (5.), 0 obtand by th followng quaton: In addton, o.8, (5.) T of Eq. (5.) drvd a T by olvng th followng rlaton: ( T 4 ) T. (5.)

9 Thrfor, whn T dcdd a by th dgn cfcaton, th currnt alfr ty gvn by th followng tranfr functon: 0 ( ) G (5.4) Th crcut xal lntd by an of th oratonal alfr ar hown by Fg. 0. At th t, th tranfr functon to G o th otor d fro th currnt rfrnc valu lfd a th followng dgn odl: G v ( ).8 o ω (5.5) ( ) 5.4 Dgn of th d alfr Th dgn cfcaton of th d alfr a follow: G of th ntgral can b. A d alfr gvn by th followng charactrtc n ordr to aly th ha conaton thod : ( + T ). (5.) + T G v. Th gan-croovr angular frquncy ω of th loo tranfr functon n th d control yt cfd by th rang 00 to 50.. Th ha argn θ of a d control yt lctd a about 0 to 5 dgr. At th t, th total gan 0 chon a 00 n ordr to t th gan-croovr angular frquncy ω. Du to 0. 8 n Eq. (5.5), th gan of th d alfr yld Whn th conator to fll th ha argn θ of 0 dgr drvd by ung th ha conaton thod, th gan-croovr angular frquncy ω yld 0 [rad/c] and th d alfr G v gvn by th followng tranfr functon: 8.55( + /90) G v. + /.5 (5.8) Th crcut xal concrnng th d alfr lntd by an of OP.alfr ar hown by Fg.. 58kΩ b 8kΩ 8kΩ 0.47µF 08kΩ 5 8kΩ o ω 8kΩ 8kΩ kω 7kΩ 0.0µ F 5 5kΩ.9kΩ.9kΩ 5V Fg. 0 Th currnt alfr of ntgral ty. Fg. Th d alfr (n th ca of th currnt alfr of ntgral ty). 9