Control Systems. Modelling Physical Systems. Assoc.Prof. Haluk Görgün. Gears DC Motors. Lecture #5. Control Systems. 10 March 2013

Transcription

1 Lcur #5 Conrol Sy Modlling Phyicl Sy Gr DC Moor Aoc.Prof. Hluk Görgün 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün

2 rnfr Funcion for Sy wih Gr Gr provid chnicl dvng o roionl y. Anyon who h riddn 0-pd bicycl know h ffc of gring. Going uphill, you hif o provid or orqu nd l pd. On h righwy, you hif o obin or pd nd l orqu. hu, gr llow you o ch h driv y nd h lod rd-off bwn pd nd orqu. For ny pplicion, gr xhibi bcklh, which occur bcu of h loo fi bwn wo hd gr. h driv gr ro hrough ll ngl bfor king conc wih h hd gr. h rul i h h ngulr roion of h oupu gr do no occur unil ll ngulr roion of h inpu gr h occurrd. 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün

3 h dinc rvld long ch gr circufrnc i h. hu: r θ r θ Or, r inc h rio of h nubr of h long h circufrnc i in h proporion h rio of h rdii W conclud h h rio of h ngulr diplcn of h gr i invrly proporionl o h rio of h nubr of h. 0 Mrch 03 Conrol Sy 3 θ θ Wh i h rlionhip bwn h inpu orqu? If w u h gr r lol, h i hy do no borb or or nrgy, h nrgy ino Gr qul h nrgy ou of Gr Sinc h rnlionl nrgy of forc i diplcn bco h roionl nrgy of orqu i ngulr diplcn, θ θ r

4 θ θ L u wh hppn o chnicl ipdnc h r drivn by gr. n quivln y θ wihou h gr: 0 Mrch 03 Conrol Sy 4 Aoc. Prof. Hluk Görgün

5 0 Mrch 03 5 fro which w wri h quion of oion : D θ ow convr θ ino n quivln θ : D θ Afr iplificion: D θ Conrol Sy Aoc. Prof. Hluk Görgün

6 oionl chnicl ipdnc cn b rflcd hrough gr rin by uliplying h chnicl ipdnc by h rio A rducion in rnforr 0 Mrch 03 Conrol Sy 6 Aoc. Prof. Hluk Görgün

7 Expl: Find h rnfr funcion, θ / for h y of Figur bov? I y b ping hi poin o rch for wo iulnou quion corrponding o ch inri. h inri, howvr, do no undrgo linrly indpndn oion, inc hy r id oghr by h gr. hu, hr i only on dgr of frdo nd hnc on quion of oion. 0 Mrch 03 Conrol Sy 7 Aoc. Prof. Hluk Görgün

8 0 Mrch 03 8 L u fir rflc h ipdnc nd D nd orqu on h inpu hf o h oupu hown in Figur D θ D G θ Conrol Sy Aoc. Prof. Hluk Görgün

9 In ordr o liin gr wih lrg rdii, gr rin i ud o ipln lrg gr rio by ccding llr gr rio: 0 Mrch 03 Conrol Sy 9 Aoc. Prof. Hluk Görgün

10 Expl: Find h rnfr funcion, θ /, for h y of Figur 0 Mrch 03 Conrol Sy 0 Aoc. Prof. Hluk Görgün

11 hi y, which u gr rin, do no hv lol gr. All of h gr hv inri, nd for o hf hr i vicou fricion o olv h probl, w wn o rflc ll of h ipdnc o h inpu hf, θ. h gr rio i no h for ll ipdnc. For xpl, D i rflcd only hrough on gr rio D /, whr 4 plu 5 i rflcd hrough wo gr rio /. fro which h quion of oion i: D θ 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün

12 G θ D θ D 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün

13 0 Mrch 03 Ooik onrol Doç.Dr. Hluk Görgün 3

14 Elcrochnicl Sy rnfr Funcion W ov o y h r hybrid of lcricl nd chnicl vribl, h lcrochnicl y ASA fligh iulor robo r wih lcrochnicl conrol y coponn. 0 Mrch 03 Conrol Sy 4 Aoc. Prof. Hluk Görgün

15 Ohr pplicion for y wih lcrochnicl coponn r robo conrol, un nd r rckr, nd copur p nd dik-driv poiion conrol. A oor i n lcrochnicl coponn h yild diplcn oupu for volg inpu, h i, chnicl oupu gnrd by n lcricl inpu. W will driv h rnfr funcion for on priculr kind of lcrochnicl y, h rur-conrolld dc rvooor Mblko, Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün 5

16 A gnic fild i dvlopd by ionry prnn gn or ionry lcrogn clld h fixd fild. A roing circui clld h rur, hrough which currn i flow, p hrough hi gnic fild righ ngl nd fl forc, F Bli, whr B i h gnic fild rngh nd l i h lngh of h conducor. h ruling orqu urn h roor, h roing br of h oor. hr i nohr phnonon h occur in h oor: A conducor oving righ ngl o gnic fild gnr volg h rinl of h conducor qul o Blv, whr i h volg nd v i h vlociy of h conducor norl o h gnic fild. Sinc h currn-crrying rur i roing in gnic fild, i volg i proporionl o pd. hu, v dθ b b ω d 0 Mrch 03 Ooik onrol Doç.Dr. Hluk Görgün 6

17 0 Mrch 03 7 Lplc rnforion: V b θ Arur quion: E V I L I orqu producd by Moor: I Conrol Sy Aoc. Prof. Hluk Görgün I E L b θ o find h rnfr funcion of h oor, ubiu Currn nd Volg; X

18 ow w u find in r of θ if w r o pr h inpu nd oupu vribl nd obin h rnfr funcion, θ /E. ypicl quivln chnicl loding on oor i h quivln inri h rur nd includ boh h rur inri nd, w will lr, h lod inri rflcd o h rur D i h quivln vicou dping h rur nd includ boh h rur vicou dping nd, w will lr, h lod vicou dping rflcd o h rur 0 Mrch 03 Conrol Sy 8 Aoc. Prof. Hluk Görgün

19 0 Mrch 03 9 D θ E D L b θ θ X Subiuing ; If w u h h rur inducnc, L, i ll coprd o h rur rinc,, which i uul for dc oor; E D b θ b D E θ α θ E Siply; X Conrol Sy Aoc. Prof. Hluk Görgün

20 L u fir dicu h chnicl conn, nd D. oor wih inri nd dping D h rur driving lod coniing of inri L nd dping D L. Auing h ll inri nd dping vlu hown r known, L And D L cn b rflcd bck o h rur o quivln inri nd dping o b ddd o nd D, rpcivly. hu, h quivln inri,, nd quivln dping, D, h rur r D L L 0 Mrch 03 Conrol Sy 0 Aoc. Prof. Hluk Görgün D D

21 ow h w hv vlud h chnicl conn, nd D, wh bou h lcricl conn h lcricl conn cn b obind hrough dynor of h oor, whr dynor ur h orqu nd pd of oor undr h condiion of conn pplid volg. L bθ E If w u h h rur inducnc, L, i ll coprd o h rur rinc,, which i uul for dc oor; dθ bω ω d whn h oor i opring dy wih dc volg inpu: ω b 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün

22 b ω If ω 0 ; If 0 ; ω ll bo b Elcricl Conn: ll b ω bo 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün

23 Expl: Givn h y nd orqu-pd curv of find h rnfr funcion θ L /E 0 Mrch 03 Conrol Sy 3 Aoc. Prof. Hluk Görgün

24 0 Mrch 03 4 L D D D L ll bo b ω E θ / /0, E θ L b D E θ Conrol Sy Aoc. Prof. Hluk Görgün

25 0 Mrch 03 Ooik onrol Doç.Dr. Hluk Görgün 5