AN AFM ROBE CONTROLLER DESIGN BASED ON µ-synthesis Ku-Ju L, Ji-Yuh Y, Chih-Ku L, Yi-Mi Li, Ch-Hu Ch Ai Jul f Cl Vl. 7, N.,. -9, Mch
Ai Jul f Cl, Vl. 7, N.,. -9, Mch AN AFM ROBE CONTROLLER DESIGN BASED ON µ-synthesis Ku-Ju L, Ji-Yuh Y, Chih-Ku L, Yi-Mi Li, Ch-Hu Ch ABSTRACT Th ic fc icc AFM i f h i l f ui ic lui. Th AFM y ii c fc bw i h l i ck h l hy. Th cll h ii h c ici fc ly iific l i u ccucy. Thi µ-yhi cll i l wih l uciy blih u bu. Th y liiy h -i if lu i uliliciv uciy. Th fc bu llw cifici f h iu v h fqucy. Siuli ul hw h h cl c l ucii. Th cu f h xi hw cicy wih h i cifici. I w k c µ-yhi cl wih wll-u ID cl 48µ/ c. Th ul vify h ui fc f h µ- cll. KyW: Aic fc icc, uliliciv uciy, µ-yhi, ID cl. I. INTRODUCTION Th ci b ic fc icc AFM u bjc wih ic lui. I i fii ic u i h ici f IC chi, cu h ik, icl ik, c. A fu i w ll i h lici [], h f ccucy f ci bc. Of, h lui f AFM h cl y h ii h ici fc bw h b i l. A AFM u l lih lv buc ff h ci b i u ll flci. A ilcic cu v h b ii c ici fc. Th fc f h cll i clli h v f h ci i ly ky l i u ccucy. Th biliy ck h ufc fil hih ccucy i h y- lui. Th biliy f h i fllw i fil ch i h ci f Muci civ Mch, 4; cc Ail 8, 4. Ku-Ju L, Ji-Yuh Y, Yi-Mi Li, Ch- Hu Ch wih D f Mchicl Eii, Nil Tiw Uiviy, Tii, Tiw 67, R.O.C.. Chih-Ku L i wih Iiu f Ali Mchic, Nil Tiw Uiviy, Tii, Tiw 67, R.O.C. h AFM. Hih fc cl f uch b y i, hu, cy. I i fuh ibl h h cl b cifi bcu h cl icly ffc h u ul. N liii i i by h ilcic cu. Thf, h bu h cl i icly l i h u lui. viu ch wk hv fcu bh h li cl c f h b cl bl. Schi l. u h H i vl f ci AFM b cll h c c fiv i f h h clicl y []. Bi l. u h fuy lic cll i cbi AFM/STM []. Bcu f h liiy ci wih h AFM y, ch hv i u h li cl chiqu chiv yic cki [4]. Th uh f [] [6] hv vl l f c, h cilv, i-l ici. Oh i [7] hw h h yic f AFM h l il, h cc fc -i, h liu f h iubc. Th iu f u lc h b. Thi µ-yhi cll f h AFM b cl y. Th µ-yhi u llw cifici f h fc lc; hu, i i ibl quify h u f iuc by h cl
K.J. L l.: A AFM b Cll Di B µ-syhi ci. Th fc-ic lihi c h b u blih fqucy bu f h u. Nli AFM yic ffc, uch hyi, ci, i-l ici, cilv liiy, -i ffc, l wih by iuci qu uliliciv uciy i h i cifici. Th cll i i, hu, bu. Bcu h lw fqucy bu i ly i, h ul cll u cl f l h c i h lw fqucy i. Siuli ul hw h h cl i l ucii, xil ul cfi h bu. Sc i h h cl liv b quliy icu h clicl ID cll hih c. I hi, w u ch y iifici ui cuv-fii h f h vll y. Th y iclu ii-iiv h-c SD, i c, i-l ici, cilv yic. Thi i ivi i v j ci. Sci cib h AFM y. Sci cib h hicl l f i-l ici h y iifici cu. Sci 4 icu h cll i h fc b cu iuli. Sci 6 h ili xil ul, Sci 7 cclui. Th i ub wih µ vi h h-iil i f h l. Th i c lihi bw h V Wl fc h ic f h b. Th cll h bi f h cilv v h c ii c fc. I h -cll cc i, h cilv i hl l h f h l ufc, h ici bw h cilv h l i uliv; i h -cc i, h cilv i hl fw f h l ufc, h ici i civ. I hi uy, h AFM w i h cc, l kw h uliv. Th Aub LS hw i Fi. f k Sciific Iu w ly i hi uy. I w ifi wih h cll vl NTU. C++ c w wi xcu h cl. Th h C w iu-b wih Avch I/O c. D lyi w f wih h MATLAB fw. II. SYSTEM DESCRITION Th AFM u h i c h ufc f l. Th i lc h f 4µ flxibl cilv i fw ic l, i iu i ll h. Wh h i ch h l, h ici cu h cilv b u h k vlly f h l ufc. A l b buc ff h f h cilv h c u h u f flci. Fiu hw h y cfiui. Fi.. Th Aub LS AFM III. SYSTEM MODELING AND IDENTIFICATION. Ti-l l i h cc i Ci Dul l wih hi fc; h l c b x by h fllwi qui [] [8]. Th i flci f h AFM b i x / 4λ 4E δ= R wr π, Fi.. Th AFM y cfiui F δ = 4E R / 4E c, wr λ + π
, 4 Ai Jul f Cl, Vl. 7, N., Mch / 4E λ c + πwr + 8λ + + c = 6, wh δ i h i l liv ilc, R i h iu f h i l, E i h cbi lic ulu, F i h cc fc, w i h hi c, σ i h Dul civ fc, λ = R / 9 σ we. Th vibl uy vibl b i. π Th cilv qui f i c b x -i- y: + ξω +ω = + x x x F x u x, 4 wh i h uc f h cilv, x i h ic-c ic bw h i l, x i h ilc f h i, u i h hy f h l. Th cilv i.7µ hick 44µ l. I il fc c i.n/, i c fqucy i kh. Th uc i. A yicl i iu i ll h. By liii h ici fc i Eq. 4, c li y i f h AFM cl y.. Sy iifici T bi ccu l f h cl y, H6A yic fqucy ly w u u h fqucy. Th iu h y w h i cu vl, h uu w h SD il. Th fc i i hi c w N. Fiu hw h xil fqucy h cuv fi y l. Th fi c f h y ccu 8H, which i bi f h cilv. Th iifi y i hi wih bl l l 4H clx l 8H. Th uch i i h hih fqucy i will b h ul yic. I hul b h h fqucy f h l y ch wih iff -i; hf, uciy i cy. IV. µ-synthesis CONTROL DESIGN 4. Muliliciv uci l Th AFM y ch h fc -i. A uliliciv uciy i u quly cib h fqucy- c uciy [9] []: G = G I + W u wh G i h l wih ucii. W u h h il l G h h ub f l i h ih hlf f h l. A ch fqucy, W u jω h xiu c bw G G, i f fuci h ifi x jω. ω R Th y i h u i h Li Fcil Tfi LFT f f h µ-yhi c. 4. Chi fc cii F y G wih c K, h cl-l fc c b cifi by h iiviy f fuci ix S = I + GK : = +. S I C By ui ificil il fil, W, h uu, h µ-yhi u u cll h chiv W S <, ω. Th u il fil W w v fc cii f h iiviy f fuci. B u - i - - M- Fqucy cuv-fii l 4. Ui µ ly bu biliy Ci h blck i wih cll K hw i Fi. 4 []. { x 9 h-9 Fqucy H v f F L, K Fi.. Fqucy ci Fi. 4. Th y u wih uciy
K.J. L l.: A AFM b Cll Di B µ-syhi ω R i Fi. 4 ucu uciy wih il ifyi x jω. A blck i f h uci cl-l y illui h bu cii h fc bjciv f i hw i Fi.. Th vibl, u, y,, h fc -i, cl ff, SD il, l hy, fc, civly. Th blck G, W u, W, K h il l, uliliciv iu uciy l, fc u bu, cll b i, civly. Th chic f W W u hw i Fi. 6. Th i u bu f 4B f il blw H. Bcu h l bv kh i uci, w llw f W u h B i h hih fqucy i. Th W u fuci i i by h uci i f h l fqucy, which i u u ci cii, iclui iff -i f fc, iff i, iff bi f h i ub.. Siuli V. SIMULATION Th µ-yhi cu ul i 7 h cll. F ffici cll ili, i h i l chck h blc uci cu. I w fu h h cll i ffciv. Fiu 7 hw ci iui bf f uci. Fiu 8 hw h SIMULINK blck. Th blck l hw h AFM i-l i h cc. Th iuli iclu h ffc f h cu ili. Th qui ui lii iul h ADC; h ui Z-O-Hl ZOH iul h DAC vic. Th lui f h AD/DA c w bi. Th iuli l iclu h ucii u ul yic y liii. Th il ici fc w N. Th l vii w iuil fil wih liu H fqucy. Fiu 9 hw h fc fil, Fi. 9b hw h cl ff. Th fc bw h i l w k N Fi. 9. Bcu h fc hw i Fi. 9c w vy ll, h cl ff w uffici cculy c h l fil. Th vic f h fc liv h i w 8B. Th l i fqucy GK i hw i Fi.. O c h h bwih w H. B Di G Fi.. Uci cl l y 4 B u i - M -4 7 4 6 h Bf uci Af uci B - - u i - -4 M- -6 9 4 h B Di W Wu 8 4 Fqucy H Fi. 7. A b i ci f iui bf f uci N C Fc uliliciv i Wu Sl hy Wu uc u y Mu l Cll Sui Z-O Hl G Fc - - 4 Fqucy H Fi. 6. Fqucy f W W u Qui Sui Fi. 8. Siuli blck i f h cl-l y
6 Ai Jul f Cl, Vl. 7, N., Mch y h l - S - Sl hy iu -........4 Ti c O-L B 6 B4 u i - G.M.:.6 B M-4 Fq: 78 H Sbl l -6 7 6 4 4 6 h7.m.: 69.7 8 Fq: 79 H 9 4 Fqucy H R f h l b Fi.. Th -l y fqucy - - - - f l - - C - -4-4 -........4 Ti c.8.6 E fc c VI. EXERIMENTAL RESULTS T h fc f h cll, Fi. hw h wh h i w l. Th f i w 6µ. Bf h i w l, i w c ui i ii f µ. A hw i Fi., h li ci cc h l 46. Du h V Wl fc, h i-l ici u civ fc f 46. Th y w.4n, which i ll h -bi DAC lui.4n. Th i i f h cll y w 4..4. N -. -.4 -.6 -.8 -........4 Ti c i i i T- - Fc bw i h l - 4 6 7 8 Ti N i c i l - i T........4 Ti c Fi. 9. Siuli ul f h l hy iu; b h f h c; c h fc ; h i-l ici. i c i l - i T - 4 6 7 8 Ti Fi.. Th wh h i w l. Th fc i w N.
K.J. L l.: A AFM b Cll Di B µ-syhi 7 Th y fc u chi il xci h -i cllc h fc. Th l i h i cii W i Fi. hw h h i i ci. Fiu - hw i c li ci i f u 8H. Th Fi. c hw h ul bi wih h cvil ID cl, Fi. b hw h ul bi wih h cl. Th l w f ilic ii fil i ilic ub. Th h l w µ qu wih µ ich. Th hih f h w 7. I i cl h h cl bi h i h h wll-u ID cll, v vy hih ci f 48µ/ ci Fi. c. A uch hih c vlciy, wh w c µ µ wih 64 ixl, h c i w ly 4. Th fc hy bi H lic wih h µ-yhi cll i hw i Fi. 4. Th qu RMS f h fc u h cl w.4n, which i 4B liv h fc -i; hf, h hw i Fi. libl wih l h % u. Ci h cu hw i Fi. wih h i cifici W i cfi h ffciv f h cl. Nic h h li fqucy f h cl w KH, h ci w f H. Th lf i wih h ll fqucy i u H. Ci h i c hih ci, ily h h ic bi wih h cl i ill iiuihbl, whil h bi wih h ID cl hw ly ll bli Fi. c... µ Y. Sl hy H wih ID... X µ.. µ Y. Sl hy H wih µ yhi b... X µ.. µ Y. Sl hy 8 H wih ID... X µ. c Sl hy 8 H wih µ yhi 8 7 6 4 - - 8 6 4-6 4-8 6 i Z i Z i Z - - - - u i - - M - -4-4 Fqucy ci xi hy - Fqucy H Fi.. Fqucy ci. Th li li i h fc u bu W f i fc ; h h li i h xil fqucy f i fc. µ. Y.... X µ Fi.. Th l hy bi H li c wih h ID cll. VII. SUMMARY AND CONCLUSIONS I hi uy, w ifi ccil AFM y u i u cl h. A hicl l w iv h bi f h cll yhi. Cll w i il b h µ cl yhi cu. Th µ 4 - i Z
8 Ai Jul f Cl, Vl. 7, N., Mch.. µ Y. Fc hy H... X µ - - - N c f l - i T Fi. 4. Th fc hy bi H li c wih h µ-yhi cll. - B - u i - M - - Fqucy ci xi hy - Fqucy H Fi.. Fqucy ci. Th li li hw h fc u bu W f i fc ; h h li hw li cu f li f fc. yhi cu ci h y liiy ul yic wih l uciy. I i i h h cu l bl cifici f h l fil cki v h fqucy i. Thf, i i ibl quify h c f cki ii i h u. Th ul cll i bl chiv bwih f H. Sc i hw h h cl chiv ui fc c h cvil cl. M i f ll, h yhi cu llw cc lc h c blih bu f h u fil. ACKNOWLEDGMENTS Thi jc w u i by h Miiy f Euci, R.O.C., i by h Nil Scic Cucil, R.O.C., u jc ub NSC 9--E- -8. REFERENCES. Th Nil Tchly R f Sicuc, Tchly N, Eii, Sicuc Iuy Acii.. Schi, G.,. Ml, H.F. K, F. Allw, A. S, Hih fc Fbck f F Sci Aic Fc Micc, Rv. Sci. Iu., Vl. 7, N. 8,. -7.. Bi, F.M., M. Bli, C. Lch, R. Luhi, E. My, H.-J. Guh, Fuy Cll Fbck Ali Cbi Sci Tuli Fc Micc, Al. hy. L., Vl. 7, N.,. -7 998. 4. F, Y.C., M.G. F, D.M. Dw, N. Jlili, Nli Cl Tchiqu f h Aic Fc Micc Sy, c., ASME I. Mch. E. C. Exi., Nw Ol, Luii,. -8.. Oh, M., EI Rifi, Y.-T. Kl, Dyic f Cc-M Aic Fc Micc, c. A. C. Cf., Chic, Illii,. 8-. 6. Ahhb, M., M.V. Slk, M. Dhlh, I. Mic, Cl f Ch i Aic Fc Micc, c. A. C. Cf., Albuququ, Nw Mxic,. 96-997. 7. Oh, M., EI Rifi, Y.-T. Kl, I-Cc Dyic f Aic Fc Micc, c. IEEE/ASME I. Cf. Av. Ill. Mch., C, Ily,. -8. 8. Mui, D., Ahi f Sh: Th JKR-DMT Tii Ui Dul Ml, J. Clli Ifc Sci., Vl., N.,. 4-69 99. 9. Bl, G.J., J.C. Dyl, K. Glv, A. ck, R. Sih, µ-alyi Syhi Tlbx, MUSYN Ic. & Th Mh Wk, Ic... Tyki, R., W C Sbiliy Alyi f Swichi Rul Ui h Sucu Siul Vlu, IEEE T. w Elc., Vl., N.,. 7-7 996.. Wlli, G.F. R. Tyki, Gli Ach f µ Syhi f Rbu Swichi Rul, IEEE T. A. Elc. Sy., Vl. 6, N.,. 4-4.
K.J. L l.: A AFM b Cll Di B µ-syhi 9 Ku-Ju L civ hi B.S. f Nil Tiw Uiviy i. H i culy cl ci i h D f Mchicl Eii NTU. Hi ch i iclu uic cl, civ vibi ili, ci b icc y. Hi hicl ch i iclu ID cl, LQG cl, ciuu/ic lii cl, µ-syhi, bu cl. Ji-Yuh Y M 87 bc b f IEEE i 987. H w b i Tii, Tiw. H civ h B.S. i chicl ii f Nil Tihu Uiviy, Hichu, Tiw i 98, h M.S. f Uiviy f Mi, MN, i 98. I 989 h civ h h.d. i chicl ii f Uiviy f Clifi, Bkly, CA. Dui hi uy Bkly, h civ h IBM Gu Fllwhi i 984-98. Sic 989, h h b wih Nil Tiw Uiviy, Tii, Tiw, wh h i culy f f Mchicl Eii. H v h u f h Cl Sy Ch i IEEE Tii Sci i 99. H l v cul f y ci iclui Iuil Tchly Rch Iiu, Tiw C Su MFG. L., Tiw. Hi ch i i h f li cl f lcchicl y, cilly i cii cl f cu ihl cii u y. H i l b f h ASME. Chih-Ku L civ hi M.S. h.d. f Cll Uiviy, i 98 987 civly, wih j i hicl li chic, i i hyic. f L i l cculy h Dic f Nuciv Ti Lby Tji-Li Iuil Rch Iiu, wll vi h Miiy f Euci i ch f chly fl l ily chly. Oh ui iclu bi h Dic f h li Divii f h Cii Rch Dvl, Nil Tiw Uiviy. Hi ch i MEMS chly y, ui chly, i & cuci f lcic y, lcic ilcic y, cii ly, bichi y. Yi-Mi Li w b i Tii, Tiw Ocb 9, 978. H civ h B.S i h M.S i i chicl ii f Nil Tiw Uiviy. Ch-Hu Ch i culy cl ci i h D f Mchicl Eii NTU.