PZT-based Modal Sensing and Compensation for Vibration Control of Moving Flexible Links

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Alberta McCoy
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1 Proeeg of he 3 r Ieraoal Coferee o Mehaal Egeerg a Meharo Prage, Czeh Rebl, Ag 4-5, 04 Paer No. 66 PZT-bae Moal Seg a Comeao for Vbrao Corol of Movg leble L Xg Zhag Aarh Uvery, Shool of Egeerg & Dearme of Egeerg Dalga Avee, 8000 C Aarh, Demar zh@ha. J. K. Mll, W. L. Cleghor Uvery of Toroo, Dearme of Mehaal Egeerg 5 Kg College Roa, Toroo, Oaro, Caaa M5S 3G8 mll@me.oroo.a; leghr@me.oroo.a Abra - Ireag aeo a effor have bee mae o he ave vbrao orol ae-bae fleble rre g Lea Zroae Taae PZT raer. Th wor ee he ave vbrao orol meho o vbrao reo of movg l moe o ml-boy mehaal yem. A omreve mehoology o orol he vbrao of he ermeae l reee wh he oerao of vbrao moe olg, moelle moe, orolle moe, loely ae moe, e. To eg he vbrao oroller he moal ae a reve llover, he eee moal ae orol IMSC meho emloye. The moal flerg a omeao are aree wh eal o mleme IMSC meho. Eermeal rel of a ml-boy mehaal yem wh fleble l are gve o verfy he reee vbrao orol meho. Keywor: PZT, Moal ae, Moal fler, Moal omeaor, leble l, Vbrao orol.. Iroo Aaor a eor mae from ezoeler maeral, h a PZT, have bee gag oerable aeae a mea for vbrao orol of fleble rre ree eae, beae of he avaageo roere of ezoeler maeral Premo, 00. Thee roere le mehaal mly, mall volme, lgh wegh, large bawh, effe overo bewee eleral eergy a mehaal eergy, a mle egrao wh varo meall a omoe rre. Comare wh gfa effor a rogre mae o he mlao a eerme emorao of ave vbrao orol he ae-bae fleble rre a mle fleble beam g PZT eor a aaor Baley a Hbbar, 985, a few reearher have re o ee h ave vbrao orol meho o ml-boy mehaal yem havg fleble omoe Lao a Sg, 993. I very ffere from fleble rre a mle beam ha rg boy moo a ela eformao are yamally ole for fleble l he mlboy mehaal yem robo malaor or meham. Th haraer lea o he olg of vbrao moe, a may ae llover. Moreover, he yam reoe meare by PZT eor le he moele or ow yam, lg for eamle, omlae a learae yam from he bearg, ball rew meham, a moor. Therefore, he vbrao of he ermeae l are very omlae, a are he ombao of free rral vbrao a fore vbrao, whh oa may freqey omoe whh are loely ae. Sllover mgh alo ome from he orolle moe a a lme mall mber of moe of fleble l a be or are reqre o be orolle rae. The llover ae orol eergy flow o he orolle moe of he yem, a rel ably a egraao of orol erformae Premo, 00. Therefore, he eee moal ae orol IMSC meho Merovh a Barh, 98, Baz a Poh, 988, Sgh e al., 003, Baz e al., 99 m be emloye o reve from he llover roblem by orollg eah moe earaely. I he IMSC, he moal oorae a/or moal veloe for he moe argee for orol m be real-me 66-

2 meare a moore. There are hree meho ha a be e o era he moal oorae from he o of he eor. Thee meho le ae oberver Broga, 974, emoral fler Hallaer e al., 98, a moal fler Merovh a Barh, 985. I ha bee how ha he e of oberver ae obervao llover from he real moe, whh a eablze he real moe. Ug emoral fler, he o of eor are roee g hgh-a or lowa fler o fler o he orbo of eah moe. Sh a meho oe o wor for he ae where he moe are loely ae. Ug moal fler, he a of erag moal oorae from he eor o from he orol a, whh erm he e of moal fler ojo wh ay moal feeba orol meho. rhermore, moal fler oly volve aal egrao, whh a moohg oerao ha a o lea o ably. Two ffere moal flerg meho have bee reee for moal fler. Oe a moal fler wh a rbe eleme Coll e al., 994. The oher a moal fler wh ree eleme Smal e al., 00. I ofe ffl o mleme moal flerg wh a rbe eleme beae reqre oe eor for eah moe. Therefore, reaoable o erform moal flerg wh ree eor real me. Seg moal oorae real me volve erolao or rve fg. All omao m be arre o wh a gle amlg ero beae he oroller are mlemee ree me. Several feeba orol ehqe have bee eveloe for vbrao orol, lg aglar veloy feeba Baley a Hbbar, 985, L-ye lear veloy feeba S e al., 004, ra feeba a ra rae feeba Sog e al. 000, of he orolle o o fleble rre. Sra rae feeba SR ha a wer ave amg freqey rage, a hee a ablze more ha oe moe mlaeoly, gve ffe bawh Sog e al To eg a mleme a SR oroller he moal ae, he mlfe moal fler are e o meare he moal oorae a veloe. To reve robable eablzao rele from he ffereao of he SR oroller, a omeaor eee o off he amlfe oe a moele yam gal wh hgh freqee, eeally for he ermeae l ml-boy mehaal yem. Th wor ree a omreheve ave vbrao orol mehoology of movg fleble l ml-boy mehaal yem g PZT raer. The vbrao haraer of movg fleble l are aalyze wh he oerao of olg yam a moele yam eo II. The SR oroller eg moal ae reee Seo III. The eg moal fler a omeaor are aree wh eal reevely Seo IV a V. I Seo IV, he eermeal rel are gve o valae he reee ave vbrao orol raege a meho. Combe wh he reee mehoology a raegy h wor, he o a olo are mae he la eo o rove omreve gh a gae for avely orollg he vbrao of movg fleble l ml-boy mehaal yem g PZT raer.. Moal Dyam of Movg Ave-Srre A ave vbrao orol rre ege a bl by bog PZT eor/aaor o he wo e of a fleble l a how gre. The PZT ahe o oe e of he l a a eor, whle he PZT ahe o he ooe l fae a a aaor. Oe eor a oe aaor oe a PZT orol ar bae o he ra rae feeba orol raegy, a are loae a he ame loao alog he legh of eah ermeae l. B Qarer o Mo Three qarer o PZT aaor m PZT eor C Moal ler Moal SR oroller Moal Syhezer A Seo Orer Comeaor g.. A mar l rre wh PZT aaor a eor ahe Zhag e al.,

3 66-3 Ug he ame moe meho bae o he boary oo, he yam eqao of a movg l a be gve moal ae a w Ω C where T he moal oorae veor of a ermeae l, m ag C he moal amg mar bae o he amo of Raylegh amg, ag Ω he rral moal ffe mar, he h orer moal freqey, a w refle he moal fore from he effe of he rg-boy moo o he ela vbrao of he fleble l, he olg bewee he rg-boy moo a he ela moo, a oher moelle fore. he moal orol fore veor raforme from beg mome reae by PZT aaor. 3. Moal Sra Rae eeba Coroller Oe ave vbrao orol raegy re o feeba orol DOC ra or/a ra rae. Th orol aroah oe o ema moal ae emao. I h meho, he eor are olloae wh he aaor, a a gve aaor orol fore a fo of he eor o a he ame loao alog he ermeae l. Th, oe PZT aaor a oe PZT eor oe a PZT orol ar bae o he ra a ra rae feeba orol raegy. Ug ra a ra rae feeba, he orol volage ale a PZT aaor eer o of he PZT aaor loae a alog he ermeae l gve a, a K V V V where a are he feeba ga erm of volage a volage rae, V he volage e he orreog PZT eor, a he h moal hae fo of he l. The moal fore veor roe by he PZT aaor eree a a K K 3 where he oorae a he rgh e of he PZT aaor, a he oorae a he lef e of he PZT aaor. Noe ha we ame ha all PZT eor are eal, a all PZT aaor are eal h wor. I rae, he oroller ege wh oly he lme low orer moe argee for orol for eamle, moe. Eqao 3 a be aroe a wre a,,,,,, r,,, 4 I eqao 4, he moal orol fore for he argee moe. he moal orol fore flow o he orolle moe, a ol rel he orol llover. The erm, ae by he ee orolle moe flowg o he moe argee for orol. The erave ao bewee orolle moe a orolle moe fally ol lea o he ably of he orol yem. rhermore, lear ha he orol fore ole

4 amog he orolle moe e he mar,, eqao 4 o a agoal mar, r,,, a hee he orolle moe are eee of eah oher. A a rel, ffly, f o moble o eerme orol ga o re he vbrao whe mlle PZT aaor are ale. The reao for ha ha ole alloao or omal orol mo lely wll reqre ga mare wh ere eee of eah oher whle DOC mle ha he ere of he orol ga mar are o eee for ml-aaor. To reve orol llover, a heomeo ha rel egraao of erformae or ably, he Ieee Moal Sae Corol IMSC emloye for he oroller eg h wor. Ug moal oorae, a feeba orol roblem of oo rre a be raforme o he roblem of orollg everal gle-egree-of-freeom SDO yem arallel, wh o erao amog he yem. Therefore, feeba oroller a be ege he eee moal ae o ha eah argee moe orolle by oe eee moal oroller aoae wh oly ow moal laeme a veloy. Wh IMSC, he moal orol fore f for he h moe oly ee o a. f gve a f 5 Eqao 5 llrae ha he olg of moal eqao e o feeba avoe wh IMSC. Combg eqao a 3, he loe-loo moal eqao a be eree wh he eee moe a f, 6 w, May aroahe, h a ole agme or omal orol, e o eerme he orol ga Eqao 6. I he omal orol aroah he orol ga are eerme hrogh omzg a rerbe erformae e. I he IMSC meho, a qara fo, he ombao of he moal oeal eergy, moal e eergy, a he reqre moal orol fore yally hoe o be he erformae e gve a f, J 0 f 7 I Eqao 7, moal wegh e o gfy he morae of vbrao eergy reo a he reqre orol effor. The loe-loo olo o Eqao 7 a be obae by olvg a mar Ra eqao, a gve a [4 / ] / / 8 4. Moal ler a Syhezer I raal eerme, he o volage of a PZT eor orreo o he hyal l hyal eformao oorae, o moal oorae. Therefore, o mleme IMSC orol, he moal oorae m be erae from he o volage of ree PZT eor real me. The moal oorae, erae real me, are rove o he moal feeba oroller. Ug he moal yhezer, he moal orol volage are raforme ba o he orol volage hyal ae, a are e a o he PZT aaor. The mlemeao of IMSC llrae gre a. Noe ha we ame all PZT eor are eal, a PZT aaor are eal a well. Se he legh of PZT aaor 66-4

5 R l mh maller ha he legh of ermeae l, aromae o be l a, where l a he legh of a PZT aaor. g.. Shema of IMSC mlemeao bae o PZT raer Zhag e al., 009. The moal fler ereo for eah mar l eree a Φ V 9 m T V Vm where T moal oorae veor of he ermeae l, V V he o veor of he m eor boe o he ermeae l, a Φ m a m moal oorae raformao mar or moal aalyzer. Φ m gve a Φ m K Τ T 0 The mar allae wh he vale of he moe hae fo a he ree eor m m m A how gre a, he moal oorae, erae real me, are rove o he moal feeba oroller. Ug he moal yhezer, he moal orol volage are raforme o he orol volage hyal ae, a are e a o he PZT aaor. 5. Moal Comeaor Deg The mlemeao of he ervave algorhm e o amlfy oe or he moele vbrao gal a hgher freqee e o ervave oerao. I rae, erable o a a 66-5

6 omeaor o ha he SR oroller ehb garaee ably a a larger roll-off a hgh freqey Sog e al The ba ea o a he ra rae feeba gal hrogh a eo orer fler wh baal amg, a geerae a feeba rooroal o he o of he fler. To beer llrae he oerao rle of SR oroller wh a omeaor, ame ha a rre may be mlfe o be a gle egree of freeom, gle--gle-o vbrao yem g oe olloae PZT eor a aaor ar. The blo agram whh erbe he orol raegy how gre 3. g. 3. Blo agram for SR oroller wh omeaor Zhag e al., 009. The eqao of he yem a he omeaor for SR orol are eree a Sog e al. 000 g 3 where 4 a moal oorae of he rre, he amg rao of he rre, aral freqey of he rre, a moal oorae of he omeaor, he he amg rao of he omeaor, he reoa freqey of he omeaor, g a ra rae ba feeba ga, a, are oa whh are eerme by he evy of he aaor a eor, reevely. I hol be oe ha eqao 3 a eqao 4 are ole by he hyal erao bewee orol gal, hrogh he oorae, a he rre. Ame ha he vbrao olo for he rre wh a gle egree of freeom gve he form a e The eay vbrao olo of he omeaor gve a e / a a / / / where / / / rom eqao 5 a eqao 6, we have 5 6. e / e e / /

Sbg eqao 7 o eqao 3, he rral vbrao eqao wh SR oroller eree a hree ffere form wh he relaoh bewee he rral aral freqey,, a he omeaor reoa freqey,. Whe, he hae agle aroahe zero.

7 Sbg eqao 7 o eqao 3, he rral vbrao eqao wh SR oroller eree a hree ffere form wh he relaoh bewee he rral aral freqey,, a he omeaor reoa freqey,. Whe, he hae agle aroahe zero. Sbg eqao 7 o 3, eqao 3 a be formlae a g 0 8 Eqao 8 learly how ha he eeal role of he SR omeaor o reae he amg rao of he rre. Whe, he hae agle eqal o /. Sbg eqao 7 o 3, eqao 3 a be eree a g 0 9 Eqao 9 how ha he SR omeaor lea o he reae of he ffe of he rre. Whe, he hae agle aroahe. Sbg eqao 7 o eqao 3, eqao 3 a be reee a g 0 0 Eqao 0 emorae ha he omeaor e o ereae he amg rao of he rre h ae. Therefore, he eg of SR orol wh he omeaor fler, he omeaor hol be ege o mae re ha he argee freqee are below he omeaor freqee. The above raegy a be eee o orol mlle moe by rog mlle omeaor arallel. Oe omeaor ege for eah argee moe. 6. Eermeal Valao I h wor, hree PZT eor a aaor are boe o he hr ermeae l a qarer o, mo a hree-qarer o, a how g.4. Three aaor a eor are elee a BM 53, mafare by Seor Tehology. The ezoeler oa C / N, 0 a Yog mol N / m. The meo of eah PZT aaor are 5.4mm 5.4mm0. 54mm a he meo of eah PZT eor are 6.35mm 6.35mm0. 54mm. The ave vbrao orol yem e g LabVIEW Real-Tme Zhag e al., 009. The amlg rae for eah hael of he A/D a D/A ofgre o be 000 Hz, a he a o volage rage of eah hael of he A/D a D/A e o be vol. The volage ga for eah hael of he Seor Tehology SS08 amlfer e o be 30. g. 4. Iermeae l boe wh PZT raer Zhag e al.,

The hree fleble l were moe o a 3-PRR arallel robo malaor whoe e-effeor move aro rlar rajeory wh a ra of 30mm, a moal eg are oe g ma hammer a aeleromeer Zhag e al., 007.

The heoreally ege ga may o be ealy omal e o he eray of he yam moel a ome oher oere faor, h a he hae rafer roere for low a fler bewee D/A o he hgh-volage PZT amlfer.

The orol ga for he orolle moe are eerme g he rooe raegy. Se he ma roe o am he vbrao, oly moal ra rae feeba ale he eerme. The orol effor weghg hoe a Eqao 7.

8 The hree fleble l were moe o a 3-PRR arallel robo malaor whoe e-effeor move aro rlar rajeory wh a ra of 30mm, a moal eg are oe g ma hammer a aeleromeer Zhag e al., 007.To ee he rral vbrao of he fleble ermeae l a mh a oble, he mamm veloy a aelerao of hree ler were eermeally e o be 0. m / a 50 m /, reevely. The heoreally ege ga may o be ealy omal e o he eray of he yam moel a ome oher oere faor, h a he hae rafer roere for low a fler bewee D/A o he hgh-volage PZT amlfer. Therefore, g ral a error o aj he ga, he ole of he fleble l were alloae o a ere loao where be vbrao aeao rel were aheve. I h wor, he fr wo fleble l moe are argee for orol. The orol ga for he orolle moe are eerme g he rooe raegy. Se he ma roe o am he vbrao, oly moal ra rae feeba ale he eerme. The orol effor weghg hoe a Eqao 7. Before he orol reo mlemee, he reoe of he orolle yem aalyze g moal fler o oba moal laeme a veloe. Wh he efe aral freqee he aral freqey 75 Hz for he fr moe, a 35 Hz for he eo moe, he wegh faor of he orol ga of he eo moe a be allae g eqao 8. The orol ga for he fr moe elee o be 3.0, a he orol ga for he eo moe elee o be 0.6. Wh hee orol ga, he fr wo moe are gfaly ree for he all hree fleble ermeae l boe wh PZT raer. A how gre 5-7, he vbrao reoe meare a he qarer o, mo, a hree-qarer o are gfaly ree. gre 8 a 9 frher how ha he fr moe vbrao of he ermeae l wa ree 70%, a gre 0 a emorae he eo moe vbrao alo ereae by 50%. g. 5. Vbrao a he qarer o. Zhag e al, 009 g. 6. Vbrao a he mo. Zhag e al, 009 g. 7. Vbrao a he hree Zhag e al,

9 g. 8. T of moe of l3 who orol. g. 9. T of moel of L3 wh orol g. 0. T of moe of L3 who orol. g.. T of moe of l3 who orol. 7. Do a Colo A PZT-bae ave vbrao orol raegy reee for movg fleble l moe o ml-boy mehaal yem g moal fler a eo omeaor bae o he IMSC raegy. The moal fler are mlfe a ege wh ame moe hae. The rooe moal fler are e for he o-le emao of moal oorae a moal veloy. The eo omeaor e o off he amlfe oe a moele yam e o he ffereao oerao he rooe oroller. The moal olg behavor of ermeae l eame wh he moal aaly of vbrao meare by he PZT eor. A effe ml-moe vbrao orol raegy ha bee rooe hrogh mofyg he IMSC raegy. ally, ave vbrao orol eerme are eflly mlemee o hree fleble l, eah of whh are eqe wh hree PZT orol ar a qarer o, mo, a hree qarer o. The eermeal rel how ha he vbrao of he fleble malaor ree effevely. Referee Baley T., a Hbbar J. J Drbe ezoeler-olymer ave vbrao orol of a alever beam. J. Gae, Corol a Dyam, 95, Baz A., a Poh S Performae of a ave orol yem wh ezoeler aaor. Joral of So a Vbrao, 6, Baz A., Poh S., a eor J. 99. Ieee moal ae orol wh ove oo feeba. Joral of Dyam yem, Meareme a Corol, 4, Broga W. L Moer Corol Theory Qam Pblher, New Yor. Coll S. A., Mller D. W., a loow A. H Drbe eor a aal fler ave rral orol. Joral of o vbrao, 73,

10 Hallaer W. L., Smore G. R., a Meqa L. C. 98. Eermeal Theoreal y of ave vbrao orol. Proeeg of he Ieraoal Moal Aaly Coferee, Orlao, USA, Lao C. Y., a Sg C. K A elaoyam aaly a orol of fleble lage g ezoeram eor a aaor. Joral of Mehaal Deg, 5, Merovh L., a Barh H. 98. Omal orol of ame fleble gyroo yem. Joral of Gae a Corol, 4, Merovh L., a Barh H The mlemeao of moal fler for orol of rre. Joral of Gae a Corol, 86, Premo A. 00. Vbrao Corol of Ave Srre: A Iroo Klwer Aaem Pblher. Sgh S. P., Prh H. S., a Agarwal V. P Effe moal orol raege for ave orol of vbrao. Joral of So a Vbrao, 6, Sog G., Shm S. P., a Agrawal B. N Ave vbrao reo of a fleble rre g mar maeral a molar orol ah. Pro. I. Meh. Eg., 4, 7-9. Smal H., Meer K., a Cey H. H. 00. A ezoeler array for eg vbrao moal oorae. Seor a Aaor A, 93, 3-3. S D., Mll J. K., Sha J., a To S. K A PZT aaor orol of a gle-l fleble malaor bae o lear veloy feeba a aaor laeme. Meharo, 4, Zhag X., Mll J. K., a Cleghor W. L Dyam Moelg a Ave Vbrao Corol of a Plaar 3-PRR Parallel Malaor wh Three leble L. PhD he, Uvery of Toroo. Zhag X., Mll J, K., a Cleghor W. L Dyam Moelg a Eermeal Valao of a 3-PRR Parallel Malaor wh leble Iermeae L. Joral of Iellge a Robo Syem, 50 4,

CONTROL ACTIONS. A two position controller has two fixed positions usually on or off.

CONTROL ACTIONS. A two position controller has two fixed positions usually on or off. VU e-learnng Coreware Conrol ngneerng (M55) CONROL ACIONS An aomac conroller comare he acal vale of he yem o wh he n (ere vale), eermne he evaon, an roce a conrol gnal ha wll rece he evaon o zero or a