CLOSED-LOOP SIGNAL SHAPING WITH INNER-LOOP MODEL MATCHING

Transcription

1 Proceedig of the ASME 7 Itertiol Mechicl Egieerig Cogre d Expoitio IMECE7 Noveer Tp Florid USA IMECE CLOSED-LOOP SIGNAL SHAPING WITH INNER-LOOP MODEL MATCHING Withit Chtltgulchi Deprtet of Mechicl Egieerig Fculty of Egieerig Ketrt Uiverity Chtuchk Bgkok Thild Kittipog Yovj Deprtet of Mechicl Egieerig Fculty of Egieerig t Srirch Ketrt Uiverity Srirch Cpu Srirch Chouri Thild Puwdo Poedeg Deprtet of Mechicl Egieerig Fculty of Egieerig Ketrt Uiverity Chtuchk Bgkok Thild ABSTRACT Iput hper i pre-filter deiged to uppre reidul virtio of flexile yte. The iput hper c e plced iide the feedck loop i frot of the flexile plt to void excitig the plt virtory ode. The perforce of thi oclled cloed-loop igl hpig i liited due to the tie dely rought out y the iput hper. The iput hper h ore tie dely whe the plt ode preter re ucerti. I thi pper ier-loop cotroller ed o the qutittive feedck theory i deiged to tch the ucerti flexile plt to referece odel. A reult the iput hper eed ot e rout d the tie dely i reduced. Other eefit iclude horter iput hper legth icreig cotroller dwidth pplicle to tie-vryig plt d reducig cot of feedck. Siultio d experiet hve cofired the effectivee of the ewly propoed techique. INTRODUCTION Reidul virtio tke plce whe ovig flexile yte rpidly fro poit to poit. Iput hpig i iple techique ued to uppre thi virtio y hpig the igl o tht it will ot excite the virtory ode of the flexile plt. Iput hpig i ed o the ide preeted i []. Recetly the iput hper i plced iide the feedck loop o-clled cloed-loop igl hpig (CLSS) [] to gi eefit uch eliitig the virtio iduced y pltoutput diturce ee i tilizig the o-collocted yte ee i hdlig hrd olieritie (cklh dedzoe turtio) d iprovig perforce of ul cotrol. Recetly the CLSS h ee pplied to ctul yte icludig ridge cre with ditriuted [3] 3D cre with PID cotroller [4] d helicopter [5]. Didvtge of CLSS poited out i [6] iclude the iility to uppre the virtio iduced y the plt-iput diturce the uexpected itility fro iccurte plt odel d ot iporttly the detrietl effect fro itroducig tie dely i the feedck loop. The iput hper coti tie dely. Thee tie dely re lrger whe the tie durtio or legth of the iput hper icree. Loger iput hper i required whe the plt odel i iccurte. Referece odel tchig h recetly ee propoed to tch the ucerti plt odel to exct referece odel. The iput hper c the e deiged uig the exct referece odel. Severl odel tchig techique propoed with the iput hper iclude euro-lidig ode cotroller [7] ccelertio feedck [8] tte-feedck with two gi [9] output decopoitio [] proportiol-itegrl cotroller [] Lypuov-ed cotroller [] itertive lerig cotroller [3] d qutittive feedck cotroller [4]. I thi pper the qutittive feedck cotroller [5] i ued the ier-loop feedck cotroller to tch the ucerti flexile plt to exct referece odel. The iput hper i plced efore the ier-loop yte d i deiged fro the exct referece odel. A proportiol-itegrl cotroller i ued i the outer-loop yte for referece igl trckig. The dvtge of the propoed techique over trditiol CLSS re follow: Copyright 7 y ASME

2 Shorter iput hper legth i required. Becue the iput hper i deiged fro exct referece odel it doe ot eed to e rout; therefore the legth c e horte. Cotroller dwidth i icreed due to le tie dely fro horter iput hper legth. The techique c e pplied to tie-vryig or olier plt ecue the ier-loop cotroller tche the vryig plt to exct referece odel. PROPOSED SYSTEM The propoed yte i how i Fig.. P i the flexile plt. F G d C re the cotroller to e deiged. IS i the iput hper. y i the flexile-ody output. u i the cotrol effort fro G. e i the error igl of the ier loop. r i the hped referece for the ier loop. v i the cotrol effort fro C. r i the elie referece. F i the referece odel for the ier loop. P c e ucerti ledig to legthy IS. A reedy F d G re the ier-loop cotroller deiged to tch the ier-loop yte to exct referece odel F. A reult IS c hve horter durtio ecue it doe ot eed to e rout. A horter-durtio IS e le tie dely i the loop which icree cotrol dwidth for C. r _ + C v IS F r e u y F + G P _ Fig. Cloed-loop igl hpig with ier-loop odel tchig. I thi pper proportiol-itegrl (PI) cotroller w ued C. F d G were deiged uig the qutittive feedck theory (QFT) to cover ll poile ucerti plt P. F i uderdped yte tht i hdled y IS. Lettig F e uderdped ited of overdped or criticlly dped reduce the cot of feedck ecue IS i feedforwrd filter. A. Plt P A two- rigid-flexile plt how i Fig. repreet y flexile plt i prctice. It lo repreet the flexile-joit root which w ued experietl hrdwre i thi pper. The ojective i to cod the flexile output y x to follow the elie referece r without reidul virtio t the ed poit. The trfer fuctio fro the cotrol effort u to the flexile output y x i give y Y c + k P( ) 4 3 U ( ) + ( c + c + c ) + ( k + cc + k ) + ( ck ) where c d c re the dpig cott k i the prig tiffe d re the rigid d the flexile e. c u x x c k Fig. Two- rigid-flexile plt. I iultio the followig preter vlue were ued: kg kg c 5 kg/ c. kg/ d k kg/. The turl frequecy d dpig rtio of the plt were coputed ω 3.74 rd/ d ζ.389. Therefore turl choice for the referece odel F i ecod-order odel: F ( ) ( 3.74) ( )( ) ( ) B. Ier-Loop Cotroller F d G I iultio c c d k were llowed to hve 5% ucertity tht i c { } c {.5..5 } d 3 k { 5 5 }. Therefore there re 3 7 poile plt P with the 4 th ce the oil plt. For ll 7 poile plt the cotroller G d the prefilter F were deiged to eet the tility rgi pecifictio PG 3 db.43 + PG < d the odel tchig pecifictio PGF F db. + PG < (3) uig loop hpig techique clled qutittive feedck theory [5]. Fig. 3 how the wort-ce oud otied fro the tility rgi d the odel tchig pecifictio o the Nichol chrt. There re 8 frequecie of iteret fro.5 rd/ to rd/ coverig low high d turl frequecy of the plt. Fig. 3 lo coti the origil ope-loop hpe of L PG where G.. () () Copyright 7 y ASME

3 Ope-Loop Gi (db) rd/ rd/.5 rd/. rd/ rd/ rd/ rd/ 5 rd/.5 rd/. rd/ rd/ rd/ 3 rd/ 5 rd/ rd/ rd/ Ope-Loop Phe (deg) Fig. 3 Ope-loop hpig: origil hpe. To tify ll the oud the ope-loop hpe ut e ltered o tht ech frequecy poit lie i the llowle regio which i thi ce i ove or outide the oud. Therefore the origil ope-loop hpe ut e oved upwrd d to the right of the Nichol chrt. To do o the ope-loop gi w icreed. A rel zero d coplex zero were ppeded to help icree the ope-loop gi d phe. The fil cotroller G fter the loop hpig i give y ( )( ) G The fil ope-loop hpe i give i Fig. 4. The prefilter F w et equl to the referece odel tht i F F o tht the odel tchig pecifictio ecoe the plt-output diturce rejectio pecifictio for which the tdrd loop hpig lgorith exit. Ope-Loop Gi (db) rd/. rd/ rd/ rd/.5 rd/. rd/ rd/ 3 rd/ 5 rd/ rd/ rd/ rd/ rd/ 5 rd/ 3 rd/ rd/ Ope-Loop Phe (deg) Fig. 4 Ope-loop hpig: fil hpe. C. Iput Shper IS The ZVD k iput hper [6] w elected i thi pper due to it populrity d it cloed-for forul. The forul for it orlized ipule plitude A i d tie loctio t i re give y where k + i K i π Ai t ( ) k i i + k + j K ω ζ j j i... k + K e ζπ ζ! r r! ( r)! i the coitio of thig tke r t tie. The iput hper i the cotiuou tie i the give y ( ) IS D. Siultio Reult. k + ti Ai e. (4) i Vi iultio everl eefit of the propoed techique re highlighted i thi ectio. ) Require Shorter Iput Shper Legth Fig. 5(Top) how the Bode gitude plot of the odel F d the ier-loop yte PGF ( PG ) / + for ll 7 ucerti plt. The ier-loop yte tche the odel well ccordig to the odel tchig pecifictio (3). Without the ier-loop yte Fig. 5(Botto) how lrge vritio of the Bode gitude plot of the 7 ucerti plt. Percetge virtio V i populr eure of virtory level [6]. It forul i give y ζωt( ω/ ω ) ti p ( ω/ ω ) i i V e A e where ω i the ctul turl frequecy ω i the odel turl frequecy p ζω jω ζ i oe of the yte flexile pole ζ i the dpig rtio A i d t i i... re the plitude d tie loctio of the ipule. Fig. 6 how the iput hper legth fuctio of the percetge virtio V. The iput hper legth equl the tie loctio of the lt ipule t. k + The dhed lie how the iput hper legth required y the yte without the ierloop odel tchig. The olid lie how tht of the yte with the ier loop. With 5% ucertity i c c d k the iput hper legth required y the yte without the ier loop icree the deired percetge virtio V decree. 3 Copyright 7 y ASME

4 With the ier-loop odel tchig the iput hper i deiged fro fixed referece odel F ; therefore the iput hper legth doe ot icree whe le percetge virtio i required. Fro Fig. 6 whe the deired percetge virtio i 43.53% yte either with or without the ier-loop yte require the iput hper legth of.98 which i the legth of the ZV iput hper. However whe 3.59% percetge virtio i eeded the yte without the ier loop require 3.9 of iput hper legth which i 4 tie of tht with the ier loop. Log iput hper legth e loger tie dely i the feedck loop which liit the cotroller perforce. Mgitude (db) Mgitude (db) Bode Digr F PGF / P Frequecy (rd/) Frequecy (rd/) ( + PG) Fig. 5 Bode gitude plot. (Top) With odel tchig. (Botto) Without odel tchig. For fixed percetge virtio V % Fig. 7 how plot etwee the ucertity percetge i c c d k d the iput hper legth with d without the ier loop. For lrger ucertity loger iput hper legth i required without the ier loop. ) Icree Cotroller Bdwidth Fro Fig. 7 for fixed percetge virtio of V % d ucertity of 5% the ZVD iput hper i required without the ier loop where oly the ZV iput hper i required whe the ier loop i preet. Fro (4) the tie dely of the ZVD iput hper i triple tht of the ZV iput hper. Thi icreig tie dely liit the perforce of the feedck cotroller C. To illutrte thi the cotroller C w choe the proportiol-itegrl (PI) cotroller. Fro utoted tuig of the PI cotroller the cotroller i ( ) ( ) C / (5) with the ier-loop odel tchig d the ZV iput hper d ( ) ( + ) C / without the ier loop d with the ZVD iput hper. Fig. 8(Top) how the Bode gitude plot of the cloed-loop yte with the ier loop for ll 7 plt vritio d Fig. 8(Botto) how thoe without the ier loop. The cloed-loop dwidth i reduced fro 3.4 rd/ with the ier loop to. rd/ without the ier loop. Thi clerly how tht the propoed yte ue horter tie dely; therefore the cotroller dwidth c e icreed. 8 ZVD ( ) t k + ZVD 6 ZVD 5 ZVD 4 ZVD 3 ZVD ZVD ZV V (%) Without ier loop With ier loop Fig. 6 Iput hper legth fuctio of percetge virtio: with d without ier loop. ( ) t k + ZV ZVD ZVD Ucertity (%) Without ier loop With ier loop Fig. 7 Iput hper legth fuctio of ucertity percetge: with d without ier loop. Aother prole cocer the itility of the cloed-loop yte without the ier-loop odel tchig. Fig. 9 how it root locu plot. Without the ier-loop odel tchig the plt P i quite ucerti d the ucerti pole y uitetiolly cro to the utle right-hlf ple. 4 Copyright 7 y ASME

5 Mgitude (db) Mgitude (db) Frequecy (rd/) Bode Editor for Cloed Loop (CL) Frequecy (rd/) Fig. ()-(c) clerly how the deteriorted virtio uppreio perforce without the ier loop whe the ucertity percetge icree. With the ier loop the virtio uppreio perforce doe ot degrde igifictly eve with ucertity high 7%. y r ( ) y r ( ) Tie ( ) Fig. 8 Bode gitude plot of the cloed-loop yte. (Top) With the ier loop. (Botto) Without the ier loop. y r ( ) Tie ( ) c Cloed-Loop Pole Noil Ucerti y r ( ) Tie ( ) Tie ( ) d Fig. 9 Root locu plot without the ier-loop odel tchig. 3) Apply to Tie-Vryig Plt Tie-vryig plt h the e effect ucerti plt i tht the ctul plt will differ fro the plt odel ued i deigig the cotroller. With the ier-loop odel tchig the ier-loop yte i deiged to tch referece odel well for ll plt vritio pecified y the ucertity percetge. A reult the trckig well the virtio uppreio perforce will ot e deteriorte whe the plt i tievryig. Fig. how the trckig reult of the flexile output y. The olid lie re the flexile output; the dotted lie re the referece r. Fig. ()-(c) re for the yte without the ierloop odel tchig. Fig. (d) i for the yte with the ier loop. The plt preter c c d k were devited fro their oil vlue ccordig to forul Actul vlue Noil vlue ( %ucertity/). Fig. Flexile output y d it elie referece. Without ier loop: () % ucertity () 35% ucertity (c) 7% ucertity. With ier loop: (d) 7% ucertity. 4) Reduce Cot of Feedck C the referece odel F e de criticlly or overly dped ited of uderdped hece there i o eed for the iput hper IS? Sice the iput hper i feed-forwrd filter it erely chge the iput igl to void excitig the flexile ode. Therefore oe eefit of uig the iput hper with uderdped referece odel i to reduce cot of feedck. Alo i geerl uderdped yte ( < ζ < ) h quicker triet repoe th tht of the criticlly dped ( ζ ) d overly dped ( ζ > ) yte. To illutrte thi criticlly dped verio of the referece odel () which i F ( ) ( 3.74) ( )( ) ( ) Copyright 7 y ASME

6 w ued i the iultio without the iput hper IS. A ew cotroller G w re-deiged uig the qutittive feedck theory ( )( ) G The pre-filter w give y F F d the feedck cotroller reied the e (5). Fig. () how the flexile output y d it referece r. Fig. () coti the cotrol effort u. Fig. (c) d (d) re thoe for the propoed uderdped referece odel with the iput hper. Quicker triet repoe c e ee uig the propoed yte y coprig Fig. () to (c). The cotrol effort i lo reduced y the propoed yte y coprig Fig. () to (d). Two opticl ecoder eure the otor hft d the lik gulr poitio. A Ntiol Itruet Lview yte w ued the coputer cotrolled yte. Lik Ecoder Sprig y r ( ) Motor Ecoder u ( N) y r ( ) u ( N) tie ( ) tie ( ) c tie ( ) d A. Plt P Fig. Flexile-joit root i the experiet. The equtio of otio of the flexile-joit root re logou to thoe of the two- yte i Fig.. Syte idetifictio of the root coit of two tep. Firt the otor hu w rotted ully while the otor hft poitio x d the lik poitio x were eured. The Mtl GUI idet w ued to idetify trfer fuctio fro x to x P ( ) X X Fig. 3() how the odeled lik poitio (i olid lie) veru the ctul lik poitio (i dhed lie). Secod frequecyvryig ie wve w give referece for the otor hft poitio to follow uig proportiol cotroller. Both otor hft poitio x d the cotrol effort u give to the otor driver ord were recorded. A trfer fuctio fro u to x w foud tie ( ) Fig. Criticlly dped ce: () flexile output d it referece d () cotrol effort. Uderdped ce: (c) flexile output d it referece d (d) cotrol effort. EXPERIMENT To how the pplicility of the propoed ier-loop odel tchig yte the techique w pplied to flexile-joit root i Fig.. 4 X ( ) 4 3. P U Fig. 3() how the odeled otor hft poitio (i olid lie) veru the ctul hft poitio (i dhed lie). Severl experiet were repeted to vlidte the odel. The overll plt P ( ) P ( ) P ( ) h two flexile ode whoe preter re ω 8.9 rd/ ζ.39 d ω 56. rd/ ζ Copyright 7 y ASME

7 B. Cloed-Loop Syte The cloed-loop yte ued i the rootic experiet i how i Fig. 4. Note tht the otor hft poitio x w ued feedck for odel tchig rther th the lik poitio x ecue of the tility iue. The referece odel w choe F ( ) whoe ω 5 rd/ d.7. i lo poile. x ( rd) x ( rd) ( 5) + (.7)( 5) + ( 5) ζ A differet choice of F ( ) () Tie () ipleeted. The e cotroller C w ued. However the iput hper IS w deiged uig the ode preter of the plt P which re ω ζ d ω ζ. r _ + C v IS r Fig. 5 Trditiol cloed-loop igl hpig. C. Experietl Reult Fig. 6 how the trckig reult. The lik gulr poitio x i plotted i olid lie veru it referece r i dotted lie. Fig. 6() i of the propoed CLSS with ier-loop odel tchig where Fig. 6() i of the trditiol CLSS. The lik poitio ocillted ore whe the trditiol CLSS w ued. Eve though there i the iput hper deiged to uppre the virtory ode of the plt the ocilltio coe fro the feedck cotroller C. To ee thi clerly Fig. 7 copre the cotrol effort ued y the propoed techique (Fig. 7()) to tht ued y the trditiol CLSS (Fig. 7()). Becue the propoed techique reduce the cot of feedck dicued erlier i the iultio ectio it cotrol effort h ore ditriutio d lower pek. P x () Tie () Fig. 3 Syte idetifictio reult. () Lik poitio. () Motor hft poitio. Lik poitio v referece (deg) r x - F Lik poitio v referece (deg) Tie () r _ + C v IS r e u x F + G P _ x P r - x Fig. 4 Cloed-loop igl hpig with ier-loop odel tchig. The tility rgi pecifictio () d the odel tchig pecifictio (3) were eforced. Fro the ope-loop hpe it w ufficiet to ue iple gi G ( ) 3. The prefilter w et equl to the referece odel tht i F F. Two ZVD iput hpig filter (4) were ccded. They were deiged uig the ode preter ω d ζ of P ( ) d ω d ζ of F ( ). The cotroller C w choe PI cotroller C ( ) For coprio the trditiol cloed-loop igl hpig yte whoe digr i how i Fig. 5 w lo Tie () Fig. 6 Lik poitio (i olid lie) veru it referece (i dotted lie). () Propoed CLSS with ier-loop odel tchig. () Trditiol CLSS. Fig. 8() how the odel tchig perforce y plottig the otor hft poitio x veru the output x fro the referece odel F. Becue x cloely tche x the ier-loop yte tche the referece odel F. Whe the plt i ucerti for exple the pylod t the tip w icreed y 3% i the experiet iilr trckig reult to tht of Fig. 6() w otied. Fig. 8() i reult of plcig gulr velocity eureet eor t the root tip. The dotted lie i of the trditiol CLSS where the olid lie i of the propoed CLSS 7 Copyright 7 y ASME

8 with ier-loop odelig tchig. The trditiol CLSS h pproxitely five tie ore virtio th the propoed CLSS. Cotrol effort (v) Cotrol effort (v) - Tie () Tie () Fig. 7 () Cotrol effort of the propoed techique. () Cotrol effort of trditiol CLSS. Shft poitio v odel output (deg) 5-5 x x Tip gulr velocity (v) Tie () Tie () Fig. 8 () Motor hft poitio (i olid lie) veru referece odel output (i dotted lie) of the propoed techique. () Tip gulr velocity of the propoed techique (i olid lie) veru tht of trditiol CLSS (i dotted lie). CONCLUSIONS A ovel techique i propoed i thi pper. A ier-loop feedck cotroller i ued to tch the ucerti flexile plt to exct referece odel. A reult the cloed-loop iput hper c e deiged fro the exct odel d c e horte. Thi led to reductio i the tie dely i the feedck loop d icreig of cotrol dwidth. The techique lo pplie to tie-vryig or olier plt. Future work iclude pplyig thi techique to ul cotrol of flexile yte i which hu opertor i the outer-loop feedck cotroller. A ore rigorou proof o the reductio of cot of feedck i lo the future work. ACKNOWLEDGMENT The uthor would like to thk Crig Borghei d Teroft for their evlutio copy of the QFT Toolox. REFERENCES [] O. J. M. Sith Poict cotrol of dped ocilltory yte Proceedig of the IRE vol. 45 o. 9 pp Sep [] J. R. Huey d W. Sighoe Tred i the tility propertie of CLSS cotroller: root-locu lyi IEEE Trctio o Cotrol Syte Techology vol. 8 o. 5 pp Sep.. [3] R. Tg d J. Hug Cotrol of ridge cre with ditriuted- pylod uder widy coditio Mechicl Syte d Sigl Proceig vol pp My 6. [4] M. J. Mghoudi Z. Mohed A. R. Hui d M. O. Tokhi A optil perforce cotrol chee for 3D cre Mechicl Syte d Sigl Proceig vol pp J. 6. [5] J. J. Potter C. J. Ad d W. Sighoe A plr experietl reote-cotrolled helicopter with upeded lod IEEE/ASME Trctio o Mechtroic vol. o. 5 pp Oct. 5. [6] W. Chtltgulchi P. Poedeg d N. Pogpich Iprovig cloed-loop igl hpig of flexile yte with Sith predictor d qutittive feedck Egieerig Jourl vol. pp. 3 Oct. 6. [7] M.-C. Pi Rout iput hpig cotrol for ulti-ode flexile tructure uig euro-lidig ode output feedck cotrol J. of the Frkli Ititute vol. 349 o. 3 pp Apr.. [8] Z. N. Moud d K. A. Alhzz Frequecy-odultio iput hpig cotrol of doule pedulu overhed cre J. of Dyic Syte Meureet d Cotrol vol. 36 o. pp. Mr. 4. [9] D. Yu d T. Chg Model referece iput hper deig with pplictio to high-peed rootic workcell with vrile lod IEEE Tr. o Idutril Electroic vol. 55 o. pp Fe. 8. [] J. H Z. Zhu Y. He d J. Qi A ovel iput hpig ethod ed o yte output J. of Soud d Virtio vol. 335 pp J. 5. [] L. Yu d T. N. Chg Model referece zero virtio cotrol of ultrhigh preciio piezoelectric opoitioer i Proc. ACC Bltiore MD pp [] D. Fujiok d W. Sighoe Cotrol effort reductio lyi of zero-virtio odel referece cotrol for cotrollig tie-vryig plt i Proc. ACC 4 Portld OR pp Copyright 7 y ASME

9 [3] W. Chtltgulchi d P. Kveeootoroh Iprovig route of iput hpig techique with odel referece itertive lerig cotrol i Proc. MENETT 4 Khoke Thild pp. 6. [4] W. Chtltgulchi D. Kijdech T. Bejleryro d S. Dyot Qutittive feedck iput hpig for flexile-joit root ipultor J. of Dyic Syte Meureet d Cotrol vol. 38 o. 6 pp. Ju. 6. [5] I. Horowitz Qutittive Feedck Deig Theory. Boulder CO: QFT Pulictio 993 pp [6] N. C. Siger d W. C. Seerig Prehpig cod iput to reduce yte virtio J. of Dyic Syte Meureet d Cotrol vol. o. pp Mr Copyright 7 y ASME