Gain-scheduling of Acceleration Estimator for Low-velocity Measurement with Encoders

Transcription

1 Jue -5, INTEX, Gyeoggi-Do, orea Gai-chedulig of Acceleratio Etimator for Low-velocity Meauremet with Ecoder Seug-Woo So, Sag-Hu Lee ad Jog-Sug Hur Electro-Mechaical Reearch Ititute, Hyudai Heavy Idutrie 0-8, Mabuk-ri, Gueog-eup, Yogi-i, Gyeoggi-do, orea (Tel : ; {o mrhlee jhur}@hhi.co.kr) Abtract: I mot of motor-drive motio cotrol ytem, a ecoder i ued to meaure a poitio of the motor ad the velocity iformatio i obtaied by meaurig the poitio icremet over a amplig period. The quatizatio effect due to limited reolutio of the ecoder iduce ome meauremet error, ad coequetly caue deterioratio of the motio performace epecially i low velocity. I thi paper, we propoe a gai-cheduled acceleratio etimator which work i wider velocity rage tha the origial acceleratio etimator. We ivetigate ad aalyze characteritic of the velocity meauremet mechaim which take ito accout the quatizatio effect of the ecoder. Next, we itroduce the acceleratio etimator ad propoe a gai-cheduled acceleratio etimator. The badwidth of the gai-cheduled acceleratio etimator i automatically adjuted by the velocity commad. Fially, it performace i evaluated by imulatio ad experimet, ad the reult are compared with thoe of a covetioal method ad the origial acceleratio etimator. eyword: ecoder, velocity meauremet, acceleratio etimator, gai-chedulig. INTRODUCTION I mot of motor-drive motio cotrol ytem, ecoder are ued to meaure the poitio, ad the velocity iformatio i acquired typically by meaurig the poitio icremet over amplig period. But the quatizatio effect by limited reolutio of the ecoder ad amplig period caue ome meauremet error of the velocity, ad it may brig out deterioratio o the motio performace. The deterioratio become eriou i low velocity rage. For high accuracy of the velocity meauremet, a high reolutio ecoder i required, however it icreae the cot of the ytem. So a umber of reearcher have propoed everal alterative uch a digital filter, model-baed oberver ad ome kid of etimator to improve the accuracy of velocity meauremet without additioal cot. Carpeter et al. reearched the improvemet of the velocity meauremet through the ue of digital filter []. A digital filter baed o a adaptive leat quare approach wa propoed ad the performace of variou digital filter wa compared through experimetal reult. Yag ad e developed a cloed-loop velocity oberver coiderig a DC motor model []. I order to reduce the ripple o the etimated velocity, the meaured iput poitio of the velocity oberver wa compeated with the previou average peed. im ad Sul uggeted a motor peed etimator uig alma filter [3]. It etimate ot oly motor peed but alo diturbace torque of the motor ad ha the robut characteritic to parameter variatio. Lee ad Sog developed a acceleratio etimator approach for velocity meauremet [4]. It i oe of the efficiet algorithm to meaure the velocity via acceleratio etimatio. The acceleratio etimator ca be regarded a a kid of low-pa filter with two gai, ad it badwidth i characterized ad limited by thee gai. Oce the gai of the acceleratio etimator are tued for a pecified velocity, it performace may fall off i other velocitie. I thi paper, we propoe a gai-chedulig method of the acceleratio etimator to meaure the velocity i wide velocity rage. It badwidth i automatically adjuted accordig to the velocity commad. I ectio, we dicu the characteritic of velocity meauremet due to the quatizatio effect of the ecoder. I ectio 3, we itroduce the acceleratio etimator ad ugget to chedule it gai to expad workig velocity rage. It i alo explaied that the gai are automatically adjuted by the velocity commad of the motio cotrol ytem. It performace i evaluated through computer imulatio ad experimet i ectio 4. The reult are compared with thoe of a covetioal method ad the origial acceleratio etimator.. VELOCITY MEASUREMENT IN MOTION CONTROL SYSTEM I may applicatio, a fid-time method which ue backward poitio differece i typically employed to obtai the velocity from the poitio of the ecoder. The k th velocity v by thi method i calculated by Eq. (). x( kt ) x(( k ) T ) vkt ( ) = () T where x i the poitio of the ecoder ad T i the amplig time. It i, however, kow that the fid-time method work more accurately i high velocity rage tha i low velocity rage due to the quatizatio effect by limited ecoder reolutio ad fid amplig period. Thi quatizatio effect trigger the poitio error maximally of ± ecoder pule per

2 amplig period. Figure how a example of the meaured ecoder pule trai. Whe the actual poitio icremet per amplig period x i.5, the meaured poitio icremet per amplig period ˆx i or. It how that uavoidable error occur i velocity meauremet. The ratio of the error to the actual velocity i relatively large i low velocity rage. Therefore it i more difficult to cotrol the motio i low velocity rage tha i high velocity rage. Jue -5, INTEX, Gyeoggi-Do, orea Thee feature make it difficult to meaure the velocity preciely, ad deteriorate the performace of the motio cotrol epecially i low velocity. For high accuracy of the velocity meauremet, a high reolutio ecoder i eeded; however it icreae the cot of the ytem. I order to improve accuracy of velocity meauremet without additioal cot, we try to apply a gai-cheduled acceleratio etimator to the motio cotrol ytem i ext ectio Fig. A example of ecoder pule trai avaagh ad Murphy reearched thi quatizatio effect of the dicrete ecoder [5]. They preeted the pectral characteritic of the differetiatio related to quatizatio error. The power pectral deity of the velocity meauremet error oly by quatizatio effect i a follow. S ( ) ( co( ) ( v f = π f δ ( f )) 4π k f k () where f k i < k x T k 0 < x mea a fractio part of x. ad the mathematical operatio From Eq. (), the velocity meauremet ha a pecific characteritic that the power ditributio i provided dicretely < k x with the Dirac delta fuctio at frequecie, fk =. T Ad the pheomeo of the overlap, kow a the foldig, ca occur at f k above the Nyquit frequecy, fn = f =. T Figure how a example of the velocity obtaied by the fid-time method durig the motio cotrol of a motor with T = mec. It average value i x 5.30 pule per amplig period. Figure 3 how the power pectrum of the experimetal data i Figure ad the theoretical data with x = 5.30 pule per amplig period. I the theoretical data, the power ditributio appear dicretely at f = 30 Hz < 5.30 < 5.30 by = 30, f = 398 Hz by = 60 ad the aliaig with f N = = 500 Hz, ad o o. There i a T imilar power ditributio i domiat frequecy rage except for low frequecy compoet, which i related to ome diturbace of cotrol ytem. Coequetly, the velocity meauremet by the fid-time method ha two repreetative feature i ecoder-baed motio cotrol ytem. ) The ratio of the error to the actual velocity icreae a the velocity low dow. ) Power pectrum of the velocity error due to quatizatio effect i ditributed dicretely with wide frequecy rage. Ecoder poitio icremet (pule per amplig time) Power pectrum time, ec (T =0.00 ec) Fig. A experimetal velocity data et by a fid-time method Theoretical Reult Experimetal Reult frequecy, Hz (T = 0.00 ec) Fig. 3 Power pectrum of velocity for experimetal ad theoretical data et 3. ACCELERATION ESTIMATOR WITH GAIN-SCHEDULING 3. A acceleratio etimator [4] The acceleratio etimator propoed by Lee ad Sog i ueful for low acceleratio ad velocity rage. It i kow that the deig of the acceleratio etimator i baed o two fact: ) The poitio iformatio baed o the ecoder igal i quite accurate. ) Numerical itegratio i more table ad accurate tha umerical differetiatio. A how i Figure 4, the acceleratio etimator i compoed of two umerical itegrator ad a PD cotroller, of which gai are ad. x i the ecoder poitio, a e i the etimated acceleratio, v e i the etimated velocity, ad i the etimated poitio. The etimated acceleratio i obtaied from PD cotrol igal a Eq. (3) itead of a

3 covetioal double differetiatio of the poitio. The velocity meauremet i acquired by itegratig the etimated acceleratio. x ae ve Jue -5, INTEX, Gyeoggi-Do, orea ζ i et to a critical dampig with a value of The procedure of the gai-chedulig i a follow. Firt, it miimum badwidth ω0 which i acceptable i the velocity meauremet hould be determied. The, et the deired low velocity vmi ad derive ω by Eq. (5). A appropriate value of a ca be eaily foud out by ivetigatig acceptable badwidth at everal velocitie. Fially, the gai ad are obtaied by Eq. (6). dx = (3) e ae ( x ) dt Fig. 4 Block diagram of a acceleratio etimator ω = ω, if v < v 0 ref mi ω = a ( v v ) ω, if v v ref mi 0 ref mi = ω = ζω (5) (6) The trafer fuctio from x to (4). x e ca be derived a Eq. ω ω 0 ω = = x ζω ω where ζ, ω are the dampig ratio ad the badwidth, repectively. (4) v mi v ref Fig. 5 The relatiohip betwee ω ad v ref for gai-chedulig of a acceleratio etimator A how i Eq. (4), the acceleratio etimator ca be regarded a a kid of ecod-order low-pa filter expreed by two parameter. The acceleratio etimator i characterized by it two gai. If the acceleratio etimator i ued to meaure the velocity i motio cotrol ytem, ζ ad ω are importat factor which determie it dyamic repoe. ζ i uually et to 0.707, which i a critical dampig, becaue it provide fat repoe without overhoot. O the other had, ω i tued appropriately accordig to applicatio eed. It ha a igificat ifluece o the performace of the motio cotrol. 3. Gai-chedulig of the acceleratio etimator I order to meaure the velocity effectively, oie filterig ad phae delay of the acceleratio etimator hould be compromied, becaue arrow badwidth for oie filterig make phae delay large; if phae delay i large, motio cotrol may become utable. A the ratio of the error to the actual velocity icreae i low velocity rage, arrow badwidth i eeded to ue the meaured velocity for motio cotrol. O the other ide, ice the ratio of the error to the actual velocity i high velocity i maller tha that i low velocity rage, it i reaoable to et the relatively wide badwidth which ca reduce ueceary delay of velocity meauremet. Oce the gai of the acceleratio etimator are fid for a pecified velocity, the fid badwidth may deteriorate the performace uch a oie atteuatio ad phae delay i other velocity rage. We propoe a gai-cheduled acceleratio etimator. The purpoe of the gai-chedulig i to et the appropriate badwidth accordig to the ratio of the error to the actual velocity. The badwidth of the gai-cheduled acceleratio etimator i automatically adjuted by the velocity commad. A the velocity commad low dow, the gai are tued to et arrow badwidth. A how i Figure 5, it badwidth ω i a fuctio of velocity commad v of cotrol ytem. ref 4. SIMULATION AND EXPERIMENT We evaluate the performace of the gai-cheduled acceleratio etimator through computer imulatio ad experimet. Figure 6 how a block diagram of a experimetal etup. The experimetal etup i compoed of a motor, a ecoder, ad a PI-cotroller with the amplig period T = mec. The motor i a 00W AC ervo motor ad a load i attached to the motor through a haft a how i Figure 7. The reolutio of the ecoder i 048 cout per revolutio ad quadrature decodig i ued. I the experimet, ζ ad ω of the acceleratio etimator are et to ad 00Hz, repectively. ζ of the gai-cheduled acceleratio etimator i alo ad it ω i expreed by Eq. (7). Each compoet ad eviromet i imulatio i modeled idetically o the experimetal etup. ω = 67.3 vref 30, if vref 0 a = 67.3, v = 0, ω = 30Hz mi 0 Fig. 6 Block diagram of experimetal etup (7)

4 Whe a motor velocity i cotrolled to follow a trapezoidal velocity commad, a fid-time method, a acceleratio etimator ad the propoed gai-cheduled acceleratio etimator are ued repectively to meaure the velocity of the motor. Maximum velocity commad i x.3653 pule per amplig period. It correpod to the velocity of.047 radia per ecod. ecoder motor load Fig. 7 Experimetal hardware Figure 8 ad Figure 9 preet the imulatio ad experimetal reult, repectively. The experimetal reult i almot imilar to the imulatio reult except the low frequecy ripple oberved i experimetal reult. It i due to ucertaitie of the model betwee the imulatio ad the experimet. Practically, the cyclic diturbace to the motor take place i experimetal etup becaue the haft aligmet betwee the motor ad the load i ot fitted perfectly. I the fid-time method, it i how that the velocity meauremet i very iaccurate ad the cotrol performace i poor. The iput torque of the motor i very oiy, ad it ca geerate the izzle i the motor. It i dagerou ice the oie raie the vibratio ad horte the lifetime of a machie. O the other had, both the acceleratio etimator ad the propoed gai-chedulig method are more table. Their velocity i cotrolled accurately with the mooth torque. The reult of the gai-cheduled acceleratio etimator differ ubtly from that of the acceleratio etimator. It i how that the gai-chedulig method i more effective to reduce the oie ear zero velocity tha the acceleratio etimator. Therefore the gai-chedulig method eem to have a advatage which prevet the motor from udeirable cotrol uch a tick-lip or directio chage by oiy iput torque i extremely low velocity. I additio, it i expected that the gai-chedulig by the velocity commad will eable the appropriate badwidth of the acceleratio etimator to be et i high velocity. Jue -5, INTEX, Gyeoggi-Do, orea etimator with repect to the phae delay of the velocity meauremet i wide velocity rage. REFERENCES [] P. S. Carpeter, R. H. Brow, J. A. Heie, ad S. C. Scheider, O Algorithm for Velocity Etimatio Uig Dicrete Poitio Ecoder, Proc. of the t IEEE It. Cof. o Idutrial Electroic, Cotrol, ad Itrumetatio, Vol., pp , 995 [] S. Yag ad S. e, Performace Evaluatio of a Velocity Oberver for Accurate Velocity Etimatio of Servo Motor Drive, IEEE Tra. o Idutry Applicatio, Vol. 36, No., pp , 000. [3] H. im ad S. Sul, A New Motor Speed Etimator uig alma Filter i Low Speed Rage, IEEE Tra. O Idutrial Electroic, Vol. 43, No. 4, pp. 498~504, 996. [4] Se-Ha Lee ad Jae-Bok Sog, Acceleratio Etimator for Low-velocity ad Low-acceleratio Regio Baed o Ecoder Poitio Data, IEEE Tra. o Mechatro., Vol. 6, pp , 00. [5] R. avaagh ad J. Murphy, The Effect of Quatizatio Noie ad Seor Noideality o Digital Differetiator-Baed Rate Meauremet, IEEE Tra. o Itrum. Mea., Vol. 47, No. 6, pp , CONCLUSION I thi paper, we propoed a gai-cheduled acceleratio etimator of a appropriate badwidth for the velocity meauremet i wide rage of velocity. We dicued characteritic of velocity meauremet due to the quatizatio effect of the dicrete ecoder. A acceleratio etimator wa itroduced, ad it gai-chedulig cheme wa propoed. It performace wa evaluated i velocity cotrol ytem through computer imulatio ad experimet. The reult howed that the gai-chedulig method wa table ad more effective to reduce the oie ear zero velocity tha the acceleratio etimator. From the reult, the poibility of the gai-chedulig by velocity commad wa verified to effectively et the badwidth of the acceleratio etimator. I the future, reearch work to demotrate the uefule of the gai-cheduled acceleratio etimator for motio cotrol ytem will be fulfilled. A it a firt tep, we are goig to evaluate the performace of the gai-cheduled acceleratio

5 Jue -5, INTEX, Gyeoggi-Do, orea (a) fid-time method (a) fid-time method (b) acceleratio etimator with ζ = ad ω = 00 (b) acceleratio etimator with ζ = ad ω = 00 (c) gai-cheduled acceleratio etimator with ζ = , ω 30 ad a = = Fig. 8 Computer imulatio reult (c) gai-cheduled acceleratio etimator with ζ = , ω 30 ad a = = Fig. 9 Experimetal reult