Precise Position Control of Pneumatic Servo System Considered Dynamic Characteristics of Servo Valve

Transcription

1 Precie Poitio Corol of Peumatic Servo Sytem Coidered Dyamic Characteritic of Takahi MIYAJIMA*, Hidekui IIDA*, Tohiori FUJITA**, eji AWASHIMA*** ad Tohiharu AGAWA*** * Graduated School Stude, Tokyo Iitute of Techology 9 Nagatuda-cho, Midori-ku, Yokohama, 6-8 Jaa ( miyajima@k-k.i.titech.ac.j) ** Deartme of Machiery Sytem Egieerig, Tokyo Deki Uiverity - adaihiki-cho, Chiyoda-ku, Tokyo, Jaa *** Preciio ad Ielligece Laboratory, Tokyo Iitute of Techology 9 Nagatuda-cho, Midori-ku, Yokohama, 6-8 Jaa ABSTRACT Precie oitioig ytem i required i the field of emi-coductor maufacturig roce. A eumatic ervo table ytem i oe of a recie oitioig ytem. The feature of the table are little frictio force ad little heat geeratio. Geerally, the coroller of thi ytem i deiged by eglectig the characteritic of ervo valve. However, i high frequecy bad, the reoe of thi ytem become uable becaue of the characteritic of the valve. I thi aer, we demorate that by coiderig the characteritic of ervo valve, the oitio corol of a eumatic ervo table could be imroved. Firt, the dyamic characteritic of ervo valve were examied. It became clear that the characteritic could be decribed a a ecod-order ytem. The, the ervo table ytem wa deiged a a fifth-order ytem. It became clear that the oitio accuracy of thi ytem were greatly imroved. EY WORDS Peumatic Sytem, Precie Poitioig,, Pole Aigme NOMENCLATURE vlv : valve gai [m/( V)] : Lalace oerator [1/] a : acceleratio [m/ ] Se : effective area [m ] f : frequecy [Hz] α : arameter of α β diagram method [-] j : jerk [m/ ] β : arameter of α β diagram method [-] a : table acceleratio gai [V/(m/ )] ζ : damig ratio [-] : flow rate gai [m/( V)] : omial agular frequecy [rad/] : table roortioal gai [V/m] : atural agular frequecy [rad/] : valve roortioal gai [V/m] (uffix) v : liearized ervo valve gai [m /V] t : value of ervo table ytem v : table velocity gai [V/(m/)] : value of ervo valve v : valve velocity gai [V/(m/)] ref : referece value 11 miyajima 1/6

2 INTRODUCTION Precie oitioig ytem are very imorta i the field of emi-coductor maufacturig roce. I thi regio electro-motio ytem are widely ued, but the heat from the motor diturb the oitio corollability ad the machiig accuracy. To overcome the heat geeratio roblem, we tried to coruct eumatic recie oitioig ytem. The feature of the eumatic ytem are little heat ad little magetic field geeratio. However, the corol of thi ytem i very difficult becaue of the oliearity of eumatic ytem uch a tick-li heomea [1] []. We have develoed a eumatic ervo table ytem with air bearig. The tick-li heomea were overcome by uig air bearig. Thi ytem reached high oitioig accuracy. However, i high gai regio, the reoe of thi ytem become uable. The reao of thi uable reoe i the dyamic characteritic of the ervo valve. Geerally i a eumatic ervo ytem, the dyamic characteritic of the ervo valve are eglected. Becaue the dyamic characteritic of the ervo valve i ufficiely high comared to that of the eumatic ervo ytem. I thi aer, the dyamic characteritic of the ervo valve were meaured exerimeally. It ca be decribed a a ecod-order ytem. Therefore, the model of the ervo table ytem coidered the dyamic characteritic of the ervo valve become a fifth-order ytem. After that, we rooed the deig method of the coroller of thi ytem. To realize the rooal corol method, the ervo valve that ca be et freely the dyamic characteritic i eceary. The we develoed a ovel ervo valve, which amed a the recie oitio corollable ervo valve. By coiderig the dyamic characteritic of the valve, it i cleared that the raide ad the oitio accuracy of thi ytem are greatly imroved. PNEUMATIC SERVO TABLE Peumatic Servo Table The eumatic ervo table ytem i oe of a recie oitioig ytem uig air ower. Thi ytem ha a air bearig o the lidig urface to reduce frictio force. By uig a air bearig, thi ytem ca corol the lider oitio accurately. Figure 1 ad how the hoto ad the chematic diagram of thi ytem. Thi ytem i coructed from a eumatic actuator with air bearig, a air of ervo valve ad a PC to corol ytem. Full Stroke of Servo Table [mm] Diameter of Peumatic Actuator [mm] Servo Table Peumatic Actuator Figure 1 Photo of Peumatic Servo Table Sytem Liear Scale Servo Am1 Electric Sigal Air Flow Peumatic Actuator Poitio Seor Air Bearig Servo Am D/A Coverter Digital I/O Pule Couer Peroal Comuter Figure Schematic Diagram of Peumatic Servo Table Sytem Third-order Model From liearized equatio of thi ytem, the oe-loo trafer fuctio of the eumatic actuator i give a a third order trafer fuctio []. ( P ) (1) ( + ) The atural agular frequecy i uder 6[rad/]. O the other had, that of the ervo valve i over 6[rad/]. From thi relatio, the dyamic characteritic of the ervo valve are egligible. By eglectig the dyamic characteritic of the ervo valve, the oe-loo trafer fuctio of the ervo valve i give by; P ( ) () v A PDD corol method wa alied to thi ytem. Thi corol method feedback oitio, velocity ad 11 miyajima /6

3 acceleratio. A a reult, the cloed-loo trafer fuctio i the rd-order model i give by [] G ( ) ) v + ) v ( 1+ ) + v a v + v (). Figure how the block diagram of the rd-order model. We deiged the feedback gai by α-β diagram method []. By uig α-β diagram method, v ad a are domiated by, α ad β. a v α 1/ ( ) / β v ( / ) v v / 1 () () The arameter α ad β are defied from a uitable gai margi ad a hae margi. After that, v ad a are domiated by. I thi third-order model, the raide ad the oitio accuracy are domiated by the value of. To imrove thee erformace, the large value of i required. However, thi ytem become uable i the exerime whe i icreaed. Thi uable heomeo i coidered to be becaue of the liearizatio of the ytem. Therefore, we tudied the mai factor of thi iability. It became clear that the mai factor wa the dyamic characteritic of the ervo valve. Therefore, the corol model that coidered the dyamic characteritic of the ervo valve mut be coidered. Fifth-order Model We meaured the dyamic characteritic of the ervo valve exerimeally. Figure how the exerimeal reult of the dyamic characteritic of the ervo valve made by FESTO MPYE--M-1 B-SA. It ca be decribed a a ecod-order trafer fuctio give i Eq. (6). Gai [db] Phae [deg] P ( ) 1[Hz], ζ + ζ f [Hz] Meaurig Reult Secod Order Trafer Fuctio (6) Peumatic Actuator x ref v ( + ) x Figure Bode Diagram of Commercially Available a v Figure Block Diagram of rd-order Model x ref + ζ + ( + ) Peumatic Actuator a v x Figure Block Diagram of th-order Model 11 miyajima /6

4 From Eq. (1) ad (6), the oe-loo trafer fuctio of thi ytem with the dyamic characteritic of the ervo valve i derived a a th-order fuctio. P all ( ) (7) + ζ + ( + ) The, the block diagram of whole ytem i how a the Figure. The cloed-loo trafer fuctio i give by G( ) ) v v ) + ζ ( ζ + v a ) ( 1+ ) + v + ( + Root Locu o Fifth-order Model v ) + + (8). We examied the varyig of the ole of thi ytem from the root locu. Figure 6 how the root locu of thi ytem. From Figure 6, it i cleared that the ole, which domiated by the ervo valve characteritic, move uable lae whe i over 8. To tabilize thi ytem, a high erformace ervo valve that ca et freely ad ζ i required. The, we develoed a ovel ervo valve which amed the recie oitio corollable ervo valve Im SERVO VALVE A eumatic recie oitio corollable ervo valve ha bee develoed[]. Figure 7 ad 8 how the exteral view ad chematic diagram of thi ervo valve. To realize high dyamic characteritic, the erformace of the dilaceme eor to meaure the ool oitio of the ervo valve i very imorta. The reolutio of thi oitio eor i ubmicro order. Becaue the frictio force of the ool diturb the corollability of the ervo valve, we attached a air bearig to thi ervo valve. The corol method of thi ervo valve i the PD-corol. The, the block diagram of thi valve i derived a Figure 9. The cloed-loo trafer fuctio of thi ervo valve i give by vlv v ( ) (9). + vlvv + vlv P From Eq. (6) ad (9), the corol gai are give by / vlv (1). v ζ / vlv It i clear that we ca deig ad ζ at a certai value by gai tuig. The reoe of thi ervo valve wa examied. I thi exerime, ad ζ wa et [Hz] ad.7. Figure 1 how the te reoe of the ool oitio. The ool oitio i ettled romtly. Figure 11 how the frequecy reoe of the ool oitio at the frequecy of [Hz]. The ool oitio follow well with the referece trajectory. Figure 1 how the bode diagram of thi valve. It i cleared that thi valve ca et ad ζ freely a we deired, ad the dyamic characteritic are greatly imroved comared with the commercially available oe (Figure ) Re Figure 6 Root Locu of th-order Model PRECISE POSITION CONTROLLABLE Figure 7 Photo of Precie Poitio Corollable 11 miyajima /6

5 Referece Trajectory Exerimeal Reult x [µm] Figure 8 Schematic Diagram of Precie Poitio Corollable t[] x _ref vlv v x Figure 11 Frequecy Reoe of Develoed (f [Hz]) Figure 9 Block Diagram of Develoed G[dB] -1 Exerimeal Reult [Hz], ζ. [Hz], ζ 1. x [µm] 7 6 Referece Poitio Exerimeal Reult φ[deg] Theoritical Curve [Hz], ζ. [Hz], ζ f[hz] t[] Figure 1 Ste Reoe of Develoed Figure 1 Bode Diagram of CONTROL METHOD AND EXPERIMENTAL RESULTS A corol method for thi fifth-order ytem wa coidered. We elected the ole aigme method a ITAE criterio. The ITAE criterio i give by G( ) (11). 11 miyajima /6

6 x [mm] 1 x ref a ref FESTO Precie Poitio Corollable a [m/ ] We coructed a eumatic ervo table ytem with the recie oitio corol ervo valve. The ITAE criterio ole aigme method wa ued for the gai tuig of thi ytem. The oitio followig error of the ervo table i reduced by the rooal corol method. The maximum oitio error i reduced to half ad the teady velocity error i reduced to oe-third. It wa how that the corollability of the ervo table i imroved by uig the recie oitio corollable ervo valve. We aim decreae of the followig error of the ervo table by tudyig better gai tuig method. REFERENCES e [µm] t [] Figure 1 Referece Trajectory ad Exerimeal Reult From Eq. (8) ad (11), the dyamic characteritic of the ervo valve ad the feedback gai of the eumatic ervo table ytem were determied. Figure 1 how the exerimeal reult of the rooal coroller ad that of the reviou corol method. Uer figure how the referece trajectorie of the ytem. The oitio referece trajectory i deiged a th-order curve to corol thi ytem accurately. Lower figure how the oitio error of the ervo table. It i clear that the oitio error i greatly imroved comared with a commercial available ervo valve by uig ITAE criterio corol method. 1. Hamiti., Voda-Beaco A., ad Roux-Buio H., Poitio Corol of a Peumatic Actuator Uder the Ifluece of Stictio. Corol Egieerig Practice, 1996, -8, Uebig M., Vaugha N.D., ad Surgeor B.W., No Liear Dyamic Modelig of a Peumatic Servo Sytem. The th Scadiavia Ieratioal Symoium o Fluid Power, agawa T., Tokahiki L.R., ad Fujita T., Accurate Poitioig of a Peumatic Servo Sytem with Air Bearig. Power Tramiio ad Motio Corol,, Nakata, Utility of Third-order Feedback Corol (Jaaee), 1978, Takahi M., azutohi S., Takahi S., Tohiori F., eji., ad Tohiharu., Develome of Peumatic High Preciio Poitio Corollable, Proc. of IEEE/CCA,, CONCLUSION We coructed a eumatic ervo table ytem coidered the dyamic characteritic of the ervo valve. It became clear that the dyamic characteritic of the ervo vale effect to the erformace of the eumatic ervo table. I thi aer we iroduced a recie oitio corollable ervo valve. Thi valve ca et freely the dyamic characteritic by gai tuig. We meaured the dyamic characteritic of thi ervo valve. From the dyamic characteritic meaureme, it i cleared that the dyamic characteritic of the ervo valve i a twice of that of a commercially available oe. 11 miyajima 6/6