High Steady-State Accuracy Pneumatic Servo Positioning System with PVA/PV Control and Friction Compensation

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1 Plee cite thi finl verion: Ning, S. nd Bone, G. M., "High Sted-Stte Accurc Pneumtic Servo Poitioning Stem with PVA/PV Control nd Friction Comention", Proceeding of the IEEE Interntionl Conference on Rootic nd Automtion, Whington, DC, ,. DOI: 1.119/ROBOT High Sted-Stte Accurc Pneumtic Servo Poitioning Stem with PVA/PV Control nd Friction Comention Shu Ning nd Gr M. Bone* Dertment of Mechnicl Engineering, McMter Univerit, Hmilton, Ontrio, Cnd, L8S 4L7. *Correonding uthor. E-mil: Atrct Pneumtic ervo ctutor hve the enefit of lowcot, clenline nd high ower-to-weight rtio. However, their reltivel oor ccurc revent them from cometing with electro-mechnicl tem when higher ccurc i needed. The cue of the ted-tte error for neumtic ervo tem with n oen-center ervo vlve i invetigted. Full nonliner nd linerized lnt model re reented. An effective friction comention method i introduced which cn e dded to n control trteg. When comined with novel PVA/PV control roch, ted-tte ccurc of ±.1mm h een verified in eeriment. Thi i tenfold imrovement over revioul reorted eerimentl reult for uch tem. Thi erformnce i chieved for oth verticl nd horizontl movement with lod rnging from. to 11. kg, without re-tuning the controller. 1. Introduction In recent er mn reercher hve invetigted neumtic ervo tem due to their otentil lowcot, clen, high ower-to-weight rtio ctutor. The comreiilit of the working medi, ir, nd the lrge ttic nd Coulom friction hve mde chieving ccurte oition control chllenging rolem. Vriou roche including: dtive control [6,9] fuzz control [,5], neurl network [,4,7] nd etended PID control [1,8] hve een invetigted recentl with vring degree of ucce. (Plee ee [8] for review of erlier neumtic ervo reerch). The et tedtte ccurc chieved in reviou work i on the order of ±.mm (ee [6,8] for emle). Thi revent neumtic ervo from cometing with electro-mechnicl tem when higher ccurc i needed. Mot of thee tem were teted onl for horizontl movement, voiding the difficult introduced grvit loding. In thi er we decrie the develoment of novel neumtic ervo tem. Full nonliner nd linerized lnt model re reented. A controller i develoed incororting friction comention nd modified form of roortionl lu velocit lu ccelertion (PVA) control. Simultion nd eerimentl reult re reorted.. The Pneumtic Servo Poitioning Stem nd It Model The neumtic tem ued in thi reerch i hown in Figure 1. A rodle clinder nd n oen-center ervo vlve oth mde Feto re utilized. The orienttion of the tem cn e djuted to, 45 nd 9 with the horizontl lne. The nonliner mthemticl model of the lnt cn e ereed following eqution: m f (,,, ) (1) m f (,,, ) () m = A K A ( ) () m = A K A ( ) (4) A A cvf Fcf Fl, M = (5), = nd ( A A ) < Ff

2 Rodle Clinder A Servo Vlve M Lod B Liner Encoder m c = c f d V k vf, V ( ), V k vd ( ), V ( ), f f > < f f nd f nd nd f nd > > Where: V Volume of the chmer ued for flow rte meurement () Blnce reure in chmer A. (6) P P P Comuter Figure 1. Pneumtic ervo oitioning tem Where: A, A Piton re in chmer A nd B c vf Coefficient of vicou friction m, M flow rte into chmer A & B f, f F cf F f F l m K M, R T, Flow rte function Coulom friction force Sttic friction force Eternl lod force Rtio of ecific het c /c v Plod m Air reure in chmer A nd B Sul reure Atmohere reure Idel g contnt Stem temerture Control outut (or vlve inut) Poition of iton nd m lod Initil ditnce etween iton nd end of clinder in chmer A nd B Eqution 1 nd indicte the flow rte nd reure chrcteritic of the vlve. We hve determined tht theoreticl nli i not ufficient to roerl model thee chrcteritic. Meurement re required ince the chrcteritic re ver different for different vlve even if their orifice dimeter i the me. To void undeired tedioune of thi er, onl the finl reult for the oen-center vlve i reented follow:, > f = , f (7) f, < f 4 k vf = (8) 4 k vd = (9) c f =. c d = -.45 f =.4 f = -. V k, < nd vf f V c ( ), nd f f f m = V k ( ), > nd > vd f V c ( ), nd > d f f (1) Where:, < f = , f (11) f, > k vf = (1) k vd = (1) c f =.1 c d =-. The hicl mening of the ove eqution will e elined riefl in ection. Although the nonlinerit of thi tem i eriou, linerized model w derived. The liner model i given the trnfer function etween the inut to the ervo vlve,, nd the oition of the m lod, follow. Y ( ) = (14) X ( ) ( ) f

3 Thi model w found to e effective for imulting the cloed-loo ehviour, rovided tht the controller comente for the min nonlinerit due to friction dicued further in ection. The trnfer function for PVA control i: X ( ) = K E( ) = Y d E( ) K Y ( ) K ( ) Y ( ) v Y ( ) (15) where d i the deired oition, e i the oition error, K i the roortionl gin, K v i the velocit gin nd K i the ccelertion gin. With PV control K =. The imultion reult for PV nd PVA control of the liner lnt model (14) i hown in Figure. B comring thi imultion reult with the eerimentl reult uing the me controller hown in Figure 8 the ilit of thi model to redict the eerimentl ehvior cn e clerl oerved.. Anli of the Cue of the Sted-Stte Error Eqution 14 how tht the lnt trnfer function i fourth order tem with n integrl term. From the viewoint of control nd the liner model imultion reult hown in Figure, if PV or PVA controller i ued, eqution 6 to 1) nd the ttic friction of the clinder ( ereed eqution 5) Figure. Eerimentl oition nd error reone for PV control without friction comention. While thee eqution re comle, ome qulittive elntion re oile. The working rincile of the oen-center vlve i hown in Figure 4. Anlogou neumtic circuit re hown on the right-hnd ide of the figure PV Control K=14 Kv=1.4 PVA Control K=14 Kv=1.4 K=.4 A B () > f Chmer A i full filling, Chmer B i full dichrging O 1 O Figure. Simulted oition reone for PV nd PVA control. the ted-tte error of thi tem for te inut hould e zero. But from the ctul te reone of thi tem under PV control hown in Figure, the tedtte error i ver oviou. It i out 5 mm when the roortionl gin K =14.. Increing K cn reduce the ted-tte error ut will lo cue undeired overhoot nd tend to detilize the tem. Before we cn comente for it, we need to undertnd the cue of the ted-tte error. From our reerch, we hve found the cue i the flow nd reure chrcteritic of the oen-center te of vlve ( ereed A B O O () f f Both chmer re filling or dichrging A B (c) < f Chmer A i full dichrging, Chmer B i full filling Figure 4. Working rincile of oen-center ervo vlve

4 When the inut to the vlve,, incree, the ool of the vlve move to the left. When > f, hown in Figure 4, chmer A i connected onl with the inlet ir nd chmer B i connected onl with the tmohere. A reult, ir flow into chmer A until the chmer reure reche the ul reure,, while the ir in chmer B dichrge to the tmohere until it reure decree to tmoheric,. When < f, hown in Figure 4c, chmer A i dichrging nd chmer B i filling in mnner imilr to 4. But when f f, hown in Figure 4, chmer A i connected to oth the inlet ir nd the tmohere through two orifice: O 1 nd O, reectivel. The reure in chmer A will rech it lnce reure,, which deend on the ize of thee two orifice. When i increed, O 1 i increed nd O i decreed o tht i increed nd vice- ver. The me roce occur in chmer B, ecet the lnce reure in chmer B,, i decreed when i increed. According to thi rincile, the mimum force roduced the clinder, F m = A - A, (16) will e chnged for different vlue. The reltionhi etween F m nd i hown in Figure 5. It i clculted uing eqution 7, 11 nd 16. Three oervtion cn e mde from thi curve. Firt, the vlve inut correonding to F m =, c, i not ut.1. Second, the inut to mke chmer A full filling, f, i.4, nd the inut to mke chmer B full filling, f, i.. Third, for rnge of vlue the force F m will e le thn F f, the ttic friction force, nd the iton will not move. The meured vlue of F f for our tem i 84 N. Therefore, when.7<<.6, the iton will not move. Thi i the dedzone of the tem nd the ultimte cue of the ted-tte error. d _ e Friction Comention PVA Plnt Figure 5. Meured reltionhi etween the mimum clinder force F m nd the vlve inut. c Fm (N) f Dedzone c Vlve Inut Figure 6. Digrm of the control tem with friction comention 4. Friction Comention Friction comention mut e dded to thi control tem to void the vlve working in the rnge of the dedzone nd the reulting ted-tte error. The digrm of the control tem with friction comention i hown in Figure 6. The ide ehind the comention i follow. When the oition error i within the rnge of deired ted tte ccurc, the control vlue hould e c, o tht the force cting on the lod i zero. When the oition error i outide thi rnge, friction comention hould e dded to the control outut. The control outut with friction comention cn now e ereed the following eqution: = c e e d or c = = c δ f e >e d nd c > = c δ f e >e d nd c < f Where: c Control outut efore friction comention. δ f, δ f Comention vlue. e d Deired m. ted-tte error. The friction comention vlue hould e choen to e lrger thn the dedzone to gurntee the iton never to unle the error, e, i le thn the deired rnge of ted-tte error. Eerimentl reult hve hown tht f nd f re uitle vlue for the comention. Eerimentl reult hve roven the effectivene of thi comention method. With e d =.1 mm, the tedtte error i reduced to ±.1mm for PV control hown in Figure 7. In fct.1mm i the reolution of the liner encoder ued in thi tem. With higher reolution encoder we would eect the ted-tte ccurc to e further imroved.

5 K=14 Kv= PV Control K=14 Kv=1.4 PVA Control K=14 Kv=1.4K= Figure 7. Eerimentl oition nd error reone of PV control with friction comention. 5. Imrovement of Dnmic Performnce The ted-tte ccurc of thi neumtic ervo oitioning tem h een gretl imroved friction comention. But the dnmic erformnce of the te reone hown in Figure 7 i not good. Adding ccelertion feedck w found to reduce the undeired ocilltion. The oition reone of the tem with PVA control i hown in Figure 8. Although the lrge ocilltion during the rietime hve een reduced ccelertion feedck, there re till ome mller virtion when the iton i ver cloe to the trget oition. An emle i hown in Figure 8. We concluded thee re due to the noie in the ccelertion meurement reulting from the doule digitl differentition of the oition meurement. Bed on thee finding, miture of PVA nd PV control, which we hve termed "PVA/PV" control, w teted with thi tem. Secificll, when the iton i certin ditnce from the trget oition, 5mm w for emle, PVA control i ued. When the iton i within thi ditnce, the ccelertion feedck i turned off, nd onl PV control i ued. Eerimentl reult hve hown tht oth the dnmic nd ted-tte erformnce re ecellent for thi new PVA/PV roch hown in Figure Figure 8. Comrion of eerimentl oition reone with PV nd PVA control Figure 8. Comrion of eerimentl error reone with PV nd PVA control. PV Control K=14 Kv=1.4 PVA Control K=14 Kv=1.4 K= K=14 Kv=1.4 K= Figure 9. Eerimentl oition nd error reone of PVA/PV control.

6 6. Routne Teting The routne of thi tem h een tudied erforming eeriment under different working condition. Figure 1 how the tem reone with the me lod m ut different orienttion. Figure 11 how the tem reone with verticl orienttion nd different lod. Finll, Figure 1 how the reone for the verticl orienttion with multile etoint nd 5. kg lod. Plee note tht the me controller tuning w ued for ll eeriment. From thee eerimentl reult, it i cler tht the routne of thi neumtic ervo oitioning tem i ver good. The ted tte error cn e ket within ±.1mm for vrile working condition. The mimum overhoot i onl.5mm even for the 1mm te chnge etween etoint Figure 1. Eerimentl reone of the tem with verticl orienttion to four et oint (1mm, mm,mm, 19mm). Concluion 5 15 Horizontl M=5kg 1 5 Verticl M=5kg Horizontl -.5 Verticl Figure 1. Eerimentl reone for horizontl nd verticl orienttion. The cue of the ted-tte error for neumtic ervo tem with n oen-center ervo vlve w invetigted. Full nonliner nd linerized lnt model were derived. Uing the nonliner lnt model, the cue of the ted-tte error w determined to e comintion of the ttic friction nd the reure/flow chrcteritic of the vlve. An effective friction comention method w then develoed. When comined with new PVA/PV control roch, ted-tte ccurc of ±.1mm w reched eerimentll. Thi i tenfold imrovement over revioul reorted reult for uch tem. Thi erformnce w chieved for oth verticl nd horizontl movement with lod rnging from. to 11. kg, without re-tuning the controller M=11.kg 1 M=5.kg 5 M=.kg M=11.kg -.5 M=.kg M=5.kg Figure 11. Eerimentl reone for the verticl orienttion with different lod me. Reference 1. S. Aziz nd G.M. Bone. Automtic Tuning of Pneumtic Servo Actutor. Advnced Rootic, 1, ,.. G.S. Choi, H.K. Lee nd G.H. Choi. Stud on the Trcking Poition Control of Pneumtic Actutor uing Neurl Network. IECON 98, , S.H. Choi, C. Ahn nd C.O. Lee. Aliction of the Fuzz Logic Adtor to the Poition Control of Pneumtic Stem uing On-Off Vlve. ASME Puliction FPST v, 1-8, 1995.

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