Intelligent PI Fuzzy Control of an Electro- Hydraulic Manipulator

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1 INTERNATIONAL JOURNAL OF CONTROL, AUTOMATION AND SYSTEMS VOL.3 NO. April 014 ISSN (Prit) ISSN (Oli) Itlligt PI Fuzzy Cotrol o a Elctro- Hydraulic Maipulator Ayma A. Aly Mchatroics Sc., Dpt. o Mchaical Egirig, Assiut uirsity, Assiut, 71516, Egypt. Currtly: Mchatroics Sc., Dpt. o Mchaical Egirig, Tai uirsity, Tai, 888, Saudi Arabia. draymalaggar@yahoo.com Aly S. Abo El-Lail Dpt. o Mchaical Egirig, Assiut uirsity, Assiut, 71516, Egypt. Abstract Th dlopmt o a uzzy-logic cotrollr or a class o idustrial hydraulic maipulator is dscribd. Th mai lmt o th cotrollr is a PI-typ uzzy cotrol tchiqu which utilizs a simpl st o mmbrship uctios ad ruls to mt th basic cotrol rquirmts o such robots. Usig th triagl shapd mmbrship uctio, th positio o th srocylidr was succssully cotrolld. Wh th systm paramtr is altrd, th cotrol algorithm is show to b robust ad mor astr compard to th traditioal PID cotrollr. Th robustss ad trackig ability o th cotrollr wr dmostratd through simulatios. Idx Trms Maipulator Positio Cotrol, Fuzzy Logic Cotrol, PID, Elctrohydraulic Srodris. I. INTRODUCTION I th last w yars rsarch dotd to uzzy logic ad its applicatio to maipulators has sigiicatly icrasd. Thr ar may articls o th succssul applicatio o uzzy cotrol to lctrically actuatd maipulator, ragig rom th applicatio o a uzzy cotrol matrix (similar to a look-up tabl) to th dirct implmtatio o uzzy ruls ad mmbrship uctios. Gral issus i tuig ad alidatio o uzzy systms ha also b addrssd i may paprs[1,, 3, 4]. Th applicatio o uzzy cotrol to hydraulically actuatd maipulators, o th othr had, is spars ad ca oly b oud i a w rsarch paprs. Zhao ad Viralo [5] combid a liar stat cotrollr with uzzy rul aluatio to produc what thy amd a uzzy stat cotrollr. Th mthod idirctly dtcts th prsc o a load, basd o uzzy rul aluatio o actuator locity, ad dcids o th gais o a stat cotrollr accordigly i ordr to mak th cotrollr issiti to load ariatios. Chou ad Lu [6] dlopd a uzzy cotrollr or a class o hydraulic sro systms. Th trackig ability o th cotrollr wr dmostratd through xprimtal studis. No rport has b oud statig problms with stady-stat rrors or low dadbad oliaritis. Hydraulically actuatd robots ar, i gral, dirt rom lctrically actuatd robots [7, 8]. I a hydraulic robot gi a zro spool displacmt (i.. al closd), th arm ca b kpt i plac du to th oil trappd o both sids o th cylidr. This mas that th hydraulic robot ca com to rst quickly wh th al spool rturs to its utral positio. I a low rictio lctric robot th lik ca still mo ad may pass th targt poit with a zro motor oltag. Th amout o orshoot dpds o th irtia ad th locity. Ngati motor oltag may b dd bor th arm rachs th dsird positio to prt xcssi orshoot. Also, a costat motor oltag is rquird i lctric robots, i ordr to kp th arm i plac i th prsc o graity. Sic th cotrol rquirmts ad charactristics o ach class o actuatio dir, thus similar uzzy ruls ad stratgis do ot work qually wll o both lctric ad hydraulic robots. Th dyamic charactristics o th sro-hydraulic systm ar always complx ad highly oliar. Moror, thr ar too may ucrtaitis i it ; or xampl, th iscosity o oil, th bulk modulus, th oil olum, th systm prssur, th war ad th caitatio [9]. Th loadig coditios ar usually rathr ustady, ad th loadig orcs chag i a wid rag durig opratio. Wh th procss is complx ad oliar with ariabl paramtrs, th cotioal cotrol thory ca ot b applid. Th modr cotrol thory ad adapti cotrol tchiqus ha b usd to cotrol that plat. Howr, th adapti cotrol rquirs accurat mathmatical cotrol modl or lot o computatioal ort to stimat ad adapt th cotrollr paramtrs [10]. Th o-mathmatical approach calld Fuzzy St Thory [11], [1] is suitabl or dlopig rliabl logic cotrollr or plats with wid paramtrs ariatios. I this papr, a itlligt Fuzzy cotrollr (IFC) is prstd or positio cotrol o a lctrohydraulic sro. 19

2 INTERNATIONAL JOURNAL OF CONTROL, AUTOMATION AND SYSTEMS VOL.3 NO. April 014 ISSN (Prit) ISSN (Oli) II. SYATEM DYNAMIC MODEL Th mai rasos to us positioig sros i idustry ar th dmads o th accuracy, th stiss ad good dyamic rsposs to th chags i th commad sigal or th load. Th lctrohydraulic systm show i Fig. 1 is comprisd o a cylidr, ad 4/3 way proportioal al. A complt mathmatical modl o such a lctrohydraulic systm, or xampl, has b gi by [13]. Howr, ths quatios ar highly complx ad diicult to utiliz i cotrol dsig. A mor practical modl may b obtaid through th liarizatio o th o-liar uctios. A mathmatical modl o th plat ca b drid rom th low quatio o th al, th cotiuity quatio ad balac o orcs at th pisto. Th al low-rat quatio is highly o-liar ad dpdt o th al displacmt rom utral, which is proportioal to th iput currt I- ad th prssur drop across th load P L. From Moog Tchical bullti, a coit orm or th sro al trasr uctio, [9] is: Q C I s 1 s s 1 whr Q is th al mai stag low rat, I is th al iput, C is th total al low gai, is th al tim costat ad, ar th udampd atural rqucy ad dampig ratio o th al rspctily. Th quatios o th sroal low to ad rom th actuator (assumig symmtric al port, zro lap dsig ad zro rtur prssur) ar as ollows, For X 0 Q C WX d sg( Ps P ) Ps P, Q CdWX sg( P ) P For X 0 Q CdWX sg( P ) P Q CdWX sg( Ps P ) Ps P (3) whr X is th spool displacmt, P s is th supply prssur, is th mass dsity o th oil, C d is th discharg coicit o th oriic, W is th width o th oriic, suix dots th aular sid ad suix dots th ull sid. Th liarizd low quatio o th actuator is gi by [6]:, (1) () q l 1. V V A A. A P A (4) l l p 3 l A X p 3 A 4 1 A A B 1 A A whr p A p q q A A Pl, ql, A A, P l is th cti load prssur, q l is th cti load low rat, A is th cti pisto ara, B is th oil bulk modulus, k 1 is th lakag coicit o th pisto, X p is th pisto displacmt, V is th oil olum udr comprssio i th aular sid o th cylidr, V is th oil olum udr comprssio i th ull sid o th cylidr, A is th aular ara o th cylidr, A is th ull ara o th cylidr. It is assumd that th loadig poit may b tratd as a mass-dampr systm. Th liarizd quatio or th orc dlopd by th actuator o th loadig poit, atr limiatig th stady stat trms, ca b writt as... a M X p Bl X p (5) whr M is th mass o th load coctratd at th loadig poit ad B l is th iscous dampig coicit o th structur at that loadig poit. Equatios (9), (10),(11) ad (1) may b maipulatd ad Laplac trasormd to gi th actuator displacmt: X, X A M B V B 3 c p t c p s ( ) s (1 A 4BA A p MVt 4BA V V A A V t 3 A 1 A svt ) s 4BA whr B p = B 1 +, is th iscous rictio coicit o th pisto, is th low/displacmt gai or th mai stag o th al, c is th total low-prssur coicit ad V t is th cti trappd oil olum. (6) 0

3 INTERNATIONAL JOURNAL OF CONTROL, AUTOMATION AND SYSTEMS VOL.3 NO. April 014 ISSN (Prit) ISSN (Oli) Fig.1 Schmatic diagram o th maipulator hydraulic circuit It ca b prstd i stadard orm so as to ral quialt alus o atural rqucy ad dampig ratio may b writt or th asymmtric actuators as 0 X p 4BA V M t ad A X A s s( s 1) 0 0 c BM V t Bp 4A Vt BM (7) III. FUZZY LOGIC CONTROLLER Fuzzy sts wr irst itroducd by Zadh [14]. Latr Zadh [15] did th trms; liguistic ariabl as a ariabl whos alus ar stcs i atural laguag. H itroducd uzzy coditioal statmts as xprssios o th orm IF A THEN B, whr A ad B ha uzzy maig;.g., IF x is small THEN y is larg, whr small ad larg ar iwd as labls o uzzy sts. A uzzy algorithm is a ordrd squc o istructios which may cotai uzzy assigmts ad coditioal statmts;.g., x is ry small, IF x is small THEN y is larg. Th xcutio o such algorithms is gord by th compositioal rul o irc [14]. Basd o Zadh s work, Mamdai dlopd a w cotrol stratgy basd o uzzy logic, [15]. H cortd huristic cotrol ruls statd by a huma oprator ito a automatic cotrol stratgy. Basd o his piorig work o uzzy logic cotrol, h implmtd th tchiqu i th cotxt o practical applicatios. Sic th thr ha b umrous applicatios o uzzy logic cotrollrs i idustry. Th irc mthod or a cotrollr basd o th compositioal rul o irc o Zadh [15], is calld compositio-basd irc. Th block diagram o th structur o uzzy cotrol systm is show i th Fig.. Th uzzy logic cotrollr dsigd iclud thr importat stps: Fuzziicatio, uzzy rasoig ad duzziicatio. Th rror ad stp chag i rror will b uzziid with th mmbrship uctio. Th usd mmbrship uctios o rror ad itgratio o th rror ar triagls shapd, which is show i Fig. 3. whr X p is th pisto positio, δ is th load dampig ratio ad o is th load atural rqucy. Closd Loop Trasr Fuctio For Th Systm Th quatios may b maipulatd to obtai th closd-loop trasr uctio rlatig th rror oltag V (s) ad th output oltag V 0 (s) rprstig th positio sigal. Th spciicatios o th systm ar idicatd i Appdix 1 ad Fig. 1. Th trasr uctio or th sigl-actuator systm is Vo o V s s ( s1)( s1) s( o s 1) whr o = tr. C. A, V o is th output oltag accordig to th pisto positio, V is th rror sigal oltag, o is th orall systm gai ad tr is th positio trasducr gai. o (8) 1 Th basic uzzy cotrollr usd i this papr is a simpl two-iput cotrollr. Th gais (scalig actors) ad Δ ar that put th rsultig ad Δ alus withi th cotrollr uirs o discours. Th uzzy cotrollr uzziis ths iput quatitis through algorithms that work with a st o mmbrship uctios. Th uzziid quatitis ar th passd through a sris o dcisio ruls; th currt status o th systm is assssd ad a st o cotrol actios ar dtrmid basd o th dgr o truth or all ruls. Bcaus orlap btw th uzzy ariabls xists, mor tha o rul ca ir simultaously. Duzziicatio is th applid usig all th output ariabls, ad a crisp cotrol actio is dtrmid. Ruls ar ormally writt basd o xpric, obsratios ad udrstadig o how th systm rspods ad th attributs it must cotai. Th basic structur o th sl-tuig uzzy PI cotrollr [13] is idtical to th cotioal uzzy PI cotrollr xcpt th sl-tuig opratio, which is show i Fig.. Th cotrollr is tud dyamically by adjustig its output scalig actor Δu i ach samplig tim by a updatig actor α F. Th alu o α F is dtrmid by uzzy ruls did o th rror ad chag o rror Δ. Th ocus is o tuig o th output

4 INTERNATIONAL JOURNAL OF CONTROL, AUTOMATION AND SYSTEMS VOL.3 NO. April 014 ISSN (Prit) ISSN (Oli) scalig actor du to its strog iluc o th prormac ad stability o th systm. Th output scalig actor o th cotrollr is modiid by a sl-tuig mchaism, which is show by th dottd li i Fig.. Th mmbrship uctios (MF) or th cotrollr iputs, ad Δ ad or th icrmtal chag i th cotrollr output Δu ar did i th commo ormalizd domai [-1,1], whras th MF or α F is did o th ormalizd domai [0,1], as show i Fig. 3b. All th MF or both ormalizd iputs, Δ ad th output Δu o th cotrollr ha b did o th ormalizd domai [-1, 1]. Fig. diagram o th sl-tuig PI uzzy cotrollr. Th rlatioships btw th scalig actors, Δ Δ u, ad th iput ad output ariabls o th sl-tuig uzzy PI cotrollr ar as ollows: =., (9) Δ =. Δ Δ, (10) Δu=(α. F Δu ). Δu, (11) u(k)=u(k-1)+ Δu(k). (1) Th ruls ad th mmbrship uctios o th implmtd sl-tuig uzzy PI cotrollr ar show i Fig. 3.a Fig. 3.(a) Fuzzy ruls or computatio o u ad MFs o, ad u.(b) Fuzzy ruls or computatio o α F ad MFs o gai updatig actor (α F). Ruls o thumb or tuig th uzzy PI cotrollr Stp 1: Tu th scalig actors, Δ Δ u, assumig α F = 1 (i.., assum a ormal PI-typ uzzy logic cotrollr). Th scalig actor is chos such that th xpctd rror is ormalizd to th domai [-1,1] to mak icit us o th rul-bass. Th, ad Δ ar tud to mak th trasit rspos o th systm rasoably. At th d o this stp, w gt a cotrollr without sl-tuig. This cotrollr is th startig poit or Stp. Stp : St th output scalig actor Δ u o th sltuig uzzy PI cotrollr gratr tha th alu o th cotrollr rsultig rom Stp 1, whil kpig th alus o ad Δ at th sam ll as i Stp 1. Th, adjust Δ u, i cssary, to gt agai almost th sam ris tim as i Stp 1. Stp 3. Fi-tuig th ruls or α F dpdig o th dsird rspos [13] accordig to prormac masurs such as th pak orshoot, th sttlig tim, th ris tim or th itgral absolut rror. Th magitud o this cotrol is, howr, small to prt orshoot or sustaid oscillatios at th st poit. Th mmbrship uctios rprstig th iput ad output alus' dgr o truth or ach st o liguistic ariabls ar simpl symmtric triagular

5 INTERNATIONAL JOURNAL OF CONTROL, AUTOMATION AND SYSTEMS VOL.3 NO. April 014 ISSN (Prit) ISSN (Oli) uctios. Thy ha suicit orlap to produc a smooth cotrol output [16]. Not that durig th simulatio, th cotrol output mmbrship uctios cotai arrow larg (PB or NB) rgios. This allowd larg cotrol oltags (i.. ull spool tral) to b mostly applid i th prsc o absolutly larg rrors; thy ar lss cti wh th positio rror has mmbrship i both small ad larg rror zos. This modiicatio hlpd to supprss orshoot. Th uzzy rasoig mthod usd i this papr is basd o Mamdai's "Miimum Opratio Rul (MOR)" ad "Ctr O Ara (COA)" duzziicatio tchiqu (s [1]). I this study th gais wr icrmtally adjustd by rpatdly prormig th stp rspos. Th program aluatd th prormac rror, altrd th gais ad rpatd th stp rspos tst util th bst prormig gais wr dtrmid. Stp rspos was asy to apply ad th miimizatio o rror or th tir stp rspos surd both low ris tim ad low orshoot. Th tchiqu was i pricipl similar to th os suggstd by Passio t al. [17], i which th gais wr tud to gt accptabl rspos gi a prormac masur o orshoot ad rspos tim. Figur 4 Systm Stp Rspos Basd o PID ad sl tuig FL Cotrollrs IV. SIMULATION RESULTS Th tud PID cotrollr is dsigd by usig o MATLAB sotwar packag udr th coditios o th orshoot do ot xcd tha 10% ad o stady stat rror, ( P = 1., I =1, D =0.75). Howr i w try to impro th rspos coditios to b zro orshoot ad o stady stat rror, ( P = 0.8, I =.55, D =0.5) th rspos will gi largr ris ad sttlig tim. Th simulatio rsults to stp rspos ar show i Figur 4 basd o th tud PID ad th sl tuig FL cotrollrs policis udr th sam loadig coditios. It ca b obsrd that th proposd cotrollr has smallr sttlig tim without orshoot ad lss ris tim. Th corrspodig cotrol sigals or ach cotrollr ar illustratd i Figur 5, it is itrstig to otic that th amplitud o th sl tuig FLC is smallr compard with both o th PID cotrol sigals, which is importat idx i dsigig ad choosig th hydraulic systm compots. Figur 5 Cotrollrs sigals o PID ad sl tuig FLC Figurs 6 rprst th sl tuig mchaism output (α F ) durig th simulatd tst. It arrid to ixd alu as th dsird rspos achid. For illustratig th robustss o th proposd cotrollr, i Fig. 7 th rspos o th systm udr proposd cotrol systm stratgy ord robust rspos with systm which is charactrizd by dlay tim. 3 Fig. 6 Auto tuig mchaism output

6 INTERNATIONAL JOURNAL OF CONTROL, AUTOMATION AND SYSTEMS VOL.3 NO. April 014 ISSN (Prit) ISSN (Oli) Fig. 7 Systm stp rspos with ad without dlay tim bas o FLC V. CONCLUSION Th problm o positio cotrol o a class o hydraulic maipulators haig modl with dlay tim has b addrssd i this papr. Th ruls o th uzzy cotrollr wr dsigd i ordr to suit th rquirmts o th hydraulic actuatio systm udr istigatio. It is show that th proposd uzzy cotrollr has a good ct ad robust cotrol prormac. Th mai adatag o th FLC: Th cotrol algorithm is simpl ad dos ot d a prcis modl. It clar th ct o th sl tuig mchaism or improig th dyamic charactristics o cotrolld systm Wh th systm is xamid by addig a dlay tim uctio, th cotrol algorithm kpt robust. This rsults is a sigiicat hacmt o th cotrol prormac o th hydraulic systm with log hoss. REFERENCES [1] Tharwat O. S. Haay, Al-Osaimy A. S. ad Ayma A. Aly," Facilitatio Rul Bas or Solidiicatio o Noliar Ral Plat Systm " Itratioal Joural o Cotrol, Automatio ad Systms, (IJCAS), Vol.3, No.1,PP.1-9, 014. [] Tharwat O. S. Haay, Ayma A. Aly ad aml A. Shoush,"Dyamic Eolig Nuro Fuzzy Systms o Qualitati Procss " Itratioal Joural o Cotrol, Automatio ad Systms, (IJCAS), Vol.3, No.1,PP.17-6, 014. [3] Tharwat O. S. Haay, H. Zaii, aml A. Shoush ad Ayma A. Aly, "Rct Trds i Sot Computig Tchiqus or Solig Ral Tim Egirig Problms" Itratioal Joural o Cotrol, Automatio ad Systms, (IJCAS), Vol.3, No.1,PP.7-33, 014. [4] Smith S. M. ad Comr D. J., " algorithm or automatd uzzy-logic cotrollr tuig", Proc. 1EEE 1st Itratioal Corc o Fuzzy Systms, pp , Sa Digo, CA,199. [5] Zhao T. ad Viralo T., "Fuzzy cotrol o a hydraulic positio sro with ukow load", Proc. IEEE d Itratioal Corc o Fuzzy Systms, pp , Sa Fracisco, CA,1993. [6] Chou C. H. ad Lu H. C., "Dsig o a ral-tim uzzy cotrollr or hydraulic sro systms", Comput. Id. 15, 19-14,1993. [7] Sphri N., Dumot G. A. M., Lawrc P. D. ad Sassai F., "Cascad cotrol o hydraulically actuatd maipulators", Robotica 8,07-16,1990. [8] otz A., Chrchas D. B., Lawrc P. D. ad Sphri N., "Gralizd prdicti cotrol o a robotic maipulator with hydraulic actuators", Robotica 10, ,199. [9] P. M. Fitz ad J. J. Palazzolo, Modllig o a O Dgr-o-Frdom Acti Hydraulic Mout, Joural o dyamic Systms, Masurmt ad cotrol, Vol. 118 Pag 439, [10]Zhao,T. ad Viralo,T., Fuzzy Stat Cotrollr ad Its Applicatio i Hydraulic Positio Sro, Fluid powr, Pag 417, [11] Rajai. Mudi ad Nikhil R. Pal, "A sl-tuig uzzy PI cotrollr", Fuzzy Sts ad Systms 115, ,000. [1]Wag ad Flow, Gratig Fuzzy Ruls By Larig From Exampls, IEEE, Vol., No. 6, No.,199. [13]Mrrit HE. "Hydraulic cotrol systm", Nw York: Wily, [14]L.A. Zadh, Fuzzy sts, Joural o Iormatio ad Cotrol, Vol.8 Pag , [15] Z.-X. Cai, Itlligt Cotrol, Elctroics Idustry prss, Bijig, Chia, [16]umbla., Moya J., Baird R., Rajagopala S. ad Jamshidi M., "Fuzzy cotrol o thr liks o a robotic maipulator", Robotics ad Mauacturig; Proc. 1SRAM '9 (Editd by M. Jamshidi t al.), pp ASME Prss, Nw York,199. [17]i M. Passio ad Stph Yurkoich, Fuzzy Cotrol, Wasly Logma, Ic., Calioria, USA, APPENDIX -A I. SPECIFICATIONS OF THE SYSTEM Diamtr o pisto Diamtr o pisto rod Strok Load atural rqucy Load dampig ratio Total low prssur coicit Val low gai, o load Natural rqucy o sro al Dampig actor o sro al Supply prssur Hous - dlay tim 11.7 mm 70.4mm 1000mm 19.6 rad/s x10-11 (m 3 /s)/(n/m ).613x10-3 m 3 /s/ma rad/s MPa ± 500kPa s 4