LabVIEW BASED POSITION CONTROL FOR A PNEUMATIC CYLINDER

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1 LVIEW BASED POSITION CONTROL FOR A PNEUMATIC CYLINDER 1 János GYEVIKI, 1 József SÁROSI, 1 Tmás ENDRŐDY, 1 Endre FORGÁCS, Péter TOMÁN 1 Deprtment of Technicl nd Process Engeerg, University of Szeged, HUNGARY Alf Busz Kft., HUNGARY ABSTRACT: Design nd ppliction of the roust nd ccurte position control for pneumtic cylder sed on the slidgmode technique is presented. The controller is implemented on LVIEW sed controller. The dvntge of the proposed lgorithm for position control is the ccurcy etter thn 10 µm. The pper descries the nonler model of the pneumtic cylder nd the three m design steps of the proposed control method; slidg surfce design, control lw selection nd chtterg free implementtion. Experimentl vestigtions on the system with proposed slidg-mode lgorithm confirmed high ccurcy nd roustness of the horizontl pneumtic cylder position control. KEYWORDS: Slidg-mode control, pneumtic positiong 1. INTRODUCTION As n importnt driver element, the pneumtic cylder is widely used dustril pplictions for mny utomtion purposes thnks to their vriety of dvntges, such s: simple, clen, low cost, high speed, high power to weight rtio, esy mtennce nd herent complce. Trditionlly, they re used for motion etween two hrd stop. The design of stle roust position controller for pneumtic servo-system is difficult sce it is very nonler time-vrt controlled plnt ecuse of the compressiility of ir, the friction force etween the piston nd the cylder, ir mss flow rte through the servo-vlve, etc. By the dvent of PCs with high computtion power, the ccurte nd roust control of pneumtic ctutors hs ecome possile. A good ckground of the pneumtic servo systems reserch cn e found [1].The erly pplictions sed on ler PID controllers proposed y Burrows nd We, 1966; Vughn, 1965 hd limited opertion re. A g schedulg PID control is proposed y Pu et l., 1993 [] to extend the opertion re. Severl ppers proposed utomticlly tuned PID controller for pneumtic servosystems t the end of lst century. Fok nd Ong, 1999 [3] reched ion of ± 0.3 mm. Another solution is to employ the dvnced nonler control strtegies developed recent yers (soft computg) [4][5]. Fujiwr et l., 1995 [6]; Mtsukum et l., 1997 [7] proposed rtificil neurl network nd Jeon et l., 1998 [8] proposed genetic lgorithm to tune the PID controller. The ccurcy ws ± 0.1 mm the est cse. Nonler dptive controllers were proposed y Wiknder, 1988 [9]; Miyt, 1989 [10]; Borow és Jri, 1991 [11]; Oym et l., 1990 [1]; McDonell, Borow, 1993 [13]; Tnk et l [14]; Li et l nd Soong et l., The est ccurcy (0.01 mm) ws reched y Wiknder, 1988 [9]; Nkno et l., 1993 [15] proposed piezo-electric method with ccurcy of µm. Slidg-mode control ws proposed y Noritsugu nd Wd, 1989 [16]; Tng nd Wlker, 1995 [17]; Pnd et l., 1997 [18]; Hmerl, 1995 [19]; Bouri et l., 1996; Surgenor nd Vughn, 1997 [0]; Pul et l., 1994 [1]; Song nd Ishid, 1997 [] ut the ccurcy ws limited. The gol of this pper is to improve the ccurcy of the existg slidg-mode type controllers (e.g. rely type). Slidg-mode control ws troduced the lte 1970's [3, 4] s control design pproch for the control of rootic mnipultors. In the erly 1980's, slidg-mode ws further troduced for the control of duction motor drives [5]. These itil works were followed y lrge numer of reserch ppers rootic mnipultor control [6], motor drive control nd power electronics [7]. However, despite the theoreticl predictions of super closed-loop system performnce of slidgmode, some of the experimentl work dicted tht slidg-mode hs limittions prctice, due to Tome VIII (yer 010), Fscicule 1, (ISSN ) 5

2 OF ENGINEERING. Tome VIII (Yer 010). Fscicule 1 (ISSN ) the need for high smplg frequency to reduce the high-frequency oscilltion phenomenon out the slidg-mode mnifold - collectively referred to s chtterg. In most of the experimentl work volvg slidg-mode, the effort spent on understndg the theoreticl sis of slidg-mode control is generlly mimized, while gret del of energy ws vested empiricl techniques to reduce chtterg. Among these experimentl studies, few succeeded showg closed-loop system ehvior which ws predicted y the theory [8]. Those who filed to relize, the experimentl designs successfully, concluded tht chtterg is mjor prolem relizg slidg-mode control prctice. The connection of slidg-mode control to model reference dptive control troduced some excitement the reserch community. In ddition, the design of slidg-mode oservers [9, 30], provided dditionl cpilities to slidg-mode sed feedck control loop. Flly, the issue of discrete-time slidg-mode ws rised from the theoreticl perspective, resultg numer of different defitions of discrete-time slidg-mode, [31, 3]. The structure of this pper is s follows. The Section II descries the nonler equtions of the pplied pneumtic system. In Section III, short troduction of slidg-mode control is presented nd it is pplied for the ctul servo-pneumtic system. The m steps of the design of the proposed slidg-mode controller re expled. The Section IV descries the experimentl set up nd presents the mesurement results.. MODEL OF THE SERVOPNEUMATIC SYSTEM In order to design roust controller nd predict the control performnce for the pneumtic test rig, theoreticl nd prcticl modellg of the rig is needed (Fig. 1). The equtions derived re sed upon Burrows [3], see Fig 1. The dynmic of the piston is modelled y the mss m, the dmpg d nd the sprg k. The friction force is denoted y F f. The piston cn e moved y the pressure difference etween the two sides of the piston. The pressures p nd p cn e fluenced y the put nd output ir flow rtes, which cn e controlled y the put nd output vlves. Of course, the role of put nd output re exchnged s the direction of the motion is chnged. Sce the put nd output vlves cn e tuned simultneously the ctul pneumtic cylder, it is sgle put system, which cn e descried y second ordered nonler motion eqution m& x = p (u)a p (u)a dx& kx F (1) where x is the position, u is the control signl mesured s percentge vlue of the put nd output spool vlves. The percentge vlue of 0% mens tht the spool vlves re closed nd 100% mens tht they re open totlly. The dynmics of the spool vlves re ignored. The other prmeters nd vriles T, V, A, Q nd c re the temperture, volume, re, het energy nd specific het respectively. The suscription refers to the loction of ctul vrile. x f F f m d T c p V A k V T c A f A A fout p dq m m dq C p T. m c out p out T. out m out Figure 1. Structure of the pneumtic cylder The clcultion of p nd p is sed on two m lws: Blnce of the put, output nd ner energies Blnce of the put, output nd ner msses 6

3 OF ENGINEERING. Tome VIII (Yer 010). Fscicule 1 (ISSN ) A. Energy lnce Denotg the ner energy of the ir y U, nd the mechnicl work mde the ir y W, the energy lnce eqution for the chmer is Δ U = ΔU + ΔQ + ΔW () Assumg ditic ehviour Δ Q = 0 nd ignorg the ketic energy of the put ir, the rte of the energy chnge is c (p V& v + p& V ) = c pt m& p A x& R (3) Assumg tht the c v cn e estimted y the specific het vlue of ir eside constnt volume, nd the c p cn e estimted y the specific het vlue of ir eside constnt pressure R = c p c v (4) then the chngg rte of the pressure cn e expressed s: c m& p c p p& = RT p A c v V c v V x& (5) Similrly, for the chmer, the chngg rte of the pressure is c m& p out c p p& = RTout + p A c V c V x& (6) B. Mss flow rte v On the sis of Bernoulli eqution, the mss flow rte cn e expressed y nonler function where μ is constnt dependg on the type of vlve nd pressure rtio v m& = μ A p (7) R T is nonler term sed upon χ+ 1 χ p χ χ p = χ (8) 1 p p Here χ is the specific het rtio. Note tht (8) is vlid only if p p > If p p 0. 58, the speed of the ir will e equl to the ctul sonic speed nd = The mss flow rte of the exhusted ir cn e expressed similrly ut the roles of the source nd dr must e exchnge. Accordg to tht nd sed on (7), yields where out is defed s χ & μ (9) mout = out Aout pout R Tout χ 1 χ 1 p χ p χ out = 1 (10) χ 1 pout pout Note tht (10) is vlid only if p pout < If p pout then p out = (11) pout A MATLAB nd SIMULINK model sed on the ove eqution is presented pper [33] order to vestigte the sic properties of pneumtic ctutors 3. DESIGN OF A SLIDING-MODE CONTROLLER A good troduction to slidg-mode control cn e found [34]. The design of slidgmode controller consists of three m steps. First step is the design of the slidg surfce, the second one is the design of the control which holds the system trjectory on the slidg surfce, nd the third nd key step is the chtterg-free implementtion. The purpose of the switchg control lw is to force out 7

4 OF ENGINEERING. Tome VIII (Yer 010). Fscicule 1 (ISSN ) the nonler plnt s stte trjectory to this surfce nd keep on it. The control hs discontuity on this surfce tht is why some uthors cll it switchg surfce. When the plnt stte trjectory is ove the surfce, feedck pth hs one g; ut if the trjectory drops elow the surfce, it hs different g. Consider sgle-put, sgle-output second-order nonler dynmic system & x = f(x, x, & u) (1) where x is the output signl (position) of the controlled plnt nd u is the control signl. If x d denotes the desired vlue, then the error etween the reference nd system sttes my e defed s e=x d - x (13) A. Slidg surfce design Clssiclly, sclr vrile s is clculted s ler comtion of the error nd its derivtive. s = e + λ e& (14) Let s ( e,e & ) = 0 defe the slidg surfce the spce of the error stte. The purpose of the slidg-mode control lw is to force the stte trjectory of the error to pproch the slidg surfce nd then move long the slidg surfce to the orig, Fig.. The process of slidg-mode control cn e divided to two phses, tht is, the pprochg phse with s(e,e) & 0 nd the slidg phse with s ( e,e & ) = 0. Here 1 denotes the pprochg phse, nd 3 denote the slidg phse. If the system is slidg-mode, the error is decresg exponentilly, where λ is time constnt type prmeter. If λ is smll, then the system response is slow ut ccurte. If it is ig, the system response is fst ut the system might chtter. B. Selection of the control lw s= y + λ y =0 e e y e 3 y ep P y e0 Figure. Slidg motion the stte spce 1 y e In order to gurntee tht the trjectory of the error vector e will trnslte from pprochg phse to slidg phse, the control strtegy must stisfy the slidg condition s (e,e) & s(e,e) & && & < 0 (15) This mens tht system trjectory should e forced to move towrd the slidg surfce. A proper control should e selected to stisfy the condition (15) ny time stnt. Let us ssume tht the desired vlue is constnt nd ccordg to (13) nd (14) follows s & = e& + λ && e = x& λ && x = x& λ f(x,x,u) & (16) If s > 0 or s < 0 the control lw should e selected wy, which ensures x & λ f(x,x,u) & < 0 or x& λ f(x,x,u) & > 0 (17) The simplest control lw tht might led to slidg-mode is the rely u = δ sign(s) (18) The rely-type controller does not ensure the existence of the slidg-mode for the whole stte spce, nd reltively ig vlue of δ is necessry, which might cuse chtterg phenomenon. If the slidg-mode exists (s=0 nd s & = 0 ), then there is contuous control, know s equivlent control which cn hold the system on the slidg surfce. u eq In prctice, there is no perfect knowledge of the whole system nd prmeters, so, only û eq, the estimte of u, cn e clculted. Sce û does not gurntee convergence to the switchg eq surfce, generl, discontuous term is usully dded to eq û eq, thus, u = û eq + δ sign(s) (19) The role of the discontuous term the control lw is to compenste the effect of the uncert perturtions nd ounded disturnce. The more knowledge of process is implied the control lw, the smller discontuous term is needed. 8

5 OF ENGINEERING. Tome VIII (Yer 010). Fscicule 1 (ISSN ) C. Chtterg free implementtion Chtterg is the m prolem of slidg-mode control nd chtterg free implementtion is the key step design of slidg-mode controller. A quite generl solution is tht the rely (which chnges control vlue suddenly) is replced y sturtion function. There is oundry lyer round the slidg surfce where the control signl is chngg contuously. If the system trjectory is close to the slidg surfce nd the control signl is smll, then the system might stick efore the gol. To void it modified sturtion function shown Fig.3. is proposed. -s k u 0 u u mx -u 0 -u mx s k s 4. THE SERVOPNEUMATIC POSITIONING SYSTEM Figure 3. Control function s modified sturtion function The system is shown Fig.4. nd Fig.5. (detils cn e found [33]). It consists of doule-ctg pneumtic rodless cylder (MECMAN 170 type) with ore of 3 mm, nd stroke of 500 mm, controlled y five-wy servo- distriutor (FESTO MPYE-5- M5-010-B type). A ler encoder (LINIMIK MSA 30 type) gives the position. Velocity nd ccelertion re oted y numericl derivtion. Pressure sensors (Motorol MPX5999D) re set ech chmer. The controller is implemented LVIEW environment. Figure 4. The experimentl setup of servo-pneumtic positiong system The control gol is to move the piston from ny itil position to the trget position. Usg the slidg pproch it is possile to mimize the positiong error. In order to design roust controller nd predict the control performnce for the pneumtic test rig, mthemticl nd experimentl (rel world) model of the test rig is needed. x TD C PC I P NI PCI-651 M Series P I Multifunkc. DAQ V SCB 68 Shielded I/O Connector Block Ps Figure 5. Configurtion of pneumtic positiong system The system pressure is set to e 6 r, the smplg time is 1 ms. In order to nlyze the positiong control methods, rel-time dt cquisition progrm ws designed LVIEW to cpture the system output dt through the connector lock to the NI PCI-651 M Series Multifunction DAQ device. 9

6 OF ENGINEERING. Tome VIII (Yer 010). Fscicule 1 (ISSN ) A Ntionl Instruments dt cquisition crd (NI 651/M) reds the signl, pressure sensors nd crementl encoder to the PC. Ntionl Instruments LVIEW will e used to collect the dt imported through the DAQ crd nd control the position (Fig. 6.). Symols x& - piston velocity, m/s & x& - piston ccelertion, m/s V - volume chmer, m 3 V - volume chmer, m 3 s - slidg surfce, slidg le p - pressure (let) cmer, P Figure 6. Front Pnel of the LVIEW progrm p - pressure (outlet) cmer, P p - supply pressure, P A - piston re from chmer side, m pout - exhust pressure, P A - piston re from chmer side, m u - control signl, % Af - re of vlve orifice for chmer, m ueq - equivlent conrol, % Afout - re of vlve orifice for chmer, m û eq - estimte equivlent control, % T - temperture, K T - temeprure of let ir, K Q - het energy chmer, J Tout - temeprure of outlet ir, K U - ner energy chmer, J m - mss of piston nd lod, kg W - mechnicl work chmer, J m - ir mss chmer, kg W - mechnicl work, J m - ir mss chmer, kg R - gs constnt, Jkg -1 K -1 m - let ir mss, kg - orifice flow function (let) mout - outlet ir mss, kg m& - let ir mss flow, kg/s out - orifice flow function (outlet) m& κ out - outlet ir mss flow, kg/s - isentropic constnt λ - slidg le coefficient, time constnt, s d - dmpg coefficient, Ns/m cp - constnt pressure specific hets of ir Ff - friction force, Ns/m k - sprg stiffness, N/m cv - constnt volume specific hets of ir x - piston position, m μ - vlve flow constnt for fill δ - discontuos g control signl μout - vlve flow constnt for exhust 5. EXPERIMENTAL RESULT The trnsient responses of the piston position nd control signl re shown Fig.7. The experiment is slidg-mode control with clssicl rely control lw. The trnsient responses of the piston position s well s control signl re shown Fig. 7. The stedy stte position error of the system with LVIEW sed rely type slidg-mode control is with ±0.01 mm, s it is shown the enlrged position trnsient response Fig.8. The ccurcy of the system is limited y the pplied position sensor. Overshoot : 0.00 mm Stedy-stte error : 0.00 mm Position [mm] Control Signl [V] Pressure [r] Time [s] Figure 7. Piston position, ir pressure nd control signl trnsient responses with rely type SM controller 30

7 OF ENGINEERING. Tome VIII (Yer 010). Fscicule 1 (ISSN ) Overshoot : 0.00 mm Stedy-stte error : 0.00 mm 100 Position [mm] Pressure [r] Control Signl [V] Time [s] Figure 8. Piston position, ir pressure nd control signl trnsient responses with rely type SM controller - enlrged round stedy stte piston position (100mm) 6. CONCLUSIONS This pper proved tht pneumtic servo systems cn e used for the ccurte roust position control, not only for the movement etween two hrd stops. The experimentl results showed tht proposed slidg-mode controller gives fst response nd good trnsient performnce. Furthermore, the controlled system is roust to the vritions of the system prmeters nd externl disturnces nd they do not require ccurte modellg. The positiong system ccurcy oted is etter thn 10μm nd it is limited y position sensor. The fl conclusion is tht proposed slidg-mode controller with modified sturtion function cn elimte chtterg, which is the m prolem the cse of slidg-mode control nd cn e used s promisg tool for ccurte control of the servo-pneumtic systems. Bsed on the lortory mesurements we cn conclude tht the pneumtic servo-systems cn e used for precise roust position control. The slidg-mode control is promisg tool for controllg such systems. The proposed modified sturtion function cn elimte the chtterg, which is the m prolem cse of slidg-mode control. Further works will e done on the BTL5-S101 type Micropulse Ler Trnsducer from Blluff with 1 µm resolution nd we will e done with pplyg the put shpg method. REFERENCES [1] Ful Xg: Block-Oriented Nonler Control of Pneumtic Actutor Systems, Doctorl Thesis Mechtronics L, Deprtment of Mche Design Royl Institute of Technology, Stockholm, Sweden, 001 [] Pu, J., Moore, P. R., Hrrison R. nd Weston, R. H.: A study of gschedulg method for controllg the motion of pneumtic servos, Sixth Bth Interntionl Fluid Power Workshop - Modellg nd Simultion, UK, 1993 [3] Fok, S. C., Ong, E. K.: Position control nd repetility of pneumtic rodless cylder system for contuous positiong, Rootics nd Computer Integrted Mnufcturg, 15, pp , 1999 [4] Gy. Mester: Neuro-Fuzzy-Genetic Controller Design for Root Mnipultors, Proc. IECON 95, IEEE,Orlndo, Florid, USA, 1, pp 87-9,1995 [5] Gy. Mester: Neuro-Fuzzy-Genetic TrckgControl of Flexile Jot roots, Proc. I. Intern. Conf. on Adv. Rootics & Intelligent Aut., Athens, Greece, pp 93-98, 1995 [6] Fujiwr, A., Ktsumt, K., Ishid, Y.: Neurl network sed dptive PID controller for pneumtic cylder, Proceedgs of the SICE Annul Conference, pp 6-8, 1995 [7] Mtsukum, T., Fujiwr, A., Nm, M., Ishid, Y.: Nonler PID controller usg neurl networks, Proceedgs of IEEE Interntionl Conference on Neurl Networks,, pp ,

8 OF ENGINEERING. Tome VIII (Yer 010). Fscicule 1 (ISSN ) [8] Jeon, Y., Lee, C., Hong, Y.: Optimiztion of the control prmeters of pneumtic servo cylder drive usg genetic lgorithms, Control Engeerg Prctice, 6, pp , 1998 [9] Wiknder, J.: Adptive Control of Pneumtic Cylders, Doctorl thesis, Royl Institute of Technology, Stockholm, 1988 [10] Miyt, K.: Pneumtic servo control system y usg dptive g pressure control Proceedgs of the First Interntionl Symposium on Fluid Power, JHPS, Tokyo, pp , 1989 [11] Borow, J. E., Jri, J.: Adptive pneumtic force ctution nd position control Journl of Dynmics Systems, Mesurements nd Control, 113, pp 67-7, 1991 [1] Oym, O, Tnzw, M., Iwdte, Y., Hmd, M.: Model reference dptive control for pneumtic cylder servo system, Journl of the Jpn Hydrulic Pneumtic Society, 1, pp , 1990 [13] McDonell, B. W., Borow, J. E.: Adptive trckg control of n ir powered root ctutor, ASME Journl of Dynmic Systems, Mesurement nd Control, 115 (3), pp , 1993 [14] Tnk, K., Ymd, Y., Skmoto, M., Uchikdo, S.: Model reference dptive control with neurl network for electro-pneumtic servo system, Proc. IEEE Conference on Control Applictions, pp , 1998 [15] Nkno, K., Horikw, O., Askge, T., Tnk, Y.: Precision pneumtic positiong system with ctive piezoelectric lockg mechnism, Proc. 5th Bth Interntionl Fluid Power Workshop on Circuit, Component nd System Design. Bth UK, 1993 [16] Noritsugu, T., Wd, T.: Adptive vrile structure control of pneumticlly ctuted root, Proceedgs of the First Interntionl Symposium on Fluid Power, JHPS, Tokyo, pp , 1989 [17] Tng, J., Wlker, G.: Vrile structure control of pneumtic ctutor, Journl of Dynmic System, Mesurement nd Control, 117, pp 88-9, 1995 [18] Pnd, S. R., Hykw, Y., Knzw, Y., Kmoym, Y.,Kwmur, S.: Prcticl design of slidgmode controller for pneumtic ctutors, Journl of Dynmic Systems, Mesurement nd Control, 119, pp , 1997 [19] Hmerl, M.: An nthropomorphic root rm driven y rtificil muscles usg vrile structure control, Proceedgs of the 1995 IEEE Interntionl Conference on Rootics nd Automtion, Ngoy, Jpn, pp , 1995 [0] Surgenor, B. W., Vughn, N. D.: Contuous slidg-mode control of pneumtic ctutor, Trnsctions of the ASME, Journl of Dynmic Systems, Mesurement nd Control, 119 (3), pp , 1997 [1] Pul, A. K., Mishr, J. K., Rdke, M.G.: Reduced order slidg-mode control for pneumtic ctutor, IEEE Trnsction on Control Systems Technology, (3), pp 71 76, 1994 [] Song, J., Ishid, Y.: Roust slidg-mode control for pneumtic servo systems, Interntionl Journl of Engeerg Science, 35 (8), pp , 1997 [3] V. Utk,: Vrile Structure Systems with Slidg-mode, IEEE Trns., (), pp 1-,1977 [4] K. D. Young: Controller Design for Mnipultor Usg Theory of Vrile Structure Systems, IEEE Trnsction on Systems, Mn nd Cyernetics, 8, pp , 1978 [5] A. Snovic, D. Izosimov,: Appliction of slidg-modes to duction motor control IEEE Trns. Industril Appl., 17 (1), pp 41-49, 1981 [6] F. Hrshim, T. Ueeshi, H. Hshimoto: Slidg-mode Control for Rootic Mnipultors, nd Eur. Conf. on Power Electronics, Grenole Proc., pp 51-56, 1987 [7] Ando, N., Korondi, P., Hshimoto, H.: Networked tele-micromnipultion systems ''Hptic Loupe", IEEE Trnsction on Industril Electronics, 51 (6), pp , 004 [8] P. Korondi, H. Hshimoto, V. Utk: Direct Torsion Control of Flexile Shft sed on n Oserver Bsed Discrete-time Slidg-mode, IEEE Trns. on Industril Electronics,, pp 91-96, 1998 [9] Xu, J. Inx, H. Hshimoto, F. Hrshim: On Design of VSS Oserver for Nonler Systems Trns. Society of Instrumenttion nd Control Engeers, 5 (), pp 0-6, 1989 [30] H. Hshimoto, H., V. I. Utk: VSS Oserver for ler time vryg system Proc. 16th Annul Conference of IEEE Industril [31] Furut, K.: Slidg-mode Control of Discrete System, System Control Letters, 14, pp , 1990 [3] Liu, S. Burrows, J. E.: An nlysis of pneumtic servo system nd its ppliction to computercontrolled root, ASME Journl of Dynmic Systems, Mesurement nd Control, 110 (3), pp 8 35, 1988 [33] J. Gyeviki, K. Rózshegyi: Development of servopneumtic positiong equipment MicroCd 004. Hungry, pp 31-36, 004 [34] P. Korondi, H. Hshimoto: Slidg-mode Design for Motion Control, Studies Applied Electromgnetics nd Mechnics, 16, p 1, 000. [35] Vittek, J., Mkys, P., Stulrjter, M., Dodds, S. J., Perrymn, R.: Servo-position Control with Dynmic Lg Precompenstor for SMPM Drivers, The Conference OPTIM 04, Brsov, Románi, 003 3