CHARACTERIZATION AND MODELING OF A PROPORTIONAL VALVE FOR CONTROL SYNTHESIS

 Rosalind Phillips
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1 CHARACTERIZATION AND MODELING OF A PROPORTIONAL VALVE FOR CONTROL SYNTHESIS Osama. OLABY, Xavier. BRN, Sylvie. SESMAT, Tanneguy. REDARCE and Eric. BIDEAX Laboraoire d Auomaique Indusrielle  hp://wwwlai.insalyon.fr LAI, Bâ S Exupéry, 25 Av Jean Capelle INSA de Lyon, 69621Villeurbanne Cedex, FRANCE ( ABSTRACT This paper presens a global characerizaion and an analyical model of he saic flow sage of an elecropneumaic proporional valve FESTO MPYE5M5010B. This sudy is useful for linear or nonlinear conrol synhesis in our applicaion for medical roboics. Firsly, he experimenal measuremens are carried ou using 3D graphs where a se of curves gives he oupu mass flow rae as a funcion of he elecrical inpu of he elecronic sage for differen values of he oupu pressure. The exhaus and supply pressures, during hese ess, are assumed o be consan. Moreover, 2D classical curves given by some consrucors can be reconsruced, such as mass flow gain, pressure gain and mass flow characerizaion. Secondly, an approximaion of he mass flow sage characerisics of his fiveway proporional valve by a polynomial funcion is described. The model elaboraed enables a good reproducion of he pressure gain and he global mass flow characerizaion curves o be obained. KEY WORDS Pneumaic proporional valve, Experimenal characerizaion, Modeling. I. INTRODCTION Pneumaic sysems are increasingly presen in a number of indusrial manufacuring procedures, handling, medical, armamen and roboics, ec. The use of proporional disribuors in pneumaic sysems has a pracical design and simple use, especially o carry ou he synhesis of he linear and nonlinear conrol laws in feedback conrol, for example posiion feedback conrol or force feedback conrol racking according o desired rajecories [1]. Moreover, he proporional valve is a power modulaor ha does no consume much energy [2],[3]. A servodisribuor is known as proporional when i provides a mass flow rae in bidirecional operaing mode which is a funcion of he inpu volage of he elecronic sage of he proporional valve. FESTO MPYE5M5010B is a proporional valve, 5/3way funcion, wih a maximum flow rae of abou 140 Nl/mn* a a supply pressure of 7 bar abs**. This mass flow rae is suiable for developing a medical robo (BirhSIM) [4],[5]. BirhSIM is a childbirh simulaor developed in collaboraion beween INSA Lyon (Insiu Naional des Sciences Appliquées) and HCL (Hospices Civils de Lyon) [6]. BirhSIM is a dynamic funcional simulaor, which akes ino accoun he movemen of a baby * 1 Nl/mn = g/s ** Thereafer, all he pressure values expressed in bar, will be in absolue bar.
2 hrough is moher s pelvis. In fac his ype of simulaor will help o each, in a realisic way, and in complee safey he medical echniques of childbirh in he midwife schools and he Faculy of Medicine. I has been developed o enable obsricans o learn how o perform he procedure for he firs ime. The operaive par of BirhSIM conains a pneumaic acuaor which produces he movemen of he head of he newborn and supplies a programmable resisance o he force of racion. The acuaor will enable BirhSIM o imiae conracions and he moher s pushing acion. This acuaor is a linear cylinder, doubleacing and single rod which suppors he head of he newborn. This cylinder can posiion he newborn, and more paricularly is head, on a horizonal axis. Two FESTO MPYE5M5010B proporional valves conrol his pneumaic cylinder. In order o carry ou he auomaic piloing of he elecropneumaic sysem, i is necessary o know he mahemaical model of he power modulaor. Servodisribuor manufacurers do no provide sufficien characerisics o obain a model of he flow rae sage of he pneumaic componens in heir documenaion [7]. No precise characerisics are provided by FESTO. This is why he global saic characerisics (por P) of he proporional valve, were esablished. Moreover, experimenal measuremens carried ou can give a precise knowledge of he mass flow rae delivered by he flow sage of his proporional valve and hen a simulaion model can be deduced. These measuremens form a able, having as inpus he oupu pressure and he elecrical inpu of he elecronic sage inegraed ino he proporional disribuor and giving he oupu mass flow rae. The procedures followed o carry ou he global characerizaion of he FESTO proporional valve confirm he possibiliy of applying a proocol carried ou previously for a servodisribuor of he Asco JOCOMATIC company [7],[8], o oher fluid power componens. Servoronic Asco JOCOMATIC is a hreeway elecropneumaic servovalve, is maximum flow rae is abou of 1400 Nl/mn. This flow rae value is much larger han ha of he FESTO MPYE5M5010B proporional valve. This aricle is organized as follows: In secion II, he FESTO proporional valve is briefly described. In secion III, experimenal resuls of a global characerizaion of his ype of pneumaic componen is provided. Secion IV presens a mahemaical model of he saic flow rae sage. The resuls obained wih his model are compared wih he experimenal resuls and wo ypes of errors are hen discussed. II. SAGE OF THE PROPORTIONAL VALVE The MPYE5M5010B proporional valve is a 5/3way funcion disribuor. I is hus composed of five pors N, P, S, E and E wih hree configuraions for he air flow (Figure 1). The five ways presen an S orifice of compressed air (i is numbered orifice (1) by he manufacurer), wo working orifices for P(4), N(2) and wo for he exhaus E(3 and 5). For a volage of 5 V, when he spool is in midposiion, he flow rae of he disribuor is heoreically null. If he inpu conrol is varied from 5 V o 0 V, he compressed air exis from por (1) owards por (2) and he exhaus goes from por (4) owards por (5). By varying he volage of 5 V o 10 V, he compressed air exis from por (1) owards por (4) and he exhaus goes from por (2) owards por (3). III. Por P(4) P(4) Por N(2) N(2) Por E(5) E(5) Por E(3) E(3) Por S(1) S(1) en foncion des enrées: en foncion des enrées: Elecronics Por P(4) Por P(4) Working proporional Pors N(2) Pn Exhaus Por E(3) P(4) Pp Exhaus Por E(5) Supply compressed air Por S(1) Figure 1. Phoograph and schema of a FESTO MPYE5M5010B proporional valve EXPERIMENTAL CHARACTERIZATION RESLTS The characerizaion suggesed for he FESTO proporional valve is a global saic characerizaion for consan exhaus and supply pressures. Global since he oupu mass flow rae is given as a funcion of boh he elecrical proporional valve inpu and of he oupu pressure, he supply and exhaus pors being as in normal working condiions which means ha none of hem is shu. Saic, because for each variaion in he elecrical inpu conrol or in he oupu working pressure, he measuremen readings (pressure and flow rae) are aken when he flow rae is in esablished mode. Figure 2 shows he esing device used for measuring he desired characerisics of he por P(4) when he por N(2) is shu. The experimenal procedure consiss of recording he oupu flow rae for each variaion of he inpu volage and of he working pressure P P. I is necessary o vary one of hese wo independen values and o keep he oher consan. I can be seen from Figure 2 ha, for his purpose, he oupu pressure P P and he supply pressure (P S =7 bar) are kep consan by using wo pressure regulaors. Considering he nonlinear characer of his ype of componen (Figure 4), i was necessary o make more volage measuremens beween 4 V and 6 V. These values correspond oo o he significan par of he pressure gain characerisic a null mass flow rae (Figure 11).
3 A/D Converer 16 bis change he volage manually The se given in Figure 5 shows he oupu mass flow rae as a funcion of he oupu pressure for 26 differen values of he inpu volage conrol from 0.153V o 10V. p p qm p PS E(5) P(4) PP Tank E(3) N(2) igh q m Tank Supply pressure regulaor (P S =7 bar) Proporional valve FESTO MPYE5M5010B Working pressure P P regulaor Figure 2. Tesing device Figure 3 shows (afer having carried ou a linear inerpolaion of he measuremen poins) he hreedimensional evoluion of he mass flow rae as a funcion of valveinpu conrol and is working pressure. In fac, if his characerisic is projeced on wo planes (,q m ) and (P P,q m ) he nework of mass flow gain (Figure 4) and he nework of mass flow rae characerizaion (Figure 5) can be obained respecively. Figure 4. Se of mass flow rae curves as a funcion of proporional valve inpu Figure 5. Se of mass flow rae curves as funcion of proporional valve oupu pressure Figure 3. 3Dglobal saic characerisics Figure 4 shows he evoluion of he oupu proporional valve mass flow rae q m as a funcion of elecrical inpu, for eigh differen values of he oupu pressure P P, disribued from 1.25 o 7 bar. In his figure is shown: The nonlineariy of he curves for values near he supply and exhaus pressures, for values of inpu conrol near he 5V value. The eigh curves are monoonous. A phenomenon of sauraion is noiced for he values of inpu conrol higher han 8 V and lower han 2V. This nework clearly shows he classical behavior of he servodisribuor orifices relaed eiher o a supply process or o an exhaus process for large absolue values of he valve proporional inpu conrol. Each of he wo ses of curves (Figure 4 and 5) deermines simply he variaion of mass flow rae agains boh an oupu pressure P P and an inpu conrol. This consiues useful informaion abou he power modulaor under sudy which is no direcly available on he manufacurer documenaion. This informaion enables a simulaion model of he saic flow sage in he form of an easily programmable 3Dable o be used for any simulaion. By inerpolaion beween he poins, i
4 gives he real global mass flow rae a he oupu por whaever are he oupu pressure and he inpu conrol. IV. ANALYTICAL CONTROL MODEL The synhesis of cerain conrol laws requires he knowledge of a flow sage model in a mahemaical form [2]. The modeling of a servodisribuor enables he mass flow rae a is oupu as a funcion of he oupu working pressure, and of he elecrical inpu conrol o be deermined. For he conrol objecive, i is ried o reproduce he saic behavior of he FESTO disribuor proporional valve, via a mahemaical expression. A mehod had been proposed, using a mahemaical expression of he mass flow rae evoluion law, depending on he global characerisics of he servodisribuor JOCOMATIC SERVOTRONIC [8]. This conrol model for he FESTO proporional valve is validaed by carrying ou a ranslaion of he valveinpu conrol o new values of conrol varying around 0V: ( = ). The value equal o V (deduced from he measuremens) corresponds o he inersecion poin of he pressure gain characerizaion orifice P and orifice N hus o he same pressure on boh oupu pors. The mahemaical expression affine in he conrol inpu is : m (, PP ) = ( PP ) + ψ ( PP, sgn( )) q ϕ (1) ( P ) q m, illusraes a mass flow rae (Nl/mn) ha P is a funcion of he working pressure P p and an inpu conrol volage. ϕ P is a polynomial funcion whose evoluion corresponds o he mass flow rae leakage (Nl/mn) from he orifice P. I is idenical for all inpu conrol values (Figure 6. ) ( ) Figure 6. Approximaion of mass flow rae measured for = 0 ϕ p : Funcion ( ) ( P, sgn( )) ψ P is a polynomial funcion of he inpu conrol sign (Figure 7) because i is differen for he > 0 < 0. inle ( ) and for he exhaus ( ) Figure 7. Approximaion of he ( P, sgn( )) P ψ funcion. The form of he mass flow rae shown in Figure 5. jusifies he approximaion by wo differen ψ funcions, one defined for posiive values of and he oher for negaive values. The nonlinear shape of he global characerisics of he mass flow rae, as a funcion of he oupu pressure and he inpu conrol, jusifies he choice of he polynomial funcion of he form (1). The minimal degrees of he polynomials ϕ ( P ), ψ ( P, < 0) ( ) and ψ P, > 0 o have he smalles absolue esimaed error, equal o 4, 4 and 5 respecively. IV.1. CONTROL MODEL VALIDATION In his paragraph, a comparison of he characerisics resuling from he approximaions wih hose resuling from he experimenal measuremens of he FESTO proporional valve ( secion III ) is presened. Figure 8 shows he evoluion of he mass flow rae as a funcion of he elecrical inpu conrol and he working pressure according o equaion (1). This wodimensional evoluion has a shape raher near ha of he saic global wodimensional characerisic of he FESTO MPYE5M5010B proporional valve, as illusraed in Figure 3. In fac i can be observed in Figures 9 and 10 ha he mass flow rae reconsiued from he equaion (1), gives good resuls comparaively o he measuremens excep for: he negaive values of he inpu conrol wih oupu pressures P P equal o 6, 6.5 and 7 bar. he posiive values of inpu conrol wih a working pressure P P near o ha of he amospheric pressure (1.25 bar and 1.5 bar).
5 Figure 8. Global saic characerisics reconsiued from he equaion (1) Figure 10. Comparison: experimenal and reconsiued se of mass flow rae curves as a funcion of oupu pressure Figure 9. Comparison: Experimenal and reconsiued se of mass flow rae curves as a funcion of valve inpu These errors are no roublesome for he uses under consideraion, because he pressure domains correspond o exreme values close o he supply or exhaus pressures which will no be examined very much. An oher way o validae he obained approximaion is o compare he pressure gain characerisic P P a null mass flow rae reconsiued from equaion (1) wih he measured characerisic. I can be observed in Figure 11 ha he approximaion gives good resuls compared o he measuremens. In fac he slope of he pressure gain reconsiued is larger han ha measured in he experimens. In his inerval he displacemen of he valve spool causes he opening of one of he working orifices P or N and he closing of he oher. Figure 11. Comparison: Experimenal and reconsiued pressure gain curve IV.2. MODELING ERROR Two crieria are presened o validae he conrol model. On one hand, an absolue error of mass flow rae is obained ha is low on all he applicaion fields of he FESTO proporional valve. On he oher hand, a relaive error of he mass flow rae for he greaes opening zone of a passage of fluid esimaed for his componen is obained. The absolue errors of he mass flow rae generaed by he conrol model given by he equaion (1) are weak (beween 15 Nl/mn and +15 Nl/mn) as shown in Figure 12. They are maximal a he edges of he pressure field P P. The relaive errors of mass flow raes generaed by he approximaions for he values of elecrical inpu conrol
6 ouside he inerval [1, +1], are beween 10% and +15% (Figure 13) was validaed by reconsiuing he global wodimensional characerizaions and he pressure gain curve a null mass flow rae. The good resuls obained show ha he characerizaion and modeling proocol of a servodisribuor carried ou previously [7] can be used for anoher pneumaic modulaors. The weak errors of he mass flow rae enabled he conrol model o be validaed. A conrol synhesis would enable he simulaor BirhSIM o be auomaed. In fac he generaion of inpu rajecories for our sysem is an imporan problem o resolve in order o ranslae he medical condiions ino an auomaion problem. Laer i will be necessary o synhesize robus conrols which will enable o ake ino accoun he known errors of he flow sage model. This will enable o minimize racking errors in a highly nonlinear field. REFERENCES Figure 12. Mass flow rae absolue errors Figure 13. Mass flow rae relaive errors These approximaions knowledge will be useful o synhesize nonlinear robus conrol law [9]. V. CONCLSION In his paper an analyical model of a MPYE5M5010B proporional 5/3way valve from he FESTO company has been presened. The mahemaical model has been obained afer realizing a global characerizaion of he saic flow sage of his servo flow conrol valve. The experimenal measuremens carried ou for a characerizaion in hreedimensions (mass flow rae, oupu pressure and elecrical inpu conrol), can be used as a simulaion model. The characerisics presened in Figure 3 can consider FESTO servopneumaic valve is suiable o carry ou he funcions of he childbirh simulaor BirhSIM. The analyical model of he FESTO proporional valve [1] KAASA, G. O., CHAPPLE, P. J., LIE, B., Modeling of an elecropneumaic cylinder acuaor for nonlinear and adapive conrol, wih applicaion o cluch acuaion in heavyduy rucks, In he 3rd Inernaional Ph.D. Symposium on Fluid Power, Terrassa, Spain, 30h June 2nd July, 2004, p [2] BRN, X., BELGHARBI, M., SESMAT, S., THOMASSET, D., SCAVARDA, S., Conrol of an elecropneumaic acuaor, comparison beween some linear and nonlinear conrol laws, Journal of Sysems and Conrol Engineering, 1999, Vol. 213, N I5, p [3] FERNANDEZJIMENEZ, A., PEREZ GARCIA, J., Compressible bench flow adapaions o he experimenal characerizaion of pneumaic componens. Applicaion o he deerminaion of flowrae characerisics of a MPYE53/8010B proporional valve, In he 3 rd Inernaional Ph.D. Symposium on Fluid Power, Terrassa, Spain, 30 h June 2 nd July, 2004, p [4] SILVEIRA R., DPIS O., PHAM M.T., DITTMAR A., REDARCE T., BETEMPS M. Design of a Mechanical birh simulaor. World Congress on Men's Healh Medicine  WCMHM /04/2004, Paris, France, [5] SILVEIRA R., DPIS O., PHAM M.T., REDARCE T., BETEMPS M. A new mechanical birh simulaor. IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems  IROS 04, 28/092/ , Sendai, Japan, 2004, pp [6] DPIS, O., DITTMAR, A., DELHOMME, G., REDARCE, T., BETEMPS, M., SILVEIRA, R., Simulaeur foncionnel e anaomique d accouchemen. French paen number: , Augus 01, [7] SESMAT, S., SCAVARDA, S. Saic characerisics of a hreeway servovalve, In: 12h Aachen Conference on Fluid Power Technology, Aachen, Allemagne, March 1213, 1996, p [8] BELGHARBI, M., THOMASSET, D., SCAVARDA, S., SESMAT, S., Analyical model of he flow sage of a pneumaic servodisribuor for simulaion and nonlinear conrol, in he Sixh Scandinavian Inernaional Conference on Fluid Power, SICFP'99, Tampere, Finland, May 2628, 1999, p [9] SMAOI, M., BRN, X., THOMASSET, D., A combined firs and second order sliding mode approach for posiion and pressure conrol of an elecropneumaic sysem, American Conrol Conference, ACC'05, Porland, Oregon, SA, June 810, 2005
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