Controller Design for a Pneumatic Actuator System with Proportional Valve

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1 Cotroller eig for a eumatic Actuator Sytem with roportioal Valve Gai Chaohui 1, *, Wag Cheggag 1 School of Electroic Egieerig, Wuha Vocatioal College of Software ad Egieerig, Wuha, Chia School of Mechaical ad Electrical Egieerig Wuha titute of echology, Wuha, Chia Abtract With the advatage of imple tructure, eumatic maipulator i equipped with o pollutio, high cot performace i the field of food proceig, microelectroic, the productio which ha bee widely ued. hi paper itroduce the cotrol of the ytem preet ituatio, aalyzig the proportioal valve i the peumatic proportioal poitio cotrol ytem ad the characteritic of the rod-le cylider, to etablih the mathematical model of the ytem, ad the tudy of the characteritic of the ytem, determie the iput igal through the experimet, through the ytem output igal, baed o the method of ytem idetificatio, the etimated ytem mathematical model i determied. Ad baed o the mathematical model, ad the LQR cotroller i deiged to cotrol ytem, uig the offlie model, realize the olie iteratio, gettig the mot optimal cotrol parameter to realize the optimal cotrol ytem. he the experimetal reult how that thi cotrol method make the ytem of cloed loop characteritic achieve a better characteritic, ytem tability alo ha a larger icreae at the ame time, compared with the traditioal proportioal cotrol, cotrol, the advatage of obtaied more atifactory reult, which ca provide a referece for the deig of the peumatic mechaim. ey word -, LQR, eumatic Actuator Sytem, Modelig, Cotroller eig, Cotrol Valve.. NROUCON eumatic maipulator with imple tructure, o pollutio, high cot, etc. i the food proceig, microelectroic ad other productio area have bee widely ued. However, due to the diadvatage of low tiffe, trog oliearity, time variability ad delay of the peumatic ytem, it i difficult to achieve the ideal effect, which make the applicatio i the field of idutry limited. eumatic techology i a key techology i the proce of realizig the automatio of productio proce, which i baed o compreed air a the workig medium [1]. After the two World War, due to the rapid progre of ciece ad techology ad ecoomic developmet, it i urget to improve the level of mechaizatio ad automatio of productio equipmet to improve product quality ad productio efficiecy. dutrial circle i the earch for high efficiecy, low cot, afe ad reliable ad ha a log ervice life of the automatio compoet ad techology, o peumatic techology came ito beig []. recet year, due to the developmet of moder cotrol theory ad microelectroic techology, epecially the developmet of computer techology, electroic techology ha bee applied i variou field [3]. At the ame time, the performace of the actuator ad the cotrol elemet i very much i the field of peumatic field. he lubricatio ad frictio characteritic of the cylider were igificatly improved, ad the dyamic ad tatic characteritic of the cotrol valve i more excellet, the repoe peed of the cotrol valve ha etered the market, at preet, may advaced idutrial productio departmet, uch a car, refrigerator, air coditioer, electrical ad electroic compoet, televiio, watche, bearig ad other productio lie, a large umber of peumatic device [4]. he baic workig priciple of peumatic ad hydraulic tramiio, workig mechaim of the compoet ad the compoitio of the circuit are imilar. However, due to the differet workig medium, the output power of hydraulic tramiio i large, the workig proce i table, ad it ca achieve a wide rage of teple peed regulatio ad ca top at ay poitio, the output diplacemet i iflueced by the exteral load ad the adjutmet preciio i high [5]. Widely ued i egieerig machiery, preure machie, automobile idutry ad automatio cotrol for a log time. Compared with the hydraulic tramiio, although the air preure of air a the medium, eay to hadle, ad eay to hadle, while the peumatic device ha the advatage of imple tructure, trog eviromet adaptability, low cot, log life, etc., but due to the large air compreor, air preure tramiio i difficult to achieve accurate cloed-loop ervo cotrol ad teple peed cotrol ad other factor, greatly limited the ue of peumatic techology, peumatic cotrol techology i limited to the eviromet ad ome imple witch cotrol [6]. recet year, the combiatio of micro electroic techology ad peumatic techology ha made ew vitality, ad the developmet of the world ha paid great attetio to the developmet of the idutry [7]. he techology of foreig air i kow a the "cheap automatio techology". At preet, developed idutrial coutrie, all automated procee about 3% with peumatic ytem, 9% of packagig machiery, 7% of the catig ad weldig O 1.513/JSSS.a SSN: x olie, prit

machie of automatic operatio device, 5%, 4% of forgig equipmet ad laudry equipmet, 3% of the coal miig machiery, % of the textile machie, hoe machie, wood proceig ad food machiery uig ga dyamic ytem,

2 machie of automatic operatio device, 5%, 4% of forgig equipmet ad laudry equipmet, 3% of the coal miig machiery, % of the textile machie, hoe machie, wood proceig ad food machiery uig ga dyamic ytem, 43% of the idutrial robot i peumatic tramiio. With the demad of idutrial productio automatio, it ca oly be reliably located at the two mechaical poitio ad it movemet peed by the igle et of oe-way throttle valve igle et of peumatic ytem, ha bee uable to meet may of the automatic cotrol requiremet [8]. he electric ervo ytem ca be very coveiet to realize teple peed regulatio ad teple peed regulatio. t ca meet the requiremet of the flexible productio of the automatio equipmet, which make it more ad more attetio ad applicatio [9]. he firt peumatic ervo valve wa developed uccefully i the hydraulic preure drive ad Cotrol Reearch titute of R.W Aache dutrial Uiverity of Wet Germay i 1979, ad the developmet of peumatic ervo cotrol wa greatly promoted by the W.Backe. May uiverity reearch ititute, the compay focued o the peumatic ervo icluded i the project, ad there are ew reult o diplay [1]. At the begiig of 8 ",.Eu et al deiged a ew type of peumatic ervo mechaim, ad tudied the tability ad preciio of the mechaim. taly' C.Belforate et al the locomotive brake techology i itroduced ito the peumatic mechaim, deig a brake device realize poitioig of the cylider at the target poitio, the poitioig accuracy i about.3mm. thi paper, the cotrol of the ytem i itroduced, ad the characteritic of the proportioal valve ad the o rod cylider are aalyzed, ad the characteritic of the ytem are tudied. hrough the experimet to determie the iput igal, the output igal i obtaied by the ytem, ad the ytem idetificatio method i baed o the ytem idetificatio. Baed o thi model, the deig of ad LQR cotroller i ued to cotrol the ytem. he model i ued to realize the optimal cotrol of the ytem. Experimetal reult ca provide referece for the deig of the peumatic mechaim.. NEUMAC ACUAOR SYSEM A. he baic model for the peumatic actuator ytem recet year, due to the rapid developmet of moder cotrol techology ad the rapid developmet of micro computer, the developmet ad applicatio of peumatic ervo techology have created coditio. he developmet of peumatic poitio cotrol, maily i everal apect: cotrol mode, cotiuou cotrol itead of quai cotiuou cotrol ad brake poitio cotrol; valve tructure, the tructure of imple peumatic proportioal valve to replace the tructure of complex peumatic ervo valve, ad the characteritic of the flow characteritic ad flow characteritic, the ue of computer cotrol: tructure deig, the ue of mechaical ad electrical combiatio. Ad rely o electric proportio cotrol techology, peumatic device i cotrol preciio ha bee a qualitative leap, electric tretch ratio / ervo cotrol ytem applicatio will be peumatic techology developmet directio ad the tedecy. he peumatic ervo ytem i coit of the cotroller, the electrical peumatic cotrol compoet, peumatic actuator, eor ad iterface circuit i geeral. he cotroller i uch a a computer, igle chip computer or programmable cotroller, etc. [11]. Electro peumatic cotrol compoet iclude electro peumatic ervo valve, electro peumatic proportioal valve ad electro peumatic valve. eumatic actuator are commoly ued i the cylider, rotatig cylider, ga, ga, motor, etc.. Seor geerally refer to the poitio eor, preure eor or peed eor. terface circuit betwee the cotroller ad the cotrol elemet, the iterface betwee the cotroller ad the eor. he baic model for the peumatic actuator ytem i hw i Fig. (1). Fig. (1). he Baic Model for the eumatic Actuator Sytem B. Hardware implemetatio thi reearch, the workig priciple of the peumatic proportioal preure ervo cotrol ytem i how i Fig. (). A the whole ytem of the cotrolled object, the FESO peumatic proportioal directioal valve i ued a the cotrol valve of the whole ytem. Baed o the ue of data collectio module Advatech CL78, the cotrol ytem i coected with the bedig the air ilet of the cylider preure eor voltage igal real-time acquiitio, through the operatio of the cotrol algorithm. Fially, through Advatech CL78 module of data outputtig cotrol igal output peumatic proportioal directioal cotrol valve, proportioal directioal cotrol valve cotrol acce to the bedig of the cylider flow, tue ito bedig cylider preure to reach the target preure, o a to cotrol the bedig of the cylider troke to et the goal of metal tube bedig agle. O 1.513/JSSS.a SSN: x olie, prit

Fig. (). he Workig riciple of the eumatic roportioal reure Servo Cotrol Sytem C. Software implemetatio thi reearch, MALAB ytem idetificatio toolbox i adopted to aalyze the ytem model.

3 Fig. (). he Workig riciple of the eumatic roportioal reure Servo Cotrol Sytem C. Software implemetatio thi reearch, MALAB ytem idetificatio toolbox i adopted to aalyze the ytem model. Sytem idetificatio toolbox i a graphical uer iterface, which i maily ued for etimatio ad aalyi of liear ad oliear model. Baed o the uer defied iput ad output, it ca be cotructed by the mathematical model of the dyamic ytem. So a to predict the output of the model baed o the etimatio. he uer ca ue the frequecy domai or time domai iput ad output data to etablih the dicrete time ad cotiuou time trafer fuctio ad proce model ad tate pace model. he detificatio oolbox provide the maximum likelihood, predictive error miimizatio (EM), ubpace ytem idetificatio, ad other idetificatio method. he uer ca realize the model to predict or forecat the repoe of the ytem ad Simulik imulatio.. he baic mathematical model of peumatic proportioal preure ytem Fig. () how that the mathematical model of the peumatic proportioal preure cotrol ytem i maily compoed of two part, the mathematical model of the proportioal directioal valve ad the bedig cylider. he mathematical model of the valve cotrolled cylider i formed by the combiatio of the two part. order to implify the derivatio proce, the followig aumptio are mde: A. he workig medium i a ideal ga. B. he upply preure ad temperature are cotat. C. he ga i the cylider i a homogeeou ga.. here are o ga leak i the cylider. Baed o the aumptio that the trafer fuctio of the proportioal directioal valve i how, the curret egative feedback amplifier i uually ued to avoid the ifluece of the characteritic of the amplifier. 1 X() U() 1 (1) X () i the hift of the valve core diplacemet; U() i the iput voltage of the proportioal valve. i the eor gai; i proportioal to the atural frequecy of the valve; i proportioal to the dampig ratio of the valve. he ope loop trafer fuctio of the bedig cylider ytem i obtaied accordig to the force balace equatio of the bedig cylider. Y() bb U() ( a a a a ) Y() i the laplace traform of the output diplacemet of the cylider, ad the X () i the diplacemet of the valve core. he mathematical model of the peumatic proportioal preure ytem i obtaied by itegratig the proportioal directioal valve ad the mathematical model of the bedig cylider ytem. By the equatio (1) ad (), the trafer fuctio of the peumatic proportioal preure ytem i how i equatio (3): k G ( 1) (3) k i the peed of the ytem, the k i the atural frequecy of the ytem; the i the dampig ratio of the ytem.. CONROLLER ESGN OF NEUMAC ACUAOR SYSEM cotroller i a liear regulator. he cotrolig output i formed by the differece betwee the give igal p() t ad actual output value y() t with the fuctio of the ratio of proportio () itegral () ad differetial () by liear () O 1.513/JSSS.a SSN: x olie, prit

4 combiatio of cotrol. he cotrol object i cotrolled. Amog them, the proportio of the cotrol ytem i proportioal to the deviatio igal et (). Oce produced, the regulator immediately i produced cotrol to reduce the deviatio. tegral part i maily ued to elimiate tatic error, improvig the ytem of o differece. he itegral fuctio i determied by the itegral time cotat i, the i i bigger, the itegral fuctio i weaker, ad vice vera. ifferetial fuctio i treated that the variatio tred ca reflect the deviatio igal (chage rate), ad ca itroduce a effective early correctio igal i the ytem, o a to peed up the ytem' movemet peed ad reduce the adjutmet time. A mathematical decriptio of the cotroller a below: 1 t t E t Ed i de t where, before the ummatio of diturbace t, the iput data of the cotrol ytem. Ad the error igal E t i defied by the followig equatio. E t p t y t (5) additio, dt (4) t i p t i the curret iput igal of the ytem. Bae o the egative feedback of the output igal, the cotroller ca be modified to chage the coefficiet of proportioal, itegral ad derivative gai i order to reduce the feedback error ad get the better cotrollig for the ytem. For liear ytem, the itegral of the two fuctio of tate variable ad cotrol variable i ued a the performace idex. he optimal cotrol problem of the two time performace idex of the liear ytem i called the two time. t optimal olutio ca be writte a a uified aalytical expreio. Ad it ca be derived from a imple tate liear feedback cotrol law, which i eay to calculate ad implemet. LQR (quadratic regulator liear) i a liear ytem with two time[1] he object i a liear ytem which i give by the tate pace form i the moder cotrol theory, ad the objective fuctio i the two fuctio of the object tate ad the cotrol iput. LQR theory i oe of the mot mature tate pace deig method i moder cotrol theory., the optimal cotrol law of LQR ca be obtaied by the tate feedback, which i eay to cotitute the cloed-loop optimal cotrol [13]. Ad the applicatio of Matlab provide the coditio for the imulatio of LQR, ad provide the coveiece for u to realize the table, accurate ad fat cotrol target. Uig the liear two time optimal cotroller for the cotrol ytem deig ad calibratio the bigget advatage i ot eceary accordig to the performace of the cloedloop pole poitio, jut eed to fid the appropriate tate variable ad cotrol variable baed o the repoe curve of the ytem. Becaue the cotroller i a error idicator J optimal cotroller, the performace of the ytem i alo the optimal J idex. May moder cotrol theorie have bee tudied a a reearch object. May paper itroduce the cotrol ytem baed o output feedback, but the cotrol effect i ot atifactory, the mai reao i the high order ad multi variable of the ytem. thi reearch, the LQR optimal regulator i adopted baed o the tate pace deig method, ad the robut tability ad the peed of the ytem i better. However, the traditioal theory for the ytem cotrollig i baed o both the iput-output relatiohip ad the trafer fuctio. the cofiguratio of LQR, the tate-pace model for the LQR proce cotrol are derived a follow: x t Ax t B t y t Cx t t t x t u t x t A B x t Bu t A x t Bu t Geerally, the optimal LQR i ofte defied a the followig equatio ad determied by the cotroller trafermatrix M that miimize. LQR H w t Qw t t R t dt (6) (7) (8) (9) (1) Amog the above equatio, Q i kow a ymmetric poitive-defiite matrix, where R i a m m matrix which i a ymmetric poitive-defiite. Ad i a poitive cotat. arameter R ad Q are elected to weigt the tep igal to the ytem ad optimize the cot fuctio repectively. the LQR cotroller deig, it i aumed that R 1 ad Q M M. he key to deig a liear two time optimal cotroller i to elect the weightig matrix R ad Q. Geerally, the greater the Q i elected, the horter the time required for the ytem to reach the teady tate. But alo reducig the R, the ytem ca achieve the deired time of the teady tate. Of coure, the actual ytem i required to allow. order to reduce the teady tate error of the ytem output, Nr i added after the referece iput. State vector i multiplied by the feedback vector. i adopted to reduce the ytem feedback error after the additio of cotat gai. Nr ca be decided by realizig the fuctio which i defied by the uer. Evetually, the performace of ad LQR cotroller are compared for aalyi purpoe. O 1.513/JSSS.a SSN: x olie, prit

5 V. COMUAONAL RESULS AN SCUSSON A. Model etimatio for the ytem he experimet data i iput to the ytem idetificatio toolbox i Matlab for variou data proceig, model etimatio, ad model aalyi tak. put igal i created by the equatio (11). he igal i take ito ue to the ytem i order to fid the differece betwee the etimated output igal ad the actual igal from the black ytem. he reult are illutrated with the iput ad output igal with the duratio of 5 ecod i Fig. (3) co 1.13co.3.5co y t t t t (11) Baed o the etimated reult, the ARX model i choe a the imulatio tructure for the cotrol ytem. order to eure the bet etimatio for the ytem the cotroller are deiged. A how i able, by varyig the coefficiet, offet value ad time iterval are tried to fid the bet olver ad performace for the ytem. y(t) (t) put ad output igal ime() Fig. (3). put ad Output Sigal ABLE. ERCEN OF BES F BY VARYNG OFFSE VALUES AN ME NERVAL Offet Value i the amplig time. ue to the bet fit percetage i above 9%, the reult are acceptable ad reaoable. he amplig rate mut be large eough o that the aalog igal ca be recotructed from the ample with ufficiet accuracy. order to avoid loig ay iformatio, the iterval mut be mall eough. B. Cotroller deig ARX331 model i adopted to imulate the output repoe by deigig the ad LQR cotroller. Biliear traformatio ad zero order hold method are ued to achieve the dicrete time model ito the cotiuou time model. he trafer fuctio are traformed ito cotiuou time model after the coverio of Biliear traformatio ad zero order hold are tated i (8) ad (9) repectively GB (1) GZOH (13) Baed o the parameter of, ad i able, cotroller i deiged to meaure the performace of the ytem. Square wave igal i iput to the ytem for the deigig ad tetig for differet cotroller deig. Cotroller type ABLE. ARAMEERS OF Cotiuou time model ( C 1.655, C.6 ), AN icrete time model ( C 6.453, C 1.78 ) O 1.513/JSSS.a SSN: x olie, prit

6 From Fig. (4) ad Fig. (5), it ca be oberved that the et time i.75 ecod, ad the rie time i.5 ecod, percetage overhoot i 4.%. additio, the teady tate error i.%. Fig. (5), ie wave igal i ued to tet the etimated model i the ytem. Obviouly, the output repoe i 55.4 degree phae compared with the iput. With the cotroller for poitioig cotrol, additioal load with differet weight are added to the ytem ,.6687,.413,.7989 Nr 1.73 (14) Compario betwee LQR ad cotroller 15 1 Square wave iput Meaured output amplitude put or output ime() Fig. (6). Compario betwee LQR ad Cotroller put or output ime() Fig. (4). Cotroller Olie etig with the Square Wave put Experimetal Machie etig (Sie iput ) Sie iput Meaured output ime() Fig. (5). cotroller Olie etig with the Sie Wave put order to compare the differece of the performace betwee the cotroller ad LQR cotroller, all the related parameter are tated a follow. he compario betwee LQR ad Cotroller i how i Fig. (6). Both LQR ad Cotroller ca be applied cotrollig for poitio of the peumatic actuator i the experimet ytem. able how the differece ad the differet performace of two differet cotroller by the imulatio. ABLE. FFERENCE BEWEEN LQR AN CONROLLERS LQR Cotroller Cotroller Rie time () Settlig time () Steady tate error () 6.15 Overhoot (%) 3.9 V. CONCLUSON he experimetal reult how that thi cotrol method make the ytem of cloed loop characteritic achieve a better characteritic, ytem tability alo ha a larger icreae at the ame time, compared with the traditioal proportioal cotrol, cotrol, the advatage of obtaied more atifactory reult, which ca provide a referece for the deig of the peumatic mechaim. he reearch cotet of thi paper lay the foudatio for the future reearch, ad poit out the directio ad provide the mea for the future reearch. REFERENCES [1] E. J. Barth ad M. Goldfarb, A Cotrol eig Method for Switchig Sytem With Applicatio to eumatic Servo Sytem. ASME Coferece roceedig, vol.1, o.5, pp , 1. [] G. othapalli ad M. Y. Haa, eig of a Neural Network Baed telliget Cotroller for a eumatic Sytem. AENG teratioal Joural of Computer Sciece, vol.35, o.1, pp. 17-, 8. [3] H.. Ali, et al., Mathematical ad telliget Modelig of Electropeumatic Servo Actuator Sytem. Autralia. Joural of Baic ad Applied Sciece, vol. 3, o., pp , 9. [4] J. E. akooglu, et al., Rapid prototypig of fuzzy cotroller peumatic ervo-ytem. he teratioal Joural of Advaced Maufacturig echology, vol. 4, o. 13, pp , 9. O 1.513/JSSS.a SSN: x olie, prit

7 [5] M. B. homa, et al., A ovel low cot peumatic poitioig ytem. Joural of maufacturig ytem, vol. 4, o.4, pp , 13. [6] Hazem. Ali, B Mohd Noor, S.M Bahi, et al., A review of eumatic Actuator (Modelig ad Cotrol). Autralia Joural of Baic ad Applied Sciece, vol. 3, o., pp [6] A. Saleem, et al., O-lie idetificatio ad cotrol of peumatic ervo drive via a mixed-reality eviromet. he teratioal Joural of Advaced Maufacturig echology, vol.4, o.5, pp , 9. [7] M.F. Rahmat, Sy Najib, N.H Suar, et al., detificatio ad oliear cotrol trategy for idutrial peumatic actuator. teratioal Joural of hyical Sciece, vol. 7, o.17, pp , 1. [8] M. aghizadeh, et al., Multimodel -cotrol of a peumatic actuator uder variable load. he teratioal Joural of Advaced Maufacturig echology, vol. 48, o. 3, pp , 1. [9] R.Ghazali, Y.M.Sam, M.F.Rahmat, et al., Recurive parameter etimatio for dicrete-time model of a electro-hydraulic ervor ytem with varyig forgettig factor. teratioal Joural of the hyical Sciece, vol. 6, o. 3, pp , 11. [1] V. Blagojevi ad M. Stojiljkovi, Mathematical ad imulik model of the peumatic ytem with bridgig of the dual actio cylider chamber. Facta uiveritati-erie: Mechaical Egieerig, vol. 5, o. 3, pp. 3-31, 7. [11] R. Richardo, et al., Self-tuig cotrol of a low-frictio peumatic actuator uder the ifluece of gravity. EEE raactio o Cotrol Sytem echology, vol. 9, o.1, pp , 1. [1] Y.. Liu ad C. C. Jiag, eumatic actuatig device with aopoitioig ability utilizig Z impact force coupled with differetial preure. reciio egieerig, vol. 31, o.3, pp , 7. O 1.513/JSSS.a SSN: x olie, prit

ECEN689: Special Topics in Optical Interconnects Circuits and Systems Spring 2016

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