Combined Feedback/Feedforward Velocity Control of Electrokinetically Driven Flow in a Network of Planar Microchannels

Transcription

1 Combind Fdback/Fdforward Vlocity Control of Elctrokintically Drivn Flow in a Ntwork of Planar Microchannls Babak Assadsangabi a,b, Said Movahd a,c, Mohammad Eghtsad a,yousf Bzargan-Lari d a Dpt. of Mchanical Enginring, Shiraz Univrsity, Shiraz, Iran b Dpt. of Elctrical Enginring, Univrsity of British Columbia, Vancouvr, BC, Canada c Dpt. of Mchanical and Mchatronic Enginring, Univrsity of Watrloo, Watrloo, ON, Canada d Mchanical Enginring Dpartmnt, Islamic Azad Univrsity, Shiraz Branch, Shiraz, Iran, (-mail: bazargan@kcc.shirazu.ac.ir) Abstract: In th prsnt study, a combind fdback/fdforward stratgy will b utilizd in ordr to control th output flow rat in a micro-t junction. First, Finit Elmnt Modl (FEM) of th lctroosmotic flow in th T-junction will b gnratd and thn this modl will form a basis for gnrating training data for building an invrs modl of th flow in th T-junction basd on Adaptiv Nural Fuzzy Infrnc Systm (ANFIS). This invrs modl srvs as a controllr in th fdforward part of th systm. Also, in ordr to mak th controllr robust against disturbancs and uncrtaintis such as dimnsional tolrancs, a Mamdani-typ fuzzy logic controllr is incorporatd in th fdback part of th controllr. Finally, simulation rsults will b prsntd in ordr to stablish th prformanc of th dsignd controllr. Kywords: Nural Ntwork, Fuzzy Logic, Elctrokintics, Elctroosmosis, Microchannl 1. INTRODUCTION Elctrokintics is a group of intrfacial phnomna that bcom prominnt in micron and submicron dimnsions. Elctrokintic phnomna wr first discovrd by Russ in 1806; howvr, it took until 1994 whn Probstin dividd linar lctrokintic phnomna into four catgoris namly lctroosmosis, lctrophorsis, straming potntial and sdimntation potntial (Karniadakis, t al., 2005). Elctroosmotic flow (which is th rsult of lctroosmosis ffct) is th motion of liquid, inducd by an applid potntial across capillary tubs or microchannls. Elctroosmotic flow has many advantags in comparison with prssur drivn flow such as bing vibration fr, compact, and having flat-form vlocity (Hu, t al., 2007). Elctroosmosis ffct in lab-on-achip microfluidic dvics has xtnsivly bn utilizd during th past dcad for various applications such as micro-pumps (Chng, t al., 2009), flow control (Dutta, t al., 2002), micromixing (KaoFng Yarn), and biological cll studis (Movahd, t al., 2011). Gnrally, microfuidic lab-on-a-chip dvics contain diffrnt units such as biological and chmical dtction units, flow control lmnts, and ncssary lctronics on a singl microchip which should b coordinatd in a way that th dvic can oprat prcisly. Howvr, microfabrication of such units is quit complicatd and pron to imprfctions in th form of manufacturing dimnsional rrors which can affct th dsird prformanc of th systm. Morovr, failur of moving parts lik mircopumps and microvalvs du to fatigu and fabrication dfcts is invitabl. To ovrcom ths problms, w utiliz lctroosmotic flow which involvs no moving parts; on th othr hand, to cop with othr sourcs of inaccuracy, w intnd to incorporat th fdback control concpt which has th potntial to compnsat for thos unknown sourcs of rror and uncrtainty. Litratur rviw shows that gnrally studis in th fild of control of th lctroosmotic flow in microchannls can b groupd into two catgoris. Th first catgory includs thos studis which only apply fdforward (opn-loop) control concpt to th control of th lctroosmotic flow. For instanc, Dutta t al. dvlopd numrical modls for dscribing fluid flow in complx micro-gomtris such as cross-flow junctions and Y-Split channls (Dutta, t al., 2002). By utilizing ths numrical modls, thy could prdict th flow rat in branchs of such micro-gomtris. Also, Hahm t al. xploitd local lctrokintic forc to control flow and spcis transport in groovd microchannls (Hahm, t al., 2007). Th scond catgory of studis includs thos which proposd practical dvics in ordr to control lctroosmotic flow in microchannls. Orosozi and collagus mployd light as a man of th actuator to control th lctroosmotic flow (Oroszi, t al., 2006). Thy could locally chang th lctric fild strngth by illuminating a photoconductiv wall, and as a rsult th lctroosmotic driving forc could b controlld. Numrous othr studis also proposd diffrnt practical mthods in ordr to control flow in microchannls, for xampl s rfrncs (Glawdl, t al., 2009; Mrutusatorn, t al., 2009). Thrfor, to th bst of our knowldg, fdback control concpt has not yt bn mployd in ordr to control th lctroosmotic flow in microfluidic systms. By dfinition, th channls that thir smallst dimnsion is btwn 10 um to 200um ar calld microchannl (Kandlikar, t al., 2006). Th microfluidic lab-on-a-chip dvics ar usually containd ntworks of th microchannls. Ths ntworks ar typically shapd by diffrnt kinds of junctions such as cross-flows, Y-splits and T-junctions. In th prsnt study, th flow control of th T-junction is invstigatd; Copyright by th Intrnational Fdration of Automatic Control (IFAC) 12313

2 howvr, th proposd approach can b asily xtndd to th othr typs of junctions. Sinc th govrning quations of th lctroosmotic flow in microchannls ar nonlinar partial diffrntial quations, th convntional modl-basd control stratgis may not b asily utilizd. Thrfor, w incorporat intllignt control stratgis in combination with th closd-loop control concpt to accuratly rgulat th lctroosmotic flow rat in a T- junction of microchannls. To implmnt th proposd controllr, w will incorporat th fdback/fdforward control stratgy. In th fdforward part of th controllr, Adaptiv Nural Fuzzy Infrnc Systm (ANFIS) is utilizd in ordr to obtain an invrs modl of th systm. In th fdback part, Mamdani-typ Fuzzy Logic controllr is utilizd to incras th robustnss of th controllr against modl uncrtaintis and disturbancs. In ordr to dsign th proposd controllr, following stps ar prformd. First, w will us Finit Elmnt Mthod (FEM) in ordr to obtain numrical modl of th T-junction; thn, this modl will gnrat th training data ndd by th ANFIS modl to acquir th invrs modl of th lctroosmotic flow in th T-junction. This invrs modl srvs as a controllr in th fdforward part of th systm. Howvr, bcaus of diffrnt uncrtaintis in th systm such as dimnsional rrors, thr is always an rror btwn th dsird flow rat and th actual on producd in th fdforward part. To rduc this rror, th fdback part is addd to th systm. This part oprats basd on th Mamdani-typ Fuzzy Logic controllr. Finally, th prformanc of th proposd controllr will b invstigatd numrically. 2. GOVERNING EQUATIONS In th prsnt study, incomprssibl flow of Nwtonian fluid with slip-vlocity boundary condition in planar microchannls is assumd. Vlocity fild of lctroosmotic flow can b obtaind by solving a following st of partial diffrntial quations (Movahd, t al., 2010). u 0 (1) Du 2 p u (2) Dt 2 0 (3) E (4) T0E us (5) u 0, p0 (6) nj 0 (7) (8) V i Eqns. (1) and (2) ar continuity and Navir-Stocks quations, rspctivly. Laplac quation (Eq. (3)) should b solvd to find th lctric potntial in th systm. Extrnal lctric fild is th gradint of lctric potntial (Eq. (4)). Hlmholtz- Smoluchowski slip vlocity (Eq. (5)) is applid on th walls of microchannls in ordr to considr lctroosmosis ffct. Opn boundary (Eq. (6)) is assumd at th nds of channls. C A O B Figur 1. Schmatic illustration of th T-junction. Boundary A is an inlt of th systm. Boundaris B and C ar controlld outlt and by pass, rspctivly. Walls of th microchannls ar lctrically isolatd (Eq. (7)). At th nds of th microchannls (plac of lctrods), w considr constant applid voltag (Eq. (8)). Assumd valus of th applid voltag hav bn prsntd in tabl Systm modling In this study, control of an lctroosmotic channl flow in a micro T-junction is invstigatd (Figur 1). Th intntion of th proposd control systm is to rgulat th flow rat in OBbranch of th T-junction by manipulation of th voltag at th nd of OC-branch. It should b notd that th voltag at th nd of OA- and OB-branchs and ζ-potntial on th walls of th T-junction ar kpt constant. Th dimnsions and flow paramtrs of th lctroosmotic flow in this microgomtry ar prsntd in tabl 1. Also, in ordr to simulat th flow in th T-junction, a commrcial finit lmnt softwar packag (Comsol Multiphysics 3.5a) is usd. 4. Controllr Dsign It is known that fdforward control is bst dployd in control systms dsign applications whr th procss or controlld variabl bhavior is wll undrstood. A wll undrstood procss is on in which th first principal quations dscribing th procss ar known for th givn application, and ar corrctly applid to adquatly dscrib th procss. On th othr hand, fdback control is typically usd whn th accuracy providd by fdforward controls is not adquat to mt th application prformanc spcifications. In th prsnt study, in ordr to dsign a robust controllr which can cop with modl uncrtaintis and disturbancs, in addition to th fdforward controllr which is th invrs modl of th plant, a Mamdani-typ Fuzzy controllr is usd in th fdback part of th systm. Figur 3 shows th proposd controllr dsign. In th following, dsign procdurs for both fdforward and fdback part of th systm ar prsntd. 4.1 Fdforward controllr Invrs modl of th T-junction As it was mntiond in th prvious sction, flow in microchannls is govrnd by complx partial diffrntial quations; thrfor, obtaining an invrs mathmatical 12314

3 Tabl 1. Paramtrs usd in systm modlling half channl branch lngth(m) hight(m) OA 150x10-6 6x10-6 OC 150x10-6 6x10-6 OB 150x10-6 6x10-6 ζ-potntial (Volt) Applid voltags(volt) 30 modl for th flow in microchannls can b quit challnging. To ovrcom this problm, w hav xploitd th modling capabilitis of th ANFIS in ordr to acquir th invrs modl of th flow in th T-junction. ANFIS has combind th advantags of Artificial Nural Ntworks (ANNs) with Fuzzy Logic (FL) which has rsultd in a powrful mthod in modling complx nonlinar systms. Unlik convntional fuzzy infrnc systms, ANFIS modling tchniqu dos not dpnd on th opinion of an xprt who is familiar with th plant and it only rquirs an input-output data st ithr from th mathmatical modl or actual prototyp of th plant. In this study, ANFIS architctur is usd to modl a dynamic systm, which is takn as a black box, i.. dscribd by its obsrvd rsponss to th introducd inputs. In th squl, th ANFIS mthod will b brifly xplaind ANFIS: Adaptiv-Ntwork-basd Fuzzy Infrnc Systm Th structur of ANFIS has 5 layrs (s figur 2) and it uss Takagi-Sugno-Kang (TSK) fuzzy infrnc modl to b th larning algorithm (Jang, 1993). Considr th structur of fuzzy infrnc systm with two inputs, x and y, and on output z. In th first ordr TSK fuzzy infrnc modl systm (FIS), th typical fuzzy if-thn rul can b xprssd as: Ruli : If ( x is A ) and ( y is B ) thn f p x q y r V c 10 i i i i i i Hr, x and y inputs constitut th prmis variabls of th fuzzy ruls. A i and B i ar th prmis paramtrs. p i, q i, and r i ar th consqunc paramtrs. Using th f i function, which ar combinations of consqunt paramtrs, and th wight valus of w i, th ovrall output function f for this TS modl is xprssd as (considr i=1, 2): w f w f f w1 f1 w f 2 2 w1 w2 Figur 2. ANFIS modl for TS fuzzy structur ( (Jang, 1993)) Q d u 1 u in Q out 1 2 u 3 Figur 3. Structur of th proposd Fdback/Fdforward controllr. Boxs 1, 2, and 3 ar invrs modl of th systm, FEM modl of th systm, and fuzzy controllr, rspctivly. ANFIS has fiv layrs; functions of ths layrs can b xplaind brifly as blow (Jang, 1993): Layr1: In this layr whr th fuzzification procss taks plac, vry nod is adaptiv. Outputs of this layr form th mmbrship valus of th prmis part. Layr2: In contrast to layr1, th nods in this layr ar fixd. Each nod output rprsnts a firing strngth of a rul. Layr3: In this layr whr th normalization procss is prformd, th nods ar fixd as thy ar in layr 2. Th ratio of th i th rul s firing strngth to th sum of all ruls firing strngths is calculatd for th corrsponding nod. Layr4: Sinc th nods in this layr oprat as a function block, whos variabls ar th input valus, thy ar adaptiv. Consquntly, th output of this layr forms TSK outputs and hnc is rfrrd to as th consqunt part. Layr 5: This is th summation layr, which consists of a singl fixd nod. It sums up all th incoming signals and producs th output Drivation of training data for ANFIS Th original input of th finit lmnt forward modl of th microchannl is th voltag on th OC branch and th output is th flow rat in th OB branch. Thrfor, th input and th output for th invrs modl ar th flow rat and th voltag, rspctivly. In ordr to lt ANFIS larn mor corrctly, adquat training data computd from th finit lmnt forward modl is ndd. Tabl 2 lists th input-output training data st usd in th ANFIS larning procss. 4.2 Fdback controllr As it was mntiond arlir, fdback part is addd to th systm to incras th robustnss of th systm against modl uncrtaintis and disturbancs; thrfor, in fdback loop, w hav xploitd a robust controllr namly, fuzzy logic controllr. In th following, th dsign procdur for th Mamdani-typ fuzzy logic controllr is brifly prsntd

4 Tabl 2. Th input-output training data st usd in th ANFIS larning procss. Voltag Flow rat Voltag Flow rat Voltag Flow rat (volt) (m 3 ) (volt) (m 3 ) (volt) (m 3 ) Fuzzy controllr Th concpts of fuzzy st thory, fuzzy IF-THEN ruls, and fuzzy rasoning ar th basis of th framwork calld fuzzy infrnc systm. A fuzzy infrnc systm (FIS) is a knowldg-basd systm that convrts linguistic variabls into its knowldg bas using fuzzy ruls and mmbrship functions. Fuzzy infrnc systms ar also known as fuzzyrul-basd systms, fuzzy modls, fuzzy associativ mmoris (FAM), or fuzzy controllrs whn usd as controllrs (Passino & Yurkovich, 1998). Basically, a fuzzy infrnc systm is composd of four functional blocks (figur 4): 1. A rul bas containing a numbr of fuzzy if-thn ruls. In th prsnt study, th FAM tabl 3 is usd as th rul bas of th infrnc systm. A databas which dfins th mmbrship functions of th fuzzy sts usd in th fuzzy ruls. In th prsnt study, triangular mmbrship functions ar usd. Hr, µ(x) is th grad of mmbrship function at x and a L, a C, and a R dnot lowr limit, cntr and uppr limit of th mmbrship function rspctivly. Figur 4. Schmatic block diagram of fuzzy infrnc systm (Passino & Yurkovich, 1998). L x a L a xa C L a a ( x) 0 othrwis R a x C a xa R C a a C R Figur 5 dpict mmbrship functions for,, and u. th valus of a 1, a 2, b 1, and b 2 ar prsntd in tabl A dcision-making unit which prforms th infrnc oprations on th ruls. In th prsnt study w will us Max- Min mthod in dcision-making unit. Max-Min mthod oprats basd on Max-Min oprator. 3. A fuzzification intrfac which transforms th crisp inputs into dgrs of match with linguistic valus. Tabl 4. FAM tabl of th Mamdani fuzzy controllr u u a b a b a b a b a b Tabl 3. FAM tabl of th Mamdani fuzzy controllr NL NS Z PS PL NL PL PS PS Z NS NS PS PS PS NS NS Z PL PS Z NS NL PS PS PS NS NS NS PL PS Z NS NS NL Figur 5. Mmbrship functions for,, and u. In th prsnt study, triangular mmbrship functions ar usd. Th assumd valus of a i and b i ar prsntd in tabl

5 4. A dfuzzification intrfac which transform th fuzzy rsults of th infrnc into a crisp output. In th prsnt study cntroid dfuzzification mthod is usd which is dfind by th following quation: ( ) * out x x y ( x) out 5. SIMULATIONS AND RESULTS In ordr to invstigat th prformanc of th dsignd controllr, systm rsponss for rgulation of flow rat to a dsird valu is numrically simulatd. Also, to xamin th robustnss of th controllr a disturbanc in th form of dimnsional inaccuracy in manufacturing of th microchannl (about 2% incras in width of th channl) is introducd in th finit lmnt modl of th T-junction. Figur 6 illustrats rror (), flow rat in OB-branch (Q OB ), and applid voltag at th nd of OC-branch (V OC ). As it can b sn from this figur, aftr th first itration in tim, th output flow rat is (m 3 /s); howvr, th dsird flow rat is (m 3 /s) (=2.32%). Thrfor, in ordr to rduc this rror, th fdback part which oprats basd on Mamdani-typ fuzzy control was addd to th systm. Clarly, it can b sn form figur 6 that aftr ach itrations in th tim, th rror bcoms smallr and th output flow rat convrgs to th dsird valu. Figur 6. This figur shows th ffcts of th proposd controllr of this study on th rsponss for rgulation of flow rat to a dsird valu. Parts (a), (b), and (c) ar for rror, flow rat, and applid voltag at point C, rspctivly. From this figur, it is clar that aftr ach itration in th tim, th rror bcoms smallr and th output flow rat convrgs to th dsird valu

6 4. CONCLUSION In this papr, th fasibility of th us of nural ntwork and fuzzy modling capabilitis in controlling and modling of microfluidic systms was invstigatd. In ordr to xplor this concpt, th simulation powr of COMSOL Multiphysics was utilizd which on on hand could numrically simulat flow in microchannls and on th othr hand could b linkd to Matlab's fuzzy and nural ntwork toolboxs. In th prsnt study, a combind Fdback/Fdforward stratgy was xploitd in ordr to control th output flow rat in a micro-t junction. First, Finit Elmnt Modl (FEM) of th lctroosmotic flow in th T-junction was gnratd and thn basd on this modl, training data wr gnratd for building an invrs modl of th flow in th T-junction basd on Adaptiv Nural Fuzzy Infrnc Systm (ANFIS). This invrs modl srvd as th controllr in th fdforward part of th systm. Also, in ordr to mak th controllr robust against disturbancs and uncrtaintis such as dimnsional tolrancs, a Mamdani-typ Fuzzy Logic controllr was incorporatd in th fdback part of th controllr. Finally, simulation rsults showd that adding th fdback controllr to th fdforward part of th controllr not only has considrably rducd th valu of th rror but also has mad th ovrall controllr robust against th uncrtaintis and disturbancs. REFERENCES Arnold, A. K., Nithiarasu, P., & Eng, P. F. (2008). Elctroosmotic flow in microchannls. Procdings of th Institution of Mchanical Enginrs, Part C: Journal of Mchanical Enginring Scinc, 222 (5), Chng, X. W., Wang, S., & Liu, S. (2009). Elctroosmotic pumps and thir applications in microfluidic. Microfluid Nanofluid, 6, Dutta, P., Bskok, A., & Warburton, A. (2002). Elctroosmotic flow control in complx microgomtris. Journal of MICROELECTROMECHAANICAL systms, 11, Glawdl, T., & Rn, C. L. (2009). Elctro-osmotic flow control for living cll analysis in microfluidic PDMS chips. Mchanics Rsarch Communications, 36 (1), Hahm, J., & Balasubramanian, A. (2007). Flow and spcis transport control in groovd microchannls using local lctrokintic forcs. Journal of Physics of Fluids, 19. Hu, G., & Li, D. (2007). Multiscal phnomna in microfluidics and nanofluidics. Chmical Enginring Scinc, 62, Jang, J. (1993). ANFIS: Adaptiv Ntwork-Basd Fuzzy Infrnc Systm. IEEE Trans. on Systms, Man and Cybrntics, 23 (3), Kandlikar, S., Garimlla, S., Li, D., Colin, S., & King, M. (2006). Hat Transfr and Fluid Flow in Minichannls and Microchannls. Nw York: Elsvir. KaoFng Yarn, S. H. Microfluidic mixing nhancmnt using lctrokintic instability undr lctric fild prturbations in a doubl T-shapd microchannl. Scinc in China Sris G: Physics Mchanics and Astronomy, 52 (4), Karniadakis, G., Bskok, A., & Aluru, N. (2005). Microfluidics and Nanofluidics Fundamntals and Simulation. Nw York: Springr. Li, D. (2004). Elctrokintics in Microfluidics. Elsvir. Li, D. (2008). Encyclopdia of Microfluidics and Nanofluidics. Springr. Movahd, S., & Li, D. (2011). Microfluidics cll lctroporation. Microfluid Nanofluid, 10 (4), Movahd, S., & Li, D. (2010). Numrical studis of continuous nutrint dlivry for tumour sphroid cultur in a microchannl by lctrokintically-inducd prssur-drivn flow. Biomdical Microdvics, 12 (6), Mrutusatorn, P., Mahfouz, M. R., & Wu, J. (. (2009). Lowvoltag dynamic control for DC lctroosmotic dvics. Snsors and Actuators A: Physical, 153 (2), Oroszi, L., Dr, A., Kiri, H., Ormos, P., & Rakovics, V. (2006). Control of lctroosmotic flow by light. Appl. Phys. Ltt., 89. Passino, K., & Yurkovich, S. (1998). Fuzzy Control. Xu, Z., Miao, J., Wang, N., Wn, W., & Shng, P. (Articl in Prss). Digital flow control of lctroosmotic pump: Onsagr cofficints and intrfacial paramtrs dtrmination. Solid Stat Communications. Yan, Y. Y., Zu, Y. Q., Rn, L. Q., & Li, J. Q. (2007). Numrical modlling of lctro-osmotically drivn flow within th microthin liquid layr nar an arthworm surfac - a biomimtic approach. Procdings of th Institution of Mchanical Enginrs, Part C: Journal of Mchanical Enginring Scinc, 221 (10),