Polymer electrolyte membrane fuel cell control with feed-forward and feedback strategy

Transcription

1 MultCraft Internatonal Journal of Engneerng, Scence and Technology Vol. 2, No. 10, 2010, pp INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY Multcraft Lmted. All rghts reserved Polymer electrolyte membrane fuel cell control wth feed-forward and feedback strategy Omar Rgab, D. L. Yu and J. B. Gomm Control Systems Research Group, School of Engneerng,Lverpool John Moores Unversty, Byrom Street, Lverpool, L3 3AF, UK Emal: Abstract Feed-forward and feedback control s developed n ths work for Polymer electrolyte membrane (PEM) fuel cell stacks. The feed-forward control s acheved usng dfferent methods, ncludng look-up table, fuzzy logc and neural network, to mprove the fuel cell stack breathng control and prevent the problem of oxygen starvaton. Frstly, the feed-forward controller s used to generate drectly an nput voltage of the compressor accordng to the current demand. Then, a PID controller s used n the feedback to adjust the dfference between the requested and the actual oxygen rato by compensatng the feed-forward controller output. The desgned system s evaluated usng a nonlnear smulaton of a fuel cell model documented n the lterature. The proposed feed-forward wth PID controller have acheved a good control performance. The smulaton showed effectveness of the control strategy. Keywords: Fuel cell; fuel cell stack; breathng control; starvaton; feed-forward; fuzzy logc; neural network. 1. Introducton There are many envronmental problems n the world today assocated wth current natural sources such as fossl fuels. Burnng fossl fuels emts CO 2 and destructs the ozone layer whch leads to clmatc change and what s known as the greenhouse effect. From ths pont, the world has been lookng for energy sources that are clean and safe on the envronment. Fuel cells are a knd of clean and safety energy source on the envronment. Polymer electrolyte membrane (PEM) fuel cells emerge as one of the most clean and promsng alternatves to reduce fossl fuel dependency (Pukrushpan et al., 2004a). In ths paper some advanced control methods are mplemented to acheve better control for the fuel cell breathng. 1.1 Fuel cell workng prncples: Fuel cells convert chemcal energy of a hydrogen fuel (on the anode sde) nto electrc energy wth water and some heat through a chemcal reacton wth oxygen (on the cathode sde) (Pukrushpan et al., 2004b), to satsfy dfferent power requrements (fgure 1). Generally, the reactants flow n and reacton products flow out whle the electrolyte remans n the cell. Fuel cells can operate contnuously as long as the necessary flows are mantaned. Fuel cells dffer from batteres n that they do not need rechargng, they operate quetly and effcently, and when hydrogen s used as fuel they generate only electrc power and drnkng water. So, they are called zero emsson engnes. Wllam Grove has dscovered the basc operatng prncple of fuel cells by reversng water n 1839 (Hoogers, 2003). In partcular, proton exchange membrane FCs (PEM- FCs), also known as polymer electrolyte membrane FCs, s consdered to be more developed than other FC technologes, because they have hgh power densty, sold electrolyte, operate at low temp, long cell and stack lfe and low corroson (Hoogers, 2003). The PEM-FC takes ts name from the specal plastc membrane used as the electrolyte. Ths membrane electrode assembly (MEA), not thcker than a few hundred mcrons, s the heart of a PEM-FC and, when suppled wth fuel and ar, generates electrc power at cell voltages around 0.7 V and power denstes of up to about 1 W/cm electrode area (Spegel, 2008).

2 57 Exhaust Hydrogen Anode 2H2 4 +4e - Water Membrane Ar Compressor Catode O e - 2H2O Water Motor External Load Fgure1. PME- FC reacton and structure Fgure 2 shows a schematc of an MEA. The MEA s typcally located between a par of current collector plates (platnummpregnated porous electrodes) wth machned flow felds for dstrbutng fuel and oxdant to the anode and cathode, respectvely. A water jacket for coolng s often placed at the back of each reactant flow feld followed by a metallc current collector plate. The cell can also contan a humdfcaton secton for the reactant gases, whch are kept close to ther saturaton level n order to prevent dehydraton of the membrane electrolyte. Many FCs are connected electrcally n seres to form an FC stack (FCS). V Electrcal Load Ist Hydrogen Tank s Hydrogen n Fuel Cell Stack Oxygen n Motor Compressor Pump Humdfer Coolng system Pump Anode Catode Water out s Water Separator Flter λ O2 Water Tank Fgure 2. PEM fuel cell structure 1.2 Fuel stack model: The fuel cell stack (FCS) model smulated n ths paper conssts of four nteractng sub-models whch are the stack voltage, the anode flow, the cathode flow, and the membrane hydraton models (Pukrushpan et al., 2005). The voltage model contans an equaton to calculate stack voltage that based on fuel cell temperature, pressure, reactant gas partal pressures and membrane humdty. In summary, the fuel cell voltage E s gven by 1 E = ( T ) fc + T fc [ln( p ) + ( p )] (1) H 2 O2 2 Fgure 3. Smulnk model of ntegrated PEM fuel cell

3 58 where, T fc the fuel cell temperature n Kelvn, p H2 and p O2 are the partal pressures of hydrogen and oxygen respectvely, detals n Pukrushpan et al. (2005, 2004c). In ths model the stack temperature s assumed to be constant at 80 o C. The model whch s used n our nvestgaton s gven n (Pukrushpan et al., 2005). The FCS Smulnk model s created n Matlab Lterature survey: The man three parameters of fuel cell stack are stack current І st, stack voltage v st and the oxygen rato λ o2. A fuel cell (FC) stack has to be operated properly to get good power effcency, relablty and smooth operaton. The man dsadvantage of the fuel cells stack system s the oxygen starvaton. Snce current s nstantaneously drawn from the load source connected to the FC, the FC control system s requred to mantan optmal temperature, membrane hydraton, and partal pressure of the reactants across the membrane to avod detrmental degradaton of the FC voltage, whch can reduce effcency. Fuel cell parameters need to be controlled to avod the oxygen starvaton phenomena when the current s drawn from the fuel cell. Some researchers have presented some methods to control the breathng of fuel cell stack n order to prevent the problem of oxygen starvaton, and some other problems, whch are now revewed. Frede and Davat. (2004) proposed the governng equatons of the transent behavor of a PEM fuel cell to show the nfluence of the operatng condtons (such as temperature, pressure and gas flows have an effected on the humdty condton of the fuel cell and ther choce s the greatest challenge n fuel cell operaton) and the current densty on nternal parameters, especally the ohmc resstance to mprove the control of fuel cell. The models were sutable for descrpton of hghly nonlnear behavor of the fuel cells. Vahd et al. (2006) have used a bank of ultra capactors supplements the fuel cell durng fast current transent n order to prevent fuel cell oxygen starvaton, ar compressor surge and choke, and smultaneously match an arbtrary level of current demand durng rapd load demands. A model-predctve controller has been desgned for optmal dstrbuton of current demand between the fuel cell and the bank of ultra capactors, whch s handled multple constrans of the hybrd system. Pukrushpan et al. (2002) mplemented a nonlnear fuel cell dynamc model for control study of fuel cell. The model has captured the transent phenomena whch nclude the flow characterstcs and nerta dynamcs of the compressor, the manfold fllng dynamcs and consequently, the reactant partal pressures. They attempted to desgn an observer based feedback and feed-forward controller that manages the tradeoff between reducton of parastc losses and fast fuel cell net power response durng rapd current (load) demands. An ar flow controller (Pukrushpan et al., 2004b) to protect the FC stack from oxygen starvaton durng step changes of current demand have been desgned, the steady-state regulaton of the oxygen excess rato n the FCS cathode have been acheved by assgnng an ntegrator to the compressor flow. Lnear observabllty technques were employed to demonstrate mprovements n transent oxygen regulaton when the FCS voltage s ncluded as a measurement for the feedback controller. A lnear optmal control desgn had been used to dentfy the frequences (the FCS voltage sgnal contans hgh frequency nformaton about the FC oxygen utlzaton, and thus, s a natural and valuable output for feedback) at whch there was a severe tradeoff between the transent system net power performance and the stack starvaton control. The lmtaton arses when the FCS system archtecture dctates that all auxlary equpment s powered drectly from the FC wth no secondary power sources. An observer was desgned by Arcak et al. (2004) to estmate anode hydrogen pressure wth an output njecton term based on stack voltage. The paper by Kunusch et al. (2009) tackles the breathng problem of subsystem of a PEM fuel cell stacks by usng a second order sldng mode strategy. The proposed control strategy s based on a super twstng algorthm that robustly solves the stablzaton problem avodng chatterng effects. The resultng approach exhbts good dynamc characterstcs, beng robust to uncertantes and dsturbances, and the results were provded showed the feasblty of the approach. A method for controllng a nonlnear underactuated system (DFore., 2009) usng augmented sldng mode control (SMC) have been nvestgated, where the proposed control approach nvolves ntroducng a transformaton matrx mappng the systems nput nfluence matrx to a transformed system that s square and thus nvertble. The proposed approach s shown to control selectable states wth proper choce of the transformaton matrx yeldng good control performance. From other hand, the methodology s appled to an under actuated nonlnear fuel cell system to show ts vablty n a real world applcaton, then a sldng mode controller s derved for the full nonlnear system wth a swtchng gan accountng for modelng errors and uncertantes. Smulaton results ndcate the vablty of the proposed control law and demonstrate the robust nature of the control law n the presence of sgnfcant modelng errors whle mantanng trackng stablty. Fnally, the augmented SMC s compared to a tradtonal lnear control archtecture llustratng the electveness and advantages n trackng performance and control effort over tradtonal methods. 2. Fuel cell control technques The FC ar flow needs to be controlled rapdly and capably. In order to avod oxygen starvaton and extend the lfe of the FC stack (Yang et al.,1998) Oxygen starvaton s a complcated phenomenon that occurs when the partal pressure of oxygen falls below a crtcal level at any locaton wthn the meander of the ar stream n the cathode (Sprnger et al., 2001). Ths phenomenon entals a rapd decrease n cell voltage, whch n severe cases can causes a hot spot, or even burn-through on the surface of a membrane. Although the oxygen starvaton s spatally varyng, ths phenomenon can be avoded by regulatng the cathode excess oxygen rato λ O2. We thus regulate ar rato n the FCS cathode by controllng compressor motor voltage V cm durng step changes n current drawn I st from the FCS. 2.1 Feed-Forward and Feedback control methods: The fuel cell model documented n (Pukrushpan et al., 2005) wll be appled to the augmented feed-back (FB) and feed-forward (FF) controllers wth dfferent desgn methods for the FF controller. Frstly the

4 59 feed-forward FF controller s used to generate drectly an nput voltage of the compressor accordng to the current demand. Then, a PID controller s used n the feedback to adjust the dfference between the requested and the actual oxygen rato by compensatng the feed-forward controller output. The nonlnear state equatons are x& NL = f ( xnl, u, d), u=v (Control sgnal), d=i cm st (Dsturbance nputs), where the control nput u s the compressor motor voltage v, and the dsturbance nput d s the current I cm st drawn from the FCS. The performance varables are excess oxygen rato y=λ O2 n the fuel cell cathode. 2.2 System confguraton: System confguraton ncludes four dfferent control schemes for the FC stack system wth FF and FB controllers as shown n fgure 4, the FF neural network method wll be dscussed later. The dsturbance (stack current I st ) can be measured; FF controller that correlates the steady state value between the control nput v cm and the dsturbance I st wll be used n the FF path. The FF controller wll mplement by dfferent methods such as a look-up table, fuzzy logc controller (5 and 9 membershp functon MF) and neural network. Analytcal modelng or expermental testng can be used to construct the nverse of compressor and compressor motor maps to fnd v & cm = f cm ( I st ) at desred oxygen flow w& cp. FF controller and FB controller can be desgned to acheve better transent response. In fact, a FF controller that cancels the effect of d to y over a wde range of frequences s desgned frst. A feedback controller (PID) s desgned to reduce the error n the output of oxygen rato λ O Settng of PID controller parameters: PID controller equaton gven n (Ogata, 1997) has the followng form: K Wc ( s) = K p + + K d s (2) s Fgure 4. Fuel cell control Constructon. (a) Look-up table FF controller and PID controller (b) Fuzzy logc FF (5&9 MF.) and PID controller. (c) Neural Network controller FF and PID controller.

5 60 where, K p, K and K d are proportonal, ntegral and dfferental gans respectvely. The PID s ntally tuned by the Zgler and Nchols for the open loop method. The measured oxygen rato s the Feedback sgnal of the system. After fne tunng, the PID controller that s used here wth Feed-forward controllers for oxygen rato regulaton s 1 W c( s) = 200 ( s) (3) s Also, the best control results and correspondng fuel cell compressor voltages are shown n fgures 9~ Feed-forward controller desgn Look-up table feed-forward controller: The FF controller here s mplemented wth a lookup table confguraton, see fgure 4(a). The values of ths table are obtaned from the model by gvng current values nto the FCS model, and then we have used the compressor motor voltage V cm to regulate the oxygen excess rato λ =2. Compressor voltage for each current value s llustrated O2 n the table 1. Table 1. Compressor voltage (v cm ) and FCS current (I st ) values Current(I st ) Compressor voltage (v cm ) K= voltage /current Feed-forward fuzzy logc controller: The fuzzy logc control technque can be appled to control of the fuel cell, snce the fuzzy logc s relatvely smple and s based on defntons of formal facts and the relatonshps among them. In fgure 4(b), the fuzzy controller conssts of the followng man elements (Tsoukalas and Uhrg, 2000; Popovc and Bhatkar, 1997): A set of control rules: IF (condton) Then (control actons), where "condton" defnes the state of the process, for whch the control adjustment specfed n the control acton should be executed. These rules are derved from the knowledge of experts wth substantal experence n the system. Membershp functons MF: whch are a smple yet versatle mathematcal tool for ndcatng flexble membershps to a set, see fgures (5a&5b). Fuzzy numbers are fuzzy subsets of the real lne. They have a peak or plateau wth membershp grade 1, over whch the members of the unverse are completely n the set. The membershp functon s ncreasng towards the peak and decreasng away from t. Fuzzy membershp functons are used n fuzzy control applcatons. A typcal case s the trangular fuzzy membershp functon and s used n ths studes (fg.5a &5b). Fuzzfcaton nterface (the nput of fuzzy controller) s used to transform a crsp set nto a fuzzy set or whch transforms the control varables nto fuzzy sets manpulated by a collecton of fuzzy rules, assembled n what s known as the fuzzy nference engne (Tsoukalas and Uhrg, 2000). The fuzzy control has the followng characterstcs.

6 61 Fgure 5(a). Input varable stack current membershp s functon Fgure 5(b). Output varable voltage membershp's functon Fve membershp fuzzy logc controller: Fuzzy controller s desgned as case of process, where the nputs of fuzzy controller s the fuel cell stack current "100~ 300A" (the current demand), and ts output output (the change of compressor voltage 100~235 volt, see table 1). The membershp functon for the nput and output fuzzy logc controller s dvded to low, med low, normal, med hgh, hgh. From the table 1, we can wrte the rules, whch should be appled for the mentoned above membershp functons as the followng way n table 2: R 1 - R 2 - R 3 - R 4 - R 5 - Table 2. Fuzzy logc controller rules If current s low If current s med low If current s normal If current s med hgh If current s hgh then voltage s low then voltage s med low then voltage s normal then voltage s med hgh then voltage s hgh Else Else Else Else Else Nne membershp fuzzy logc controller: In the same above prncple n tem , the fuzzy logc controller wth 9 MF s desgned but the number MF and fuzzy logc wll be dfferent (9 MF and 9 rules). From fgure 10, we can see clearly that there s a small over shoot at the frst step when we used 5 MF fuzzy logc controller wth delay tme at the sxth. However 9 MF fuzzy logc controller recovered ths problem as shown n fgure Neural network feed-forward controller: Neural network technque can be appled n the controllng of the fuel cell stack system, see fgure 4(c), snce the control process s a mult-varable wth non-lnear behavor. The neural network here wll be used to desgn the FF controller because the neural net work can estmate the compressor voltage value whch correspondng for any current demand value. The detals of neural network structure are n (Tsoukalas and Uhrg, 2000; Haykn, 1999). The data, whch s gven n table 1, wll be used to tran the neural network. The neural network structure s llustrated n fgure 6. The values of the fuel cell current (I st ) wll be as an nput to neural network model. In ths case the nput layer of neural network s one, see fgure 6, and other parameters (voltage and k value) as an output sgnals. In ths case the output layer has two outputs y 1, y 2. The number of hdden layer nodes s chosen to be 9 bases on the test performed n ths work. Accordng to the test the network wth 9 hdden layer nodes s a more approprate one and gves very small absolute error between desred and calculated output (about ). The nput and hdden layers s connectng by weghts w1 and ts number s 9 as matrx (9 1). The hdden layer and outputs layer are connected by weghts w2 j ts number s 18 (a matrx 2 9). Bas layers b1 j has value equal to 1 (Tsoukalas and Uhrg, 2000) are connected wth the hdden layers by weghts wb 1j as matrx 9 1. Also bas layers b 2 should be ntroduced, ts value s equal to 1 and connected to the output layers by weghts wb 1 as matrx 2 1. In order to demonstrate supervsed learnng, the neural network ncludes the desred output vector O wth the components O 1,O 2 the computed output vector Y wth the component y 1,y 2, comparator, and weght-adjustng algorthm, ths arrangement s shown n fgure 6. In order to start the process, all weghts n the neural network (fgure 6) are randomly adjusted to small random value (-1~1) (Haykn., 1999). When the current values I st s

7 62 appled to the neural net work, t produces an output vector Y, whch s compared wth the vector O by the comparator to produce the error vector e calculated by equaton (4). The error s appled to weght-adjustng algorthm to adjust the weghts. e = O Y (4) The last process s repeated over and over untl the error s reduced to some specfed value or an rreducble small quantty. At that pont the output vector Y and the desred output vector O are substantally equvalent, and the neural network s sad to have been traned to map nput vector I st nto the desred output vector O The tranng procedure for the mentoned neural network (fgure. 6) wth the data of the fuel cell (table 1) as follows: the calculaton s done by Matlap verson 2009a accordng to the followng equaton: At frst, the random values between (-1, 1) for the weghts (w1 j, wb1 j, w2 j, wb2 ) to calculate the output Y j of neural net work (fgure 6) are ntroduced. V = w1 I + b1 wb1, = 1,...,9 (5) st u = Tanh( V ), = 1,...,9 (6) where V s the summaton part and u j s the actvaton part of hdden layers (Tsoukalas and Uhrg, 2000), where, w1j, the weghts whch connect between the nput layers and the hdden layers. Its numbers are 9 as matrx (9 1), b 1j bas layers. Its number s 9 and has values equal to 1, wb j, the weghts whch connect between the bas layers and hdden layers ther numbers are 9 as matrx (9 1). The output y s calculated from the followng equaton (Tsoukalas and Uhrg, 2000). 9 y j = ( u w ) + b 2 w b 2 (7) j = 1 where; w j s the weghts whch connect between the hdden layer and the output layer (Fgure 6), and ther numbers are 18 as matrx (2 9), b2 Output bas layers, ther numbers are 2 and have values equal to 1, wb2, the weghts, whch connect between the output bas layers b2 and the output layers y j (fgure 6) ther numbers are 2 as matrx (2 1). The error e s calculated from the followng equaton: e = O - y (8) j j j O 2 Desred Output Pattern Error (e) O 1 Comparator Weght Adjustment Algorthm bas layers =1~2 y 1 y hdden layers wb 1j b2 w 11 wb 2 w 11 w 12 w 13 Actual output w 14 w 15 output layers nput weghts w j w 92 w 17 w 18 w 19 b1j bas layers j =1~9 nput weghts w 1j 1 w 16 nput layer Input data (Current values) Fgure 6. Neural network Model wth Supervsed Learnng. I st

8 63 where O j, the output gven n operatonal data or desred output, Y j, the output computed by the neural network, j = (1~ 2). The weghts of the network are adjusted by applyng back-propagaton functon to mnmze the error. w j (The change n the weghts w j ) s calculated from lner back-propagaton functon gven n (Tsoukalas and Uhrg, 2000). The steps mentoned above are done for each current value (about 21 values), and repeated wth changng the number of hdden layers and the type of actvaton functon untl we obtan the beast case (errors go to zero). The weghts values whch are correspondng to the zero error are recorded, and then the tranng for the neural network of fgure 6 s completed and the output of NN can be calculated from equaton (8), the Matlap verson 2009a s used n our calculaton. where, w s a matrx (2 9), u s (9 1) and b2 wb2 s matrx(2 1) y = w u + b2 wb2 (9) 2.5 Smulatons and Evaluaton: Qualty of controllng s defned by buldng up the output response of the fuel cell stack, and determnes the values of Mean Absolute Error (MAE), where N N MAE = 1 2 y( k) = 1 e( k). (10) N k= 1 N k= 1 The current demand changng depends on the type of the external electrcal load. Usually the current n low demand s 100 Ampere. The maxmum current demand s about 300 Ampere. In our smulatons, as shown n fgure 7, a current demand changng gradually from 100 to 300 each 4 second. Ths almost covers the whole fuel cell stack operatng condton. Fgure 7. Current demand changng durng control. The compressor voltage s to be controlled between the 100 and 235 voltage and the oxygen rato s to be controlled between the -0.8% and +0.2% bounds of deal value λ O2 =2,.e. 99.2% 2 O % 2. The output response of the FCS by usng the suggested control methods s compared wth the output response of the tradtonal Proportonal Feed-forward controller (PFF wth k=164/191) as shown n fgures 8, 9, 10, 11 and 12. Fgure 8. Output Response of FCS wth proportonal and PID controllers at dfferent stack current

9 64 Fgure 9. Output response of fuel cell control loop by usng lookup table Feed-Forward Controller Fgure 10. Output response of fuel cell control loop by usng 5 MF. FL Feed-Forward controller Fgure 11. Output response fuel cell stack automatc control loop by usng 9 MF. Fuzzy Logc controller Fgure 12. Output Response of FCS wth neural network and PID controllers at dfferent stack current So, from the fgures we can see clearly that the Feed-forward neural network (FF-NN) has better performance than other controllers. The second performance s that usng look-up table. Then, fuzzy logc wth 9 MF followed by 5 MF and the last one s the PFF. However, the fgure 8 shows a delay tme at the frst step about 4 sec n the output response of oxygen rato when the Proportonal Feed-forward Controller s used, n the second step there s about 2.5% overshoot as the same as 5 th step. In the same tme the FF-NN, look-up table, 9 &5 MF controllers reduced ths delay tme and the overshoot as shown n fgures 9, 10,11 and 12.

10 65 Table 3, Evaluated Results Controller's type Mean Absolute Error(MAE) PID FB Controller P+ FF Controller PIDFB Controller+ Lookup table FF PIDFB Controller+ 5 MF. FL controller PIDFB Controller +9MF. FL Controller PIDFB Controller +NNFF Controller The results of smulaton and evaluaton by MAE are summarzed n Table Concluson Based on the results summarzed n Table 3, t s found that: Neural Network FF controller + FB controller, they gve better performance than other methods of control. The dfference between fve and nne membershps functon s about of MAE and 9 MF s better than 5 MF, but of them are better than proportonal Feed-forward controller. The mean absolute error of Look-up table FF controller + FB controller s So, we can say Lookup table s better performed than Proportonal Feed-forward controller. The neural network FF controller has better performance than other controllers because the neural network can estmate the correspondng compressor voltage for each current demand, t s mean absolute error s = Abbrevatons PEM MEA FF PID FB FC PEMFC FCS MF NN MF FL FF-NN PFF Polymer electrolyte membrane membrane electrode assembly Feed-forward Proportonal ntegral dfferental controller Feed Back Fuel cell Polymer electrolyte membrane fuel cell Fuel cell stack Member shp functon Neural net work Member shp fuzzy logc controller Feed forward neural net work Proportonal feed forward References Arcak, M., Gorgun, H., Pedersen, L. M., Vargondab, S., A nonlnear observer desgn for fuel cell hydrogen estmaton. IEEE Transactons on Control Systems Technology, Vol. 12, No. 1, pp DFore, D. C., Sldng mode control appled to an underactuated fuel cell system, Rochester Insttute of Technology Rochester, New York. Frede, W., Davat, B., Mathematcal model and characterzaton of the transent behavor of a PEM fuel cell. IEEE Transactons on Power Electroncs, Vol. 19, No. 5, pp Hoogers, G., Fuel Cell Technology Hand Book, Trer Unversty of Appled Scences, CRC Press LLC. Haykn Smon., Neural Network a Comprehensve Foundaton., Second ed. Prentce-Hall. Inc. New Jersey. Kunusch, C., Puleston, P. F., Mayosky, M. A., Rera, J., Sldng mode strategy for PEM fuel cells stacks breathng control usng a super-twstng algorthm, IEEE Transactons on Control Systems Technology, Vol. 17, No. 1, pp Vahd, A., Stefanopoulou, A., Peng, H., Current management n a hybrd fuel cell power system: a model predctve control approch, IEEE Transactons on Control Systems Technology, Vol. 14, No. 6, pp Ogata, K., Modern Control Engneerng. Thrd ed. New Jersey.

11 66 Pukrushpan, J. T., Stefanopoulou, A., Peng, H., Control of fuel cell power systems. Sprnger, Vol. 13, No. 1, pp Pukrushpan, J. T., Stefanopoulou, A., Peng, H., Modelng and control for PEM fuel cell stack system. Proceedngs of the Amercan Control Conference Anchorage, AK, Vol. 5, pp Pukrushpan, J. T., Stefanopoulou, A., Peng, H., 2004a. Control of fuel cell breathng. IEEE Control Systems Magazne. Vol. 24, No. 2, pp Pukrushpan, J. T., Stefanopoulou, A., Peng, H., 2004b. Control of fuel cell power systems prncples: modelng, analyss and feedback desgn, Sprnger-Verlag London Lmted. Pukrushpan, J. T., Stefanopoulou, A., Peng, H., Control of natural gas catalytc partal oxdaton for hydrogen generaton n fuel cell applcatons, IEEE Transactons on Control Systems Technology, Vol. 13, No. 1, pp Popovc, D., Bhatkar V. P., Dstrbuted computer control for ndustral automaton. New York. Spegel, C., PEM Fuel Cell modelng and smulaton usng Matlab, Academc Press s an mprnt of Elsever. Sprnger, T.E., R. Rockward, T.A. Zawodznsk, and S. Gottesfeld, Model for polymer electrolyte fuel cell operaton on reformate feed, J. Electrochem. Soc., Vol. 148, No.1, PP. A11-A23. Yang, W. C., Bates, B., Fletcher, N., Pow, R., Control challenges and methodologes n fuel cell vehcle development, SAE nternatonal, Paper No. 98C054. Tsoukalas, H. L., Uhrg, E. R., Fuzzy and neural approaches n engneerng. John Wley- Interscence Publcaton, New York. Bographcal notes Engneer Omar Ragb receved B.Eng. degree n electrcal engneerng and automatc control from Brght Star Unversty of Technology, Lbya, n 1994, and M.sc. n automatc control engneerng from Tabbn Insttute for Metallurgcal Studes, Egypt, n He was an Automatc Control and Instruments Engneer at Derna Cement Plant, Lbya ( ), he was as an Automatc Control and Instruments Engneer at Petroleum Golf Company, Lbya ( ), he was Electrcal engneer at Al-Gabble Alakther dary factory, Lbya (2001), he was a Demonstrator n electrcal engneerng department at Omar Al-Mukhtar Unversty, Lbya ( ), he was a Lecturer assstant n Electrcal Engneerng Department at Omar Al-Mukhtar Unversty Lbya ( ), He s now a PhD student n school of engneerng at Lverpool John Moores Unversty (LJMU), UK, and Hs research nterests nclude control systems research, Usng a programmable logc controller n automatc control system, Cement rotary kln control research. Hs current research nterests nclude advanced control systems for a fuel cell systems, adaptve neural networks and ther control applcatons, model predctve control for fuel cell stack, n these areas he has publshed 2 conference papers and preparng 2 journals. Professor Dngl Yu receved B.Eng from Harbn Cvl Engneerng College, Chna n 1982, M.Sc from Jln Unversty of Technology (JUT), Chna n 1986, and the PhD from Coventry Unversty, U.K. n 1995, all n Control Engneerng. Dr. Yu was a lecturer at JUT from 1986 to 1990, a vstng researcher at Unversty of Salford, U.K. n 1991, a post-doctoral research fellow at Lverpool John Moores Unversty (LJMU) from 1995 to He joned LJMU Engneerng School n 1998 as a Senor Lecturer and was promoted to a Reader n 2003, then to Professor of Control Systems n He s the assocate edtor of two journals, Internatonal Journal of Modellng Identfcaton and Control and Internatonal Journal of Informaton & Systems Scences. He organzed two specal ssues n 2006, Fault Detecton, Dagnoss and Fault Tolerant Control for Dynamc Systems and Intellgent Montorng and Control for Industral systems. He serves as a member of the IFAC SAVEPROCESS Commttee, and has been IPC member for many nternatonal conferences. He s a fellow of IET and Senor Member of IEEE. He leads the Control Systems Research group at LJMU. Hs current research nterests nclude fault detecton and fault tolerant control of blnear and nonlnear systems, adaptve neural networks and ther control applcatons, model predctve control for chemcal processes and automotve engnes and real-tme evaluatons, n these areas he has publshed more than 160 journal and conference papers. Dr. J. Barry Gomm receved the B. Eng. frst class degree n electrcal and electronc engneerng n 1987 and the Ph. D. degree n process fault detecton n 1991 from Lverpool John Moores Unversty (LJMU), UK. He joned the academc staff at LJMU n 1991 and s a reader n ntellgent control systems. Hs research nterests nclude neural networks for modelng, control and fault dagnoss of non-lnear processes, ntellgent methods for control, system dentfcaton, adaptve systems, chemcal process, and automotve applcatons. Receved June 2010 Accepted November 2010 Fnal acceptance n revsed form December 2010