Control-Oriented Modeling.pdf

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Nicolas RomaniResearch Department,

Renault,

1 Avenue du Golf,

78288 Guyancourt, France;

Automatic Control Department, Ecole Suprieure

dElectricit (Suplec),

Plateau du Moulon,

91192 Gif-sur-Yvette,

Francee-mail: [email protected]

Emmanuel GodoyAutomatic Control Department,

Ecole Suprieure dElectricit (Suplec),

Plateau du Moulon,

91192 Gif-sur-Yvette,

France

e-mail: [email protected]

Dominique BeauvoisAutomatic Control Department,

Ecole Suprieure dElectricit (Suplec),

Plateau du Moulon,

91192 Gif-sur-Yvette,France


Vincent Le LayResearch Department,

Renault,

1 Avenue du Golf,

78288 Guyancourt,

France


Control-Oriented Modeling andAnalysis of Air ManagementSystem for Fuel Reforming Fuel

Cell VehicleWith the purpose of meeting the specifically restrictive requirements of fuel reforming fuelcell vehicle, this paper brings into focus the issues of the transient operation of fuel cellsystems and presents a control-oriented dynamic model of fuel cell air managementsystem, suited for multivariable controller design, system optimization, and supervisorycontrol strategy. In a first step, the dual analytical approach based on lumped anddistributed parameter models is detailed: The partial differential equations deduced frommass/energy conservation laws and inertial dynamics are reduced to ordinary differentialequations using spatial discretization and then combined with semiempirical actuatormodels to form the overall air system model. In a second step, a classical approach is

followed to obtain a local linearization of the model. A validation of both nonlinear andlinearized versions is performed by computational fluid dynamics simulations and experi-ments on a dedicated air system test bench. Thanks to dynamic analysis (pole/zero map),

operating point impact and model order reduction are investigated. Finally, the multiin-put multioutput state-space modelwhich balances model fidelity with modelsimplicitycan be coupled with reformer, stack, and thermal models to understand thesystem complexity and to develop model-based control methodologies.

DOI: 10.1115/1.2784323

Keywords: fuel cell systems, fuel reforming, air management system, thermal pneumaticmodels, bond-graph topology, control-oriented modeling, dynamic system analysis, fuelcell power plant model

Introduction

Fuel cell vehicles FCVs are expected to become, in the nearfuture, competitive with conventional internal combustion engine

vehicles in terms of performance, efficiency, and compliance withemission reduction schedules. This is why research into fuel cell

FC systems has undergone a rapid increment, and many auto-motive companies and research laboratories are now engaged inthe study and development of FCV prototypes. The results of such

researches have led to improve the durability and reliability ofproton exchange membrane PEM , also known as polymer elec-trolyte membrane, and fuel cell stacks FCSs , and to enhance theperformance of the subsystems that compose the fuel cell power

plant FCPP .In order to maximize PEM FC physical advantages, it is neces-

sary to propose efficient control strategies of FCS internal param-

eters partial pressures, stoichiometric ratios, and hydration thatcan ensure optimal working points and reduced stress to its com-ponents. A FCS alone may have good steady-state performances,but if the required control variables mass flow rates, pressures,and temperatures are not attainable, the good performance willnot be realized in a vehicle application. Moreover, technological

challenges increase if onboard hydrogen generation and purifica-tion by fuel reforming solution is used instead of compressedhydrogen storage.

In this context, an increasing emphasis is being placed in FCV

development on transient operation, control strategies, and inte-gration, for the same purpose of fuel economy and emissions.

Thus, a both physical and control-oriented modelingapproacheither to obtain a better understanding of the system

complexity and to predict its dynamic behavior, or to choose theoptimal technology and plant layout that should be adopted

represents a powerful instrument for FC design.In this paper, with regard to system optimization and transient

performance, we concentrate on the air management system AMS , which impacts on the overall efficiency of FCV andwhich requires specific refinements in control strategy design.Among a large number of publications on FCV modeling, moreand more are introducing dynamics and control issues e.g., Refs.

13 , but relatively few are including the dynamics of the AMS e.g., Ref. 4 i.e., considering the dynamics of air compressor,

control valve and manifold filling, and their consequences to theFCPP behaviorand let alone the couplings between control vari-ables in the multibranch and high-pressure AMS of the fuel re-forming application e.g., Ref. 5 .

Different previous works have already pointed out issues linkedto direct air supply control for onboard hydrogen storage, e.g.,Refs. 68 and choice between high- and low-pressure operation

e.g., Ref. 9 . However, here, with the help of knowledge-basedmodels and appropriate test facility, the objective is to develop adynamic and control-oriented model for our complex and highlycoupled AMS, to verify experimentally our modelsand later ourcontrol lawsand thus to put the emphasis on the need of robust

Manuscript received November 30, 2005; final manuscript received June 12,

2006; published online January 31, 2008. Review conducted by Roberto Bove.

Journal of Fuel Cell Science and Technology FEBRUARY 2008, Vol. 5 / 011009-1

Copyright 2008 by ASME

Downloaded 24 Sep 2009 to 202.44.14.194. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm


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multiinput multioutput MIMO control strategies for multiplecontrol objectives flow/pressure control, efficiency optimization .

The remainder of the paper is organized as follows: After ashort description of FCPP and AMS in a fuel reforming FCV inSec. 1, the physical modeling approach based on the bond-graphtechnique and simulation support for dynamic model develop-ment is demonstrated in Sec. 2. We will present how a FC-dedicated and validated thermal pneumatic library has been speci-fied and developed in MATLAB/SIMULINK . In Sec. 3, we willdevelop a reduced AMS model, suitable for dynamic analysis andcontrol applications. This mathematical and configurable modelwill thus be integrated in the FCPP global model in Sec. 4 beforefinishing this paper with concluding remarks and an outline forfuture work.

1 Fuel Cell Vehicle Overview

1.1 Fuel Cell System. FC systems are electrochemical de-vices that offer clean and efficient energy production by convert-ing the chemical energy of a gaseous fuel directly into electricity.The FC concept 10 dates back to the early 1800s, and its inven-tion has largely been attributed to Grove. Although the availabilityof fossil fuel has limited interest in FCs as a power source, recentadvances in membrane and electrode materials, reduced usage ofnoble metal catalysts, and efficient power electronics have

sparked interest in direct electricity generation using FCs.In particular, the PEM FC technology seems to be well adapted

to automotive traction application: Negligible emissions waterand heat as by-products only , high energy conversion efficiency

65% to 80% at normal operating conditions , high power density,solid electrolyte, long cell and stack life, and low corrosion.Moreover, these FCs operate at low temperature 50100C ,which enables a fast startup Fig. 1 .

However, the dependence of PEM FCs on high-purity hydrogenreactant requires novel hydrogen generation technologies: Fuelprocessing systems FPSs , or reformers, that reform liquid hydro-carbon fuel into hydrogen-rich gas reformate can be consideredas a near-term solution. Controlling FPS to provide hydrogen ondemand can mitigate problems associated with storage and distri-bution, but it implies new design and control issues.

1.2 Fuel Cell Power Plant. In a FCV, the stack is consideredas the heart of the system, and the principle of electricity genera-tion from a PEM FC is straightforward when the correct materialproperties, cell structure, and reactants are in place. Therefore, aFCS requires to be integrated with other components to form aFCPP, and the FC power response is limited by air and hydrogenfeed both are closely linked in reforming application , flow rateand pressure regulation, and heat and water managements.

During transient, since current is instantaneously drawn fromthe load source connected to the stack, the FC breathing controlsystem is required to maintain optimal temperature, membranehydration, stoichiometric ratios, and partial pressure of the reac-

tants across the membrane so as to avoid degradation of stackvoltage, ensure high efficiency, and extend stack life. These criti-cal parameters must be controlled over a wide range of currentand power by a set of actuators such as valves, motorized com-pressor, expander vane, condensers, etc.

The resulting power plant, composed of four major control flowsubsystems for air, reformed hydrogen, heat, and water, Fig. 2 , isneeded to make fine and fast adjustment to satisfy performance,safety and reliability.

1.3 Fuel Cell Air Management System

1.3.1 Air Management System Description. Considering theFCPP complexity in fuel reforming application, it clearly appearsthat transient behavior is one of the key requirements for the suc-cess of FCV. To overcome this challenge, AMS issues are criticalsince this active subsystem implies static and dynamic perfor-mances of the stack and, thus, the overall efficiency of the FCPP.The AMS needs to be controlled rapidly and efficiently in order tosupply fast increase of mass flow, to compensate stack efficiencydrops, and to achieve good dynamic power response of the powerplant. More precisely, the appropriate actuators must regulate

the stoichiometric ratio molar ratio of supplied reactant di-vided by the amount actually used to produce electricalpower of oxygen in the cathode channel,

the FPS air inflow and thus stoichiometric ratio of reformedhydrogen in the anode channel ,

the optimal conditions for a good stack operation overalloperating pressure for efficiency, anode/cathode pressuredifference for membrane mechanical strength, and tempera-ture for membrane hydration ,

the air bleed dash of air bypassed from the cathode chan-nel to the anode to oxidize CO and prevent stack from em-poisoning , and

the optimal conditions for water and heat management pressures and temperatures for water balance .

The AMS under consideration Fig. 3 is based on a two-stagecompression group a compressor and its electric motor, plus anexpander vane and control valves that regulate air mass flows and

pressures in the system. For a FCPP with FPS, typical operatingconditions for FCS are defined by an air mass flow/pressure pro-file Fig. 4 , deduced both from current/reactant mass flow pro-file, thanks to Faraday law, and from FCPP water balance andpressure drops. The dry air flows to the FCS cathode and FPS arecontrolled to feed the power generation reaction and to avoidstack starvation, and the pressures are controlled to ensure waterbalance and stack efficiency optimization.

Functionally, the air is compressed in the compression group:The speed of the air compressor both increases the air pressureand sets the total air flow rate. A flow control valve at the entry ofthe cathodic line plus air bleed valve performs air flow distribu-tion in the different branches. Two pressure control valves down-

Fig. 1 Details on FCS structure and operationFig. 2 Scheme of FCPP

011009-2 / Vol. 5, FEBRUARY 2008 Transactions of the ASME



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stream the stack maintain pressure levels required for an optimalstack operation. The expander further increases the pressure by

recovering energy from the exhaust air stream.Air pressurization greatly increases the temperature of the air

stream. To prevent damage to the stack, the hot air stream passesthrough a heat exchanger to cool it to the FCS operating tempera-ture. The depleted hot air that exits the stack contains water as aproduct of the electrochemical reaction. This water is primarily inthe vapor state and is largely recovered by passing the air througha condenser. The heat and water are transferred to their respectivemanagement system. Downstream of the pressure control valves,the air turns the expander vane and is vented to the atmosphere.

1.3.2 Experimental Air System. Starting from the AMS de-fined above, technological choices, practical constraints, andproject progress have to be taken into account in the test benchdefinition as in simulation environment.

As our stack operates with a dry cathode, our air systemdoes not include a humidifier.

As chemical reactions have low influence on fluid dynamics,the stack and reformer are replaced by pneumatic chambers

that can be qualitatively representative of the behavior of thereal subsystems a dynamics linked to volume filling and

thermal and pressure losses . Likewise, heat exchanger and condensers are not integrated

in our air system since their pneumatic influence can bereduced to a volume filling and a pressure drop.

The expander vane is not included in this study.

The resulting air system test bench Fig. 5 not representative ofthe overall AMS but easily configurableis a major support formodel validation, actuator characterization, system topology test-ing, and control law development.

1.3.3 Air Management System Control Issues. From a controlpoint of view, the objectives of AMS are both to improve perfor-mances flow and pressure responses and to reduce consumption.Indeed, pressurization results in higher stack power density inlower size and cost, too , but compressor power remains the larg-est auxiliary loss up to 20% of the total FCPP power .

Moreover, the challenge for AMS modeling and control designis due to a nonlinear behavior attributed to the complex interactionof the fluid, thermal, electromechanical, and mechanical mecha-nisms. We have detailed that nearly all variables that affect the

Fig. 3 Scheme of the AMS

Fig. 4 Optimal FCPP operating profile Fig. 5 The AMS test bench




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state of the gas pressure, temperature, and mass flow rate influ-ence FCS potential, efficiency, or power output. So, air manage-ment and control tasks have to take into account the nonlinear,multivariable, coupled, and disturbed character of the consideredmultiple-line AMS, and the controller design that will follow hasto remain simple for real-time implementation and calibration. Inthis perspective, creating a physical dynamic model is an essentialfirst step, not only for the understanding of the AMS behavior, butalso for the control design.

As mentioned before, the quantities to be controlled are the airmass flows through both anodic and cathodic lines, and, concur-rently, the pressures in the air path. For each operating point varia-tion, both flows and pressures are affected. But since flow andpressure are coupled quantities, changing the compressor speed

likewise changing a valve openingmodifies flows and pressurestogether. In our specific case, these couplings can even appearbetween anodic and cathodic lines. So, considering our nonlinearand highly coupled MIMO system, robust MIMO control strate-gies are necessary to achieve multiple objectives, such as flows,pressures, temperatures, and efficiency controls.

The development of such strategies requires either empiricalmodels black boxes and extensive and costly trial-and-errortesting or a simple, accurate, and knowledge-based model and itsreduced validation procedures. It is the second that we have fol-lowed by developing a dynamic system model that balancesmodel fidelity with model simplicity. The continuation of this pa-per addresses the critical need to incorporate a realistic model ofthe AMS in the FC system performance analysis.

2 Air Supply System Physical Modeling

2.1 Physical Modeling Approach

2.1.1 Multiple Modeling Objectives. Given the central role ofAMS dynamics in FC system behavior and efficiency, we begandeveloping a modeling approach that can lead to improved systemdesign and control. Generally, every control problem encompassesthe following steps: System definition, modeling, analysis, controldesign, testing through experimental implementation, and finaloptimization. Our objective was to define a relevant model-basedmethodology for prototyping FC AMS control Fig. 6 .

In our specific case, the issue was to obtain both a detailedphysical model to better understand phenomena that we observeon our dedicated test bench and a proper reduced model to controlthe main dynamics and states of the system. This coupled devel-

opment of knowledge-based model and control-oriented model ina thermofluid domain is a complicated process, which requiressufficient experimental work to ensure relative reliance on theinterpretation made from the models. Indeed, the incertitude ondata, the interdisciplinary nature, and the existence of multiplelayers of modeling and multiple objectives of control make theintegration of modeling and control activities a critical step to-ward system development.

2.1.2 Coupled Modeling Methodology. In the automotive de-velopment process, there is an increasing need for detailed andaccurate simulations, which can be used for the analysis of com-ponent interactions under transient operating conditions. The

originality of this work is that a structured and coupled method-ology has been further integrated with a general-purpose systemdynamics and control simulation tool 11 .

Modeling compressible fluid dynamics, and the inherent non-linearity of acoustic phenomena, is usually a domain for compu-tational fluid dynamics CFD simulation: Several numerical solv-ers such as FLUENT, AMESIM, and GT-POWER can deal with this kindof problem. Nevertheless, fast MATLAB/SIMULINK simulations usedfor dynamic analysis and control law design require a consider-ation of network simulations with a simplified analytical approachas an alternative to standard CFD simulations: Lumped or distrib-uted parameter models can lead to satisfying results while requir-ing much less computational resources.

So, by starting from the physics equations of the phenomenaand applying a common bond-graph technique, an integrated ex-perimental and numerical approach has been applied to obtain twotopologies for the thermofluid dynamic models:

The distributed parameter concept consists in developing adetailed model for fine understanding: Highly representativeand predictive model one-dimensional and nonlinear acous-tic equations , which can predict the system response accu-rately and be used for simplified model verification.

The lumped parameter concept consists in developing adedicated model for control activity: Reliable and simplifiedmodel zero-dimensional and nonlinear thermodynamicequations for the analysis of main dynamics and relevantcontrolled parameters at the system level, which can predictthe system response correctly and can be used for controller

design and performance analysis.

These models have been developed and implemented in aMATLAB/SIMULINK environment for the simulation of mass flows,pressures, and temperatures. Each component is modeled sepa-rately actuators by algebraic relationships, cartographies, andproperly identified dynamics; manifolds by nonlinear differentialdeduced from mass/energy conservation laws and inertial dynam-ics and then combined to form the overall system model, easilyconfigurable and applicable to various configurations of AMS.

At every step of the development process, the static and dy-namic responses of MATLAB/SIMULINK models have been com-pared to appropriate CFD results AMESIM for 0D and GT-POWERfor 1D : The objective is to make a first qualitative validation andto verify model consistency. Next, models have also been vali-

dated using experimental results. Additional simulations havebeen performed with the FLUENT code to improve heat exchangecharacterization. This coupled modeling approach has made usmore independent of measuring errors.

2.1.3 Bond-Graph and Multiport Approach. Bond-graph tech-nique and its systematic multiport formalism have been integratedas a complementary engineering tool to unify the approach ofsystem dynamics and to fulfill the growing needs of constantlyimproving performance. This methodology 12 is well adapted toresearch projects for physical modeling, component choice, andcontrol activities. It could be extended to the power plant modeldevelopment, so as to connect multidomain subsystems easily and

Fig. 6 MOdel-based control design methodology.




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lead to a common energetic study of the overall system.Indeed, the representation of a dynamic system starting from

the notion of multiport consists in highlighting the energy ex-changes between a subsystem and its environment through itsconnecting ports. The power exchange through a bond is ex-pressed by the product of two complementary variables, effort

intensive variables: Temperature and pressure and flux exten-sive variables: Mass flow and volume variation rate , independentof the field of physics considered Table 1 .

Thanks to the bond-graph topology Table 2 , we have elabo-rated a proper thermopneumatic library to model various AMSconfigurations by combining predefined elements passive R-C-Ielements, active sources Se-Sf, and 0-1 junctions .

The next section is intended to cover topics related to modelinggeneral fluid flows through an internal pneumatic network and topresent and discuss the models for the AMS components. Thisincludes theoretical equations, modeling assumptions, and bond-graph representations regarding the basic components and thefluid properties.

2.2 Thermal Pneumatic Pipe Models. Since an engineeringapproach to compressible fluid dynamics requires highly flexibleand combinable models, the approach used in the present work isfirstly to develop the global AMS model pneumatic networkwhich can include up to three branches in clearly identifiableparts to separate any simplifying assumptions: Actuators com-pressor and valves , on the one hand, thermal pneumatic pipes,orifices, and associated losses heat transfer and pressure losses ,on the other hand. This allows simulation of the behavior of el-

ementary components and, thus, future refinement of each part ofthe model.

2.2.1 Assumptions on Fluid Properties. In order to simplifythe analysis of thermofluid models and to identify separately theelementary physical phenomena, we consider one-phase, com-pressible and one-dimensional fluid flows, and distinguish the fol-lowing subfunctions: Transportation of fluid energy through pneu-matic pipes, fluid energy storage element, fluid energy controlthrough fixed or variable orifices, transformation of mechanicalenergy into fluid energy, and energy losses thermal exchange,friction, etc. .

We assume that gaseous species are perfect, and we verify thatmodels are not affected by the variation of the isentropic coeffi-cient dependent of gas type . Compressibility, turbulence, viscos-ity, and conductivity of fluids are dynamically calculated in our

models. Humidity, gas mixture, and reacting processes are ne-glected, but their influence on the pneumatic behavior are takeninto account in our AMS control specifications.

2.2.2 General Flow Solution. According to nonlinear acoustictheory, general flow model involves the simultaneous solution ofcontinuity Eq. 1 , energy Eq. 2 and momentum Eq. 3partial derivative equations NavierStokes PDE , simplified tolead to one-dimensional Euler equations:

t+

v

x= 0 1

etott

+ vhtot

x= 0 2

v

t+

Ptot

x= 0 3

with

= m/V

v = Qm/S

etot

= u + ec

htot = h + v2/2

Ptot = P + v2

The mass conservation is used to model a dynamic behavior ofgas species in each volume. The energy conservation is applied inorder to account for the effect of pressure and temperature varia-tions bond-graph capacitive element . The momentum conserva-tion allows us to model dynamic flow transmission and pressurelosses bond-graph inertial element .

2.2.3 Discretized Euler Equations.

Euler PDE are discretized to remove spatial dependence and toobtain an elementary ordinary derivative equations ODE model:Eqs. 4 6 . Flow solution is carried out across the flow directionby time integration of the coupled and nonlinear differential equa-tions, volume by volume and boundary by boundary. The scalarvariablesprimary mass and internal energy and secondary

pressure, temperature, and total enthalpy are assumed to beuniform over each volume. The vector variables mass flow and

enthalpy flow are calculated for each boundary by momentumequation resolution,

dm

dt= Qmin Qmout

4

d metotdt

= Qmin hin +vin

2

2 Qmout hout +

vout2

2 5

d mv

dt= Sin Pin + invin

2 Sout Pout + outvout2 6

Table 1 Bond-graph variables in fluidic domain

Power variables W t = e t *f t

Effort e t Pressure P PaFlux f t Flow rate Q m3 / s

Energy variables E t = W t dtDisplacement g t = f t dt Volume V m3Impulsion p t = e t dt Pressure impulsion Pa s

Table 2 Fluidic sources, passive elements, and junctions

Se Effort source Pressure source P Pa

Sf Flux source Flow rate source Q m3/ s

R Resistive element Orifice, porous pipe R =P /Q Pa s /m3C Capacitivie element Volume, manifold C= V/ P s2 m4 /kgI Inertial element Pipe I= /Q N s2 /m30 Parallel junction f=0 P calculation1 Series juncti on e = 0 Q calculation




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2.2.4 Friction Losses. Flow losses in pipes due to frictionalong the walls are calculated, taking into account the Reynoldsnumber and the surface roughness of the walls. The friction coef-ficient for smooth walls is given by

P =fv

2

2 7

with distinction of turbulent and laminar regions,

fturb =0.08

Re0.75

flam =16

Re

For rough wall surface roughness height h and turbulent flow,the friction coefficient is given by Nikuradses formula:

f =0.25

2 log10 D/2h + 1.742

2.2.5 Singular Pressure Losses. Singular pressure losses inpipes, due to tapers, bends, or irregular cross sections, can byintroducing an empirical pressure loss coefficient. For example,in a smooth bend of angle of curvature and radius of curvature

RC, it is given by

P =pv

2

2 8

with

p =

900.13 + 1.85

D

2Rc

3.52.2.6 Thermal Exchanges. Thermal exchanges from internal

fluid to pipe wall are modeled using a heat transfer coefficient,deduced from fluid velocity and thermophysical properties, andwall surface finish. A simplified model that calculates a globalconvective exchange coefficient between gases and walls can bededuced from the definition of thermal conductivity hT= Nu/L,

with Nu=a Reb

Pr1/3

, or from the Colburn analogy: hT= 1 /2fvCp Pr

2/3.Parameters a , b are deduced from empirical steady-state cor-

relations in the GT-POWER software. Then, the internal heat transfercoefficient hT, the predicted fluid temperature T, and the internalwall temperature Twall are used to calculate the total heat transfer,

QT = hTS T Twall 9

However, the wall temperature is difficult to measure. So, a de-tailed model 13 , which couples forced convection heat fluxQTforced

, wall thermal capacitance, and free convection heat flux

QTfreecalculations, has been developed, also,

dTwall

dt=

QTforced+ QTfree

VCP

10

2.2.7 Global Pipe Model. The global pipe modeldefined byEqs. 11 13 assumes that pipes are cylindrical, with constantsection, and that gas is transferred in the axial direction with uni-form velocity. It includes calculations of friction losses, convec-tive heat transfer through walls, and pressure loss coefficients totake into account the effects of network geometry bond-graphresistive elements .

By working with a constant volume thus with null macro-scopic kinetic energy , on the one hand, and with static pressures,on the other hand, we can only consider internal energy and ne-glect advected momentum .v2 in Euler ODE,

dm

dt= Qmin Qmout

11

d mu

dt= Qminhin Qmouthout hTS

T Twall 12

dQmout

dt=

S

L Pin Pout 4f

S

D

v2

2 p

S

L

v2

2 13

2.2.8 Lumped/Distributed Parameter Models. Starting fromthese general flow equations and the resulting pipe model Fig. 7 ,two different methods are used to discretize the FC AMS.

The first is to break the system up into several differentcomponents, such as several pipes, flow splits, and/or mani-folds 0D or lumped parameter model , where pressures andtemperatures are calculated, and to replace momentumequation by flow connections valves and orifices . Thisapproach relies on a localization of the fundamental physicalphenomena.

The second is to discretize each pipe into many volumes pseudo-1D or distributed parameter model and to let mo-mentum equation ensure flow transmission at the bound-aries. This approach formalizes the notion of the distribution

of system properties in space and allows the calculations ofpressure waves, mass flows, inertia, and energy losses inpipes.

2.3 Flow Sources, Connections, and Boundaries

2.3.1 Compressor Model. The heart of the AMS is a compres-sion group, reduced on our test bench to a volumetric compressorand its electric motor, which will generate air mass flow and in-crease pressure in the overall system flux source generating massand enthalpy flows in the bond-graph technique . Analytical com-pressor models based on lumped rotational equation and first ther-modynamics principle are well known but difficult to stall,

Jcompdcomp

dt= motor comp 14

where motor=f Umotor,comp is the compressor motor torque and

comp is the load torque,

comp =Cp

comp

Tatm

comp

PcompPatm

1 /

1 Qmcomp 15

Air flow Qmcomp =f Pcomp / Patm,comp through the compressor

and isentropic efficiency comp are given by experimental staticmaps. Thermodynamic equations are used to calculate the exit airtemperature,

Tcomp = Tatm +Tatm

comp

PcompPatm

1 /

1 16

Fig. 7 Bond-graph scheme of the general pipe model




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2.3.2 Orifice Models. In order to compute mass flow and ve-locity when momentum equation is not solved 0D models or tocontrol fluid energy the physical components such as pipes or

manifolds must be joined together by flow connections, whichsubstitute the inertia effect. In the bond-graph technique, it isidentified as an R element.

For modeling pressure losses in abrupt contractions or expan-sions in the flow system, an orifice model Bernoulli law with asemiempirical pressure loss coefficient should be used,

Qm = S2PP 17

for abrupt expansion and abrupt contraction:

p =1

0.59 + 0.41 S2/S13

12

p = 1 S1

S2

2

For control valves, several technologies exist, but the physicalphenomenon orifices with controlled variable cross-section area

is common. As a first approximation, orifices can be modeled byan algebraic expression that links the difference of pressure to themass flow rate Barr Saint Venant law ,

Qm = V P2P1

1/

P11 P2P1

1 / 2 1 rT1

18

A simplified orifice law can be deduced from laminar flowassumption,

Qm = V P2 P1 19The choice of control valves throttle and needle valves impliesthe identification of the discharge coefficient V linked to thegeometry of opening section and a specific dynamics.

2.3.3 Environment Boundaries. Environment pressures and

temperatures at the boundaries may be specified as constants ormeet a set experimental profile. For example, in the case of ex-pander integration, the inlet pressure and temperature of the vanecould be dynamically modified by a dedicated vane model.

2.4 Experimental Validation. After a detailed validation pro-cess based on several sets of experimental data transient systemresponses based on control input steps, at full load and part load ,both 0D and 1D predicted results have been compared with em-pirical results. The considered measures are instantaneous pres-sure and temperature at a specified point of the system in thecathode outlet manifold for instance, Fig. 8 .

The comparison between simulation and tests shows a satisfy-

ing agreement. Predicted dynamic responses are slightly fasterthan measured ones, but they agree in the steady-state value theprecision of temperature sensors is about 1 deg or 2 deg : The

measured responses appear to be a filtered version of the simu-lated ones; this difference is likely caused by sensor timeresponse.

Finally, results indicate that a lumped parameter model can ac-curately represent pneumatic phenomena in our current configu-ration with considered volumes, mass flow range, and pressurelevel . However, for future steps of development and vehicle in-tegration, detailed 1D models could be useful for AMS design andtuning, or even for intake and exhaust noise analysis.

3 Air Supply System Control-Oriented Modeling

3.1 Model Assumptions. In this section, we describe the dif-ferent steps leading to an AMS model sufficiently simple to beused for online control. So as to study the dynamics of paramountphysical phenomena, the influence of actuators, and the coupledbehaviors of air flows and pressures, the AMS global model Fig.9 has been implemented in the MATLAB/SIMULINK software.

Pneumatic phenomena are represented by lumped parametermodels. Pressure and temperature in the manifold are de-duced from the capacitive effect compressibility and inter-nal energy : Flow variables are calculated, thanks to actua-tor algebraic equations.

Considering dimensions of our AMS, pipe losses are ne-glected. Outlet compressor temperature inlet temperaturefor the pneumatic chamber is dealt with as a parameterrather than a state variable of the model. This temperature issupposed to remain constant thanks to the cooling system.

Functionally, air mass flows through the system are regu-lated by compressor rotational speed and by flow control

valve opening, and pressures in anode and cathode by pres-sure control valve opening. Other flow connections are assumed by split volume and

FPS pressure drops.

It is important to note that AMS global model will be adapted tovarious configurations up to three branches . However, in a con-trol engineering approach, the objective is to make a dynamicanalysis on a reduced and flexible model, so as to deduce whatcan provide a control law in transient and disturbed conditions.

For clarity and readability concern, we will present the state-space model development and the linearized model analysis on areference model Fig. 10 , which captures compressor, valve, and

Fig. 8 Example of pipe model validation




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volume filling dynamics in a one-branch system. All these studieshave been later applied to the two-branch model.

3.2 Reduced Model for Control

3.2.1 State-Space Equations. The transient pneumatic phe-nomena captured in the control-oriented model are mathemati-cally described by the following state-space equations:

dm

dt= Qmin Qmout

20

d mu

dt= Qminhin Qmouthout

21

Pneumatic state variables are mass m and internal energy mu .The links between these state variables and the available experi-mental measures mass flow, pressure, and temperature give thefollowing definitions:

mu = mCVT= V 1

p

h = CPT=r

1T

whence the two first state-space equations of our model areobtained,

dm

dt= Qmin Qmout

22

dPout

dt=

r

VQmin

Tin PoutQmout

m 23

Assuming second order actuator dynamics, compressor rotationalspeed C and valve opening UV and also their derivative C and

U V are additional state variables governed by the following trans-fer functions:

C

Cref

=1

1 + aCs + bCs2 24

UV

UVref

=1

1 + aVs + bVs2 25

The empirical coefficients aC, bC, aV, and bV are deduced fromdynamic performances specified for compressor speed and

valve opening local regulations.

3.2.2 Output Equations. Output equations of the system aregiven by ideal gas law and actuator static laws.

Ideal gas law is used to calculate temperature in volume:

Tout =V

r

Pout

m 26

We choose to use the simplified valve equation:

Fig. 9 Structure and variables of the global AMS model two branches

Fig. 10 Structure and variables of the reference model




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Qmout= KVUVPout Ppost 27

with KV as the opening section coefficient given by a dedi-cated actuator map and Ppost as the outlet environmentcondition.

For simulation of reduced AMS model, a fast-executingstatic compressor mapwhich provides the experimentalair flow rate through the compressor in the function of rota-tional speed and compression rateis used. Thanks to theidentification of appropriate transfer gains Fig. 11 , the re-lation between mass flow, compression rate, and rotationalspeed can be characterized by a linear equation,

Qmin= KC1C + KC2PoutPatm 28

with KC1, KC2 as the compressor parameters assumed to beconstant and Patm as the inlet environment condition. Therobustness of this model in relation to fundamental com-pressor nonlinearities is performed by the local speedregulation.

3.2.3 State-Space System. Considering V, Tin as parametersand Patm, Ppost as disturbances supposed to be constant duringsystem operation , we obtain a six-state MIMO system, namely

inputs: u=Cref

UVref

states: x=

m

Pout

C

C

UV

U V

outputs: y=QminPoutQmoutTout

where Qmin , Pout are the outputs to be controlled and Qmout, Toutare introduced for model validation and supervision purpose. Fi-nally, the mathematical state-space model is given by

x1 = KC1x3 + KC2

x2

Patm KVx5x2 Ppost

x2 =r

VTinKC1

x3 +r

VTinKC2

x2

Patm

x2

x1KVx5x2 Ppost

x3 = x4

x4 =1

bC u1 x3 aCx4

x5 = x6

x6 =1

bV u2 x5 aVx6

y1 = KC1u1 + KC2

x2

Patm

y2 = x2

y3 = KVx5x2 Ppost

y4 =Vx2

rx1

The nonlinear properties of the system under study appear inproducts and ratios of state-space variables, on the one hand, and

in a square root function, on the other hand.

3.3 Linearized Model Analysis. We will present here steady-state and dynamic properties of the linearized model. In particular,we will study the sensitivity of these characteristics with the op-erating point and also the coupling Fig. 12 and the parameterinfluence in order to

detect some need for adapting regulation algorithms to op-erating point o.p.

choose an ad hoc o.p. for the synthesis of a single regulator

3.3.1 Model Scaling. Controlling the AMS means dealing withnumbers that span a large set of values from0.001 kg to 300,000 Pa , thus leading to numerical instabilitywhen designing and simulating control laws. A systematic method

known as scaling 14 has been applied so as to make modelanalysis and controller design numerically simpler and more ac-curate. For the purpose of clarity, the scaling will not appear in theupcoming analysis, and the results will be presented with non-scaled pressure and flow rate ranges.

3.3.2 System Linearization. A classical approach is followedto obtain a local linearization of the AMS model around the op-erating point x0 :u0 ,

X= AX+ BU

The operating point x0 :u0 of the system is defined by the couple

Qmin , Pout , which has to follow a predetermined profile so as to

Fig. 11 Linear compressor model and static flow map

Fig. 12 Direct and coupled system transfer functions




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optimize the global FCPP efficiency. For this study, we will workon the following mass flow and pressure ranges:Qm

in

0.005 kg/s;0.05 kg/ s and Pout 1105 Pa;3105 Pa .

3.3.3 Operating Point Influence. This study introduces the im-plication of pressurization in the dynamic behavior of AMS andprovides a good control engineering perspective. Indeed, one ofthe important optimization tradeoffs in FCV development is theoperating pressure: High pressure improves stack power density,but low pressure has a benefit of low parasitic loss in air flowdevices.

The sixth-order linearized model presents two couples of in-variant eigenvalues complex conjugates associated withactuatorsand two real eigenvaluesassociated with pneumaticphenomenawhich are varying with the operating point. The fol-lowing figures illustrate the influence of operating point on thereal eigenvalues 1 and 2, on the one hand Fig. 13 , and on thestatic gains of the different direct and coupled transfers Hij of the

system, on the other hand Fig. 14 . Thanks to these results, wecan deduce

a low-level variation of the slow time constant representa-tive of physical process on the considered pressure and

mass flow ranges,

a low-level dispersion of gains at constant pressure with afactor of 3 or 4 , and

a sensible dispersion at constant mass flow, especially for

H2j transfers because of low-level gains at low pressure .

So, we can conclude that the low-pressure operation has the

potential to provide faster transient responses than the high-

pressure operation 8 , and we can suppose that a single controlstructure could be sufficient for a high-pressure configuration.

3.3.4 Sensivity on Parameters. It is interesting to explore

qualitatively the sensitivity of system dynamics to parameter vol-ume and inlet temperature variation. The conclusions of this sen-

sitivity analysis Fig. 15 are that, in our operating conditions, the

parameter Tin has a low impact on system dynamics, but the pa-rameter V has a significant influence on the real eigenvalues 1

Fig. 13 Influence of pressure and mass flow on system eigenvalues

Fig. 14 Influence of pressure and mass flow on system static gains




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and 2. So, an important AMS volume would penalize thedynamic responses of the system independently of actuatorperformances .

3.4 Comparison Between Nonlinear and LinearizedModels. After its dynamic analysis, the linearized model is vali-

dated by a comparison to the nonlinear model, which has beenexperimentally verified. The validation process consists of a risingstep on the compressor rotational speed input, followed by afalling step on the valve opening input.

The values of the constants and parameters used in simulationsare given in Table 3.

We can observe in following in Fig. 16:

equivalent dynamics on outputs Qmin , Pout , Qmout , Tout ; sensible errors on steady-state values due to static gain dis-

persion when the operation point is modified.

So, a reduced and linearizedbut physically basedmodel can

Fig. 15 Influence of parameters on system eigenvalues

Table 3 Simulation constants and parameters

1.4 aC 2.50E 02

Patm 101,325 Pa aV 3.10E 02

Ppost 101,325 Pa bC 1.70E 03

287 J /kg K bV 6.60E 04

Tatm 293 K KC19.30E 06

Tin 350 K KC28.00E 03

V 0.01 m3 KV 1.00E 05

Fig. 16 Comparison of linear and nonlinear model outputs




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still predict the system response correctly by including the appro-priate dynamics. This model can then be used to design and dem-onstrate performances of MIMO control strategies.

4 Fuel Cell Power Plant Model Overview

With the purpose of achieving both low-level control and en-ergy management in the global FCPP, the first perspective of theAMS model is to be connected to the other dynamic systems: heatexchanger and later condensers , reformer, and stack. We will not

present the detailed models of these multidomain components.Starting from input-output interfaces, we will apply our physicalmultiport approach to build the FCPP model. In this way, wewill be able to underline AMS influence on the FCPP dynamicbehavior.

4.1 Heat Exchanger Model. The cooling system consists ofheat exchangers or condensers that remove the excess heat. Forinstance, the air temperature leaving the compressor is usuallyhigh due to the increased pressure. To protect the FC membranefrom damage, the air may need to be cooled down by a dedicatedheat exchanger Fig. 17 , which includes dynamic thermal ex-change and static pressure drop.

4.2 Fuel Processing System Model. We can assume that theFPS model Fig. 18 15,16 contains a chemical model that gen-

erates hydrogen outlet mass flow from air, fuel inlet mass flows,and a static pressure loss map.

4.3 Stack Model. Considering interactions with the AMSmodel, the FCS model Fig. 19 15 contains four main submod-els: The anode and cathode flow models with their associatedpressure losses , the stack temperature model with its coolingpower input , and the stack voltage model with carbon monoxidepoisoning . Indeed, one of the problems of reforming hydrocar-bons is the production of carbon monoxide CO , which is a poi-son for the stack and which penalizes the stack electrical voltage.This effect can be mitigated by introducing an air bleed in theanode channel 17 .

4.4 Integration in the Fuel Cell Power Plant Model. TheAMS model can be extended to a three-branch system to be inte-grated in the global FCPP model. The basic components still con-sist of air compressor, pipes, and manifolds between the compo-nents and control valves for flow and pressure regulation issues.

Model reduction techniques and dynamic analysis detailed inSec. 3 are still available and lead to a 14-state model. Thanks to itscontrol-oriented formalism, it will be used for the

understanding of the AMS complexity due to its nonlinearthermofluid behavior

evaluation of actuator technologies and AMS impact on the

overall energy balance rapid changes of AMS topologies both transient and steady-state analysis and simulation development of model-based control methodologies supervision and fault diagnosis

The long term goal of the work is to improve the global FCsystem operation by correctly specifying and allocating subsystemrequirements.

In the final FCPP model presented below Fig. 20 , the air bleedbranch is not included for readability concern.

Conclusion and Perspectives

With the purpose of meeting the specifically restrictive require-ments of fuel reforming FCV, this paper presents a dynamic ther-

mal pneumatic model of a complex AMS and its control-orientedmathematical version, specifically suited for multivariable con-troller design and system optimization. As a matter of fact, thephysical-based model retains sufficient details to accurately pre-dict system dynamic response while also being simple enough tobe of value in determining appropriate control strategies.

Although the dynamic stack and reformer behaviors are notincluded, these studies established a good basis for understandingthe great technical complexity of multibranch AMS and the FCPPintegration. The challenge was to give physical knowledge, dedi-cated MATLAB/SIMULINK library, and experimental support to con-trol activity. Moreover, it is demonstrated that, thanks to a struc-tured modeling methodology, we will be able to apply a model-

Fig. 17 Structure of heat exchanger model

Fig. 18 Structure of FPS model

Fig. 19 Structure of FCS model




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based control activity to various configurations of AMS and thusachieve significant energy savings in the overall FC system. Thefinal perspective is to ensure a safe operation of the entire FCPP,with high efficiency and sufficient transient performance.

Subscripts and AbbreviationsAMS air management systemCFD computational fluid dynamics

FC fuel cell

FCPP fuel cell power plantFCS fuel cell stackFPS fuel processing systemHE heat exchanger

MIMO multi-inputs multi-outputsPEM proton exchange membrane

1,2 upstream, downstreamatm atmosphere

C compressorcomp compressor outlet

in inletout outlet

post posterior conditionsref reference inputtot total

V valve

Nomenclature

CP,V specific heat capacities, J/kg/KD diameter, mec mass total energy, J/kg

etot mass total energy, J/kg isentropic coefficient

htot mass total enthalpy, J/kgI current, A

L length, mm mass, kg

Nu Nusselt number efficiencyP pressure, Pa

Pr Prandtl numberQh enthalpy flow, J/sQm mass flow, kg/sQT heat flux, W

r air constant, J/kg/KRe Reynolds number density, kg/m3

S section area, m2

T temperature, K torque, Nm

u mass internal energy, J/kgU voltage, volt

v speed, m/sV volume, m3

rotational speed, rpmW power, Wf friction loss coef.p pressure loss coef.

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Fig. 20 The global FCPP model


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