Control of an Ultrahigh-Speed Centrifugal Compressor for the Air Management of Fuel Cell Systems

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1

Control of an Ultra High Speed CentrifugalCompressor for the Air Management of

Fuel Cell SystemsDongdong Zhao Student Member, IEEE, Benjamin Blunier, Member, IEEE, Fei Gao, Member, IEEE,

Manfeng Dou, Member, IEEE, and Abdellatif Miraoui, Senior Member, IEEE,

Abstract—This paper proposes a control technology of an ultrahigh speed centrifugal compressor for the air management ofproton exchange membrane fuel cells (PEMFCs) for automotiveapplications. The mathematical model of the air managementsystem (AMS) is validated experimentally. The implementationof a fast butterfly valve with a PI controller overcomes thedifficulty of pressure ratio control so as to make the system workon the optimal operating points. The application of a referencelimiter restricts the trajectory of the operating points in the rightregion of the surge line to ensure the safety of the compressor.Experimental results show the goodness of reference trackingproperty in terms of mass flow and pressure. Meanwhile thesurge phenomenon is prevented by the reference limiter.

Index Terms—Automotive applications, compressors, fuel cells,surge protection, ultra high speed.

I. INTRODUCTION

Thanks to their high power density, proton exchange mem-brane fuel cells (PEMFCs) provide a good tank-to-wheel effi-ciency compared to heat engines, which makes them suitablefor automotive applications [1]. Over the last decade thetechnology of Fuel Cell Systems (FCS) has increasingly devel-oped and new models have been come up with for assessingdifferent control strategies, also in the objective to increasethe FC stack lifetime and reduce its maintenance [2] [3]. Thesupply of oxygen to the cathode is one of the key factors inthe operation of a fuel cell [4]. The air compressor whichconsumes up to 15 % of fuel cell generated power is a crucialcomponent in the air management system (AMS). Therefore,the size and efficiency of compressor directly influence theoverall system efficiency [5]. A scroll compressor driven byan induction motor is employed in [6], [7]. In [8], a twin-screw compressor is used for the high-pressure condition and ablower is used for the low-pressure condition. Automotive fuelcell industry needs compact, lightweight, low-cost and high

Manuscript received August 28, 2012; revised March 29, 2013 and May20, 2013; accepted August 29, 2013. Paper 2012-IACC-479.R2, presented atthe 2012 IEEE Industry Application Society Annual Meeting, Las Vegas, NVUSA, October 7-12, and approved for publication in the IEEE TRANSAC-TIONS ON INDUSTRY APPLICATION by the Industrial Automation andControl Committee of the IEEE Industry Application Society.

D. Zhao, B. Blunier, F. Gao, and A. Miraoui are with the Universi-ty of Technology of Belfort-Montbeliard, 90010 Belfort, France (e-mail:[email protected]; [email protected]; [email protected]; [email protected]).

M. Dou is with the Institute of REPM Electrical Machines and ControlTechnology, Northwestern Polytechnical University, 710072 Xi’an, China (e-mail: [email protected]).

efficiency compressors. Screw or Roots-type superchargers arecommonly chosen for the easier technical implementation.The centrifugal technology has major advantages of compact-ness, low noise and high efficiency. But it is more criticalto implement in terms of pressure control [7]. Moreover,surge instability strongly limits the operating range and theperformance of compression systems. In order to overcome thedrawbacks of the centrifugal compressor, active surge controlused in the air management system has been studied in [9].A load governor introduced in [10] controls the current drawnfrom the fuel cell to ensure the surge constraint.

In this study, an ultra-high speed centrifugal compressoris employed for the air management of fuel cell systemsfor automotive application. The technical challenges and ob-jectives for fuel cell systems in automotive applications aregiven by the Department of Energy (DOE). To the best of theauthors’ knowledge, this is the highest speed (maximum speedup to 260,000 krpm) compressor realized so far for fuel cellair management applications [11]. Details of the compressordesign has been described in [12]. The main interest ofthis paper is to analyze and control this compressor. Firstly,Relative gain array (RGA) method is used to get the couplingdegree of the compressor control. Then, a fast discharge valvewith a PI controller is introduced to control the supplied airpressure. Therefore, the mass flow and pressure of the air canbe controlled simultaneously. At last, a reference limiter isdeveloped to prevent the compressor surge. Compared with thereference governor [10] [13], the reference limiter introducedin this paper is more suitable for the highly nonlinear andcomplex system because it is not a model based method.

This paper is organized as follows. Section II gives a generaldescription of the AMS. At the same time the requirementsto AMS for automotive applications are presented. In sec-tion III, the mathematical model of the AMS is developed.In section IV, two decentralized PI controllers are designed tocontrol the mass flow and pressure. Meanwhile a referencelimiter is developed to prevent the compressor surge. Thevalidation of the mathematical model and experimental resultsare given in section V.

II. FUEL CELL AIR MANAGEMENT

A fuel cell requires the power dependent supply of clean airto be delivered at a proper pressure in order to function effec-tively. In transportation applications, because of the dynamic



2

Anode

Cathode

Compressor

controller

filter

air

condenser

humidifier

air

DC

DC

load

mass flow

pressurecurrent

voltage

DC

AC

valve control

valve

sensor

Motorspeed

Fig. 1. Air management system

load characteristic, the fuel cell needs to work at differentoperating points. During transients, current is instantaneouslydrawn from the load source connected to the fuel cell stack.An air management system is needed to provide sufficientoxygen for the fuel cell and regulate the pressure to a propervalue to make the fuel cell work at its optimal efficiency. Agreat deal of equipments (see Fig. 1) are needed to fulfillthese tasks. Explicit descriptions of the AMS and the tasks ofeach component are presented in [1]. The main componentsconsidered in this paper are shown inside the dashed lineof Fig. 1. The requirements to the AMS for automotiveapplications are described in the following subsections.

A. Compactness

Air management for fuel cell systems is a challenge becausecommercial compressors and humidification systems are notsuitable for automotive applications [1] in view of their largesize. It is well known that compared with other displacementcompressors, centrifugal compressors have the advantages ofcompactness and high efficiency. Comprehensive comparisonsbetween centrifugal compressor and positive displacementcompressors (scroll compressor, lobe compressor, screw com-pressor, etc.) have been published by B.Blunier [1], [14]. Theadoption of ultra high speed technology in compressor designresults in the ultra compactness. The advantage of this highrotational speed is the decrease of the impeller radius andtherefore an increase in power density in turbo machinery [15].Also the electrical motor power density is roughly proportionalto the speed. The design of this compressor is presented in[12], which is based on a similar small high-speed compressordata in [15].

B. Pressure control

B. Blunier [1] not only points out the advantages of the cen-trifugal compressor, but also indicates some drawbacks. Themain difficulties for centrifugal compressor applications arepressure and surge controls. Unlike displacement compressors,pressure control is challenging for centrifugal compressor as itis strongly coupled with the mass flow control. The mass flowis promptly regulated according to the load situations, which

Air outlet

Air inlet

Permanent-magnet

synchronous motor

Fig. 2. Realized compressor prototype

greatly varies the pressure ratio if it is not adjusted in time. Insevere cases, the pressure may be dragged out of the normaloperating region, which will paralyze the whole system. Thehighly nonlinear characteristic of mass flow, pressure, andspeed also adds to the difficulty of pressure control. For thestack, large pressure ripples may damage the membrane andproduce voltage pulsation, which should be avoided. In thispaper, a discharge valve installed at the outlet of the manifoldis employed to control the pressure ratio.

C. Surge control

Surge is defined as the operating point at which the com-pressor peak head capability and minimum flow limit arereached. The compressor loses the ability to maintain thepeak head when surge occurs and the entire system becomesunstable [16]. Surge is an unstable state, which gives rise tooscillations of mass flow and pressure ratio, and severely re-duces compressor efficiency. Moreover, it can possibly damagethe compressor in the most severe cases [17]. An effectiveand direct way to deal with the surge constraint is to makethe compressor operate to the right of the surge line. In thispaper, a reference limiter is designed to cope with the surgeconstraint.

III. SYSTEM MODELING

A. Compressor characteristics

The realized compressor prototype (Fig. 2) has a weightof 0.6 kg which is fifty times lower than a comparablescroll compressor. The compressor has been evaluated andcharacterized on a test bench. The measured compressorefficiency at its rated operating point (250,000 rpm, 13 g/s,pressure ratio of 1.4 bar, inlet temperature 300 K) is 74.8 %.The motor efficiency in the rated operating point is 92 %. Theexperimental compressor map is shown in Fig. 4(a). Fig. 4(b)gives the compressor power map. In the low mass flow region,the compressor has to operate around the surge line to measurethe compressor power map. In this case, the power oscillationsmay occur. In the high mass flow region, the losses from themotor and impeller result that the measured data is alwayslarger than the calculated power map as shown in Fig. 4(b)

In order to find out the mathematical relation of mass flow,pressure ratio and compressor speed, a neural network based



3

15 neurons 8 neurons

2 hidden layers

mass flow

speed

pressure

Fig. 3. Neural network model

on the back propagation (BP) algorithm is trained off-line onthe basis of the experimental data. The structure of the neuralnetwork is shown in Fig. 3. There is no acceptable theoryto decide the number of the hidden layer and the numberof neurons. In this study, they are chosen according to theempirical equation and experimental trials. Fig. 4(a) shows thatthe neural network model is in very good agreement with themeasured data. Therefore, it can be mathematically expressedas follows:

q = h(ω, p) (1)

where q, ω, p are the mass flow out of the compressor,compressor angular velocity, compressor outlet pressure ratiorespectively.

B. Manifold model

The manifold represents the lumped volume of the pipesbetween the compressor and the fuel cell stack. The dynamicsof the air pressure in the manifold directly relates to thecompressor characteristic. According to the mass conservationprinciple, the dynamics of the air mass m accumulated in themanifold volume and the manifold pressure p can be expressedthrough the following equations [18]–[20]:

dmdt

= q − qout (2)

dpdt

=γRa

MairV(qTin − qoutTout) (3)

where qout is the air mass flow out of the manifold. Tin, Tout

are the compressor outlet gas temperature and manifold airtemperature respectively. γ is the thermal ratio coefficient ofthe air and Ra is the gas constant of the air. V is the manifoldvolume. In the case of air, γ = 1.4, Ra = 8.3 . In this paper,the air temperature in the manifold is assumed to be constantand equal to the compressor outlet air temperature. That isTin = Tout = T . Then, (3) can be expressed as follows:

dpdt

=γRaT

MairV(q − qout) (4)

Nozzle flow equations are used to calculate qout, which isdivided into two regions by the critical pressure ratio ξ.

ξ =

(patmp

)crit

=

(2

γ + 1

) γγ−1

(5)

0 5 10 15 201

1.1

1.2

1.3

1.4

1.5

1.6

Compressor Map

Mass flow (g/s)

Pre

ssu

re r

atio

(−

)

Experimental dataNeural network model

260 krpm250 krpm240 krpm230 krpm220 krpm210 krpm200 krpm175 krpm150 krpm125 krpm100 krpm 75 krpm 50 krpm

medium and weak coupling region

strong coupling region

(a) Measured compressor map and neural network model map.

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mass flow (g/s)

Com

pres

sor

pow

er (

Shaf

t pow

er)

(kW

)

100 krpm120 krpm140 krpm160 krpm180 krpm200 krpm210 krpm220 krpm230 krpm240 krpm250 krpm260 krpm

0 4.2 8.4 12.7 16.9 21.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Standard inlet volume (l/s)

(b) Measured and calculated power map of the compressor.

Fig. 4. Compressor map and power map.

For patm

p > ξ,

qout = Cdp·Sctrl(θ)

√√√√ 2γMair

(γ − 1)RT

[(patmp

) 2γ

−(patmp

) γ+1γ

](6)

For patm

p ≤ ξ,

qout = Cdp · Sctrl(θ)

√√√√γMair

RT

(2

γ − 1

) 1+γ1−γ

(7)

where θ, patm, Mair are the open angle of valve, atmospherepressure and molar mass of air respectively.Cd is the dischargecoefficient of the Nozzle. Sctrl(θ) is the open area of the valve.The critical pressure ratio ξ is calculated equal to 0.528. Inthis paper, the pressure p is below 1.6 bar. Assuming patm =



4

4.1 kf

4 A

200 V

Fig. 5. A-C line voltage (CH1) and phase A current (CH2), at rated operatingpoint, 13 g/s, 1.4 bar.

TABLE ISPECIFICATIONS OF THE PMSM

Number of pole pairs 1Moment of inertia 5.5×10-7 kg· m2

Magnet flux linkage 6 mVsRated/max power 600 W / 1100 WRated/max torque 22.9×10-3 N·m / 37.5×10-3 N·mStator resistance 0.9ΩStator inductance 160 µH

1 bar, gives patm

p > 1/1.6 > 0.528. Therefore, only (6) isadopted for the mathematical model development. Accordingto the analysis above, the lumped formulation of qout can beexpressed as follows:

qout = φ(θ, p) (8)

C. Actuator model

The compressor is driven by a permanent magnet syn-chronous motor (PMSM) with a PAM (pulse-amplitude mod-ulation) converter, which is shown in Fig. 6. Details of thisdrive method have been described in [15] [21]. Compared withPWM, the PAM results in lower losses, which is more suitablefor high-speed electrical machines [22]. The characteristic ofthe voltage and current at the rated operating point is shownin Fig. 5. Parameters of the PMSM are given in TABLE I.

The following equations show the dynamic properties of thecompressor angular velocity ω:

dω

dt=

1

J(Tcm − Tcp) (9)

where J is the moment of inertia. Tcm and Tcp are the electro-magnetic torque produced by the PMSM and the compressortorque respectively. They can be expressed as follows (withLd = Lq):

Tcm =3

2PΨf iq (10)

Tcp =Cp

ω

Tatm

ηcp

[(p

patm

) γ−1γ

− 1

]· q (11)

where P is the number of pole pairs. Ψf is the PM rotorflux linkage. iq is the q axis components of the stator winding

D1 D2 D3

D4 D5 D6

T1 T2 T3

T4 T5 T6

DC/AC INVERTERDC/DC

CDC

VDC LPMSM &

Compressor

Sensorless position and

speed calculation

, ,a b cu

Control algorithm

Speed PI

*

i

+-

+-

Torque PI

PWM

Controller

Fig. 6. Block diagram of the PAM converter and control system for drivingan ultra-high speed compressor.

current. Ld, Lq are d, q axis inductances. Cp is the specificheat capacity of the air. ηcp is the compressor efficiency.Tatm is the upstream temperature. The motor controller basedon PAM algorithm is well designed, so that the motor speedhas a good reference tracking characteristic.

In the system, a fast butterfly valve with a PI controller isemployed to control the valve position. The valve position θis in direct proportion to the current ivl flowing through theconverter, θ ∝ ivl. As the inertia of the valve is much smallerthan the compressor, the valve position has a much fasterresponse than the compressor speed. Therefore, the neglectof the valve response time does not influence the dynamics ofthe mass flow and pressure. In this case, the valve position θcan be deemed as input directly instead of ivl.

IV. CONTROLLER DESIGN

A. Mass flow and pressure controlFrom the above mathematical models, the state space equa-

tions of the AMS are derived as follows:

p =γRaT

MairV(h(ω, p)− φ(θ, p)) = f1(ω, p, θ) (12)

ω = f2(ω, p, ω∗) (13)

q = h(ω, p) (14)

where ω∗ is the compressor angular velocity reference. Thevector representations of the control variables and state vari-ables are u = [ω∗, θ]T and x = [p, ω]T respectively.The air mass flow and pressure ratio are viewed as outputs,y = [q, p]T . At an operating point, the linearized formula ofthe two inputs two outputs system can be described as follows:[

q(s)p(s)

]=

[Gp11(s) Gp12(s)Gp21(s) Gp22(s)

] [ω∗(s)θ(s)

](15)

Here, we define:

Gp(s) =

[Gp11(s) Gp12(s)Gp21(s) Gp22(s)

](16)

Using the relative gain array (RGA) method in control theory[23], the interactions among multiple control loops are quanti-tatively analyzed. The RGA is a 2× 2 matrix for a two inputstwo outputs system:



5

TABLE IIDYNAMIC RGA TABLE

p=1.40 p=1.30q (g/s) RGA q (g/s) RGA

15.85 0.6959 0.30410.3041 0.6959

15.89 0.7279 0.27210.2721 0.7279

14.86 0.6679 0.33210.3321 0.6679

14.96 0.7008 0.29920.2992 0.7008

13.87 0.6361 0.36390.3639 0.6361

13.89 0.6716 0.32840.3284 0.6761

12.88 0.6023 0.36390.3639 0.6023

12.08 0.6030 0.39070.3907 0.6030

9.88 0.5655 0.43450.4345 0.5655

9.98 0.5641 0.43590.4359 0.5641

RGA =

[λ11 λ12

λ21 λ22

](17)

where

λij =

∂yi

∂uj|ur=cont, (r = j)

∂yi

∂uj|yr=cont, (r = i)

, (i = 1, 2; j = 1, 2)

where y1, y2 represent the system outputs q and p respectively.u1, u2 represent the control inputs ω∗, θ respectively. Assum-ing that the system’s steady-state transfer function matrix isGp(0), its RGA is given by:

RGA = Gp(0) · (G−1p (0))T (18)

Equation (15) is a linearized formulation at a given op-erating point. This system is highly nonlinear, which meansthat the matrix Gp(s) changes as the operating point changes.In order to analyze the interactions between the inputs andoutputs, the system is linearized at different operating pointsunder a wide range by Simulink LTI toolbox. Parts of theRGA are listed in Table II which indicates that coupling degreeincreases as the mass flow decreases and pressure increases.It should be noted that in the strong coupling region shownin Fig. 4(a), where λ11 and λ22 are very close to 0.5, themass flow and pressure cannot be controlled simultaneouslyand small vibrations possibly drag the system into the surgeregion. Therefore in the experiment we define a control surgeline to the right of this strong coupling region to prevent theoperation going into the unstable region thereby out of control.Two decoupled PI controllers are developed to control themass flow and pressure separately. The control objective is tomake the mass flow and pressure ratio track their referencessimultaneously.

Differentiating the mass flow q and pressure ratio p withrespect to time yields:

q = Hp(x)f1(x, θ) +Hω(x)f2(x, ω∗) (19)

p = f1(x, θ) (20)

where Hω(x) = ∂h∂ω and Hp(x) = ∂h

∂p . (19) (20) show thatthe relative degree sj = 1, (j = 1, 2). The references of massflow and pressure, q∗and p∗, are available online accordingto the power that the fuel cell needs. Taking r= [q∗, p∗], theregulation error is e = y− r. The integral action is introducedas follows:

e0 = e

iK

pK

!

aK

!!

r

y

Plantu

Fig. 7. PI control with anti windup

The PI controller takes the following form:

u = kpe+ kie0 (21)

It is conventional to verify the augmented system as followsis closed-loop stable so as to identify the feasible values of kpand ki.

xe = χ(x, e0, e)

where xe = [x, e0, e]T . Whereas the choice of a Lyapunov-like

function candidate and getting the solution of the inequalityare all difficult tasks. In this paper, kp and ki are selectedempirically and validated by experimental trials. Some basicprinciples guided us to tune the PI parameters in the experi-mental trails.

• We put the fast response of the mass flow in the firstplace. Fast response of the mass flow can effectivelyavoid/shorten fuel cell starvation, which is a very importproblem in the fuel cell system. This requirement can berealized by increasing the proportion gain.

• Then, the overshoot of the pressure has to be suppressedduring transient. Because the large overshoot of thepressure possibly make the system go to the strong cou-pling region or surge region. Increasing the integrationgain and decreasing the proportion gain are methods torealize it.

• At last, the oscillation of the pressure in steady state hasto be controlled no more than 200 mbar [1], becausegreater pressure ripples may damage the stack mem-brane. This indicates that appropriate value of integrationgain should balance with the other two requirementsabove.

In practical applications, the control variables have somehard constraints: 0 ≤ ω∗ ≤ 8760π, 0 ≤ θ ≤ 0.5π. Insome situations, the saturations of actuator may result severedeterioration in performance. In this paper, anti windup designis employed to cope with integrator windup, as shown inFig. 7.

B. Surge control

In order to avoid compressor surge, a reference limiter isdesigned to prevent the trajectory crossing the surge line. Acontrol surge line is defined, p = ϕ(q), which provides a safetymargin for the surge control. The reference limiter is expressedas follows:

p∗ = minϕ(q), pref (22)q∗ = maxϕ−1(p∗), qref (23)

where pref and qref are the pressure and mass flow referencesrespectively. p∗ and q∗ mentioned in section IV-A turn into



6

Fig. 8. Simulation trajectory ((0, 1) → A → B → A)

the outputs of the reference limiter. The characteristics of thetrajectory during the operation are analyzed as follows.

Due to the small inertia and appropriate configuration of thePI control parameters, the valve has a much faster responsethan the compressor, which makes the trajectory of the com-pressor operate clockwise (see Fig. 8). Take the set points Aand B for example.

1) Case 1: pref > p, qref > q. (A(q, p) → B(qref, pref))In this situation, the PI controller results in the decre-ment of the valve angle (∆ θ < 0) and the incrementof the compressor speed (∆ω > 0), which exactlyhave an inverse impact on the mass flow and pressureratio: ∆ θ < 0 reduces (increases) the mass flow (pres-sure), whereas ∆ω > 0 increases (reduces) mass flow(pressure). The faster response of the valve makes thepressure reach the set point in the first place. The massflow decreases at first and then increases to the set point,which is a clockwise trajectory as shown in Fig. 8.

2) Case 2: pref < p, qref < q. (B(q, p) → A(qref, pref))In this situation, the PI controller leads the compressorspeed to decrease and the valve angle to increase, whichis the inverse of the first case. The trajectory is shownin Fig. 8, which is also clockwise.

The same conclusion can be obtained in the same way for theother two situations: pref > p, qref < q (case 3) and pref <p, qref > q (case 4).

Through the above analysises, only in the case 1 and case3 there are possibilities that the trajectory cross the surge line.As the mass flow is small, (22) forces the set points to go alongthe control surge line to restrain the fast raise of pressure, so asto prevent the surge phenomenon. (23) makes sure that the setpoints are on the right side of the control surge line. It shouldbe noticed that, as an overshoot is inevitable for PI control,it is possible that the operating points cross the control surgeline, thereby resulting in a decline of pressure. In severe cases,it leads p∗ to vibrate along the control surge line, thus inducespressure oscillations. This oscillation phenomenon will beverified experimentally in section V. The following reference

Reference

limiter

PI control with anti

windupValve

controller

System

(Compressor

Valve

Fuel cell)

System states

Controller

refq

refp *p

*q*

*

Motor

controller

( , ) !( , )q p ( , )q p

Fig. 9. System controller

limiter is developed to improve the above reference limiter:

p∗(k) =

minϕ(q(k)), pref, p(k) < ϕ(q(k));

p∗(k − 1), p(k) ≥ ϕ(q(k));(24)

q∗(k) = maxϕ−1(p∗(k)), qref (25)

where p(k) and q(k) represent the discrete form of themeasured mass flow and pressure respectively. In the case ofpref > p, (24) assures that p∗ is monotone nondecreasing untilp∗ = pref , so as to avoid pressure oscillation.

Summarizing the two subsections above, the controller isdepicted in Fig. 9, which is also the stretch out view of thecontroller block diagram in Fig. 1.

V. EXPERIMENTAL RESULTS

A. Experimental setup

An experimental rig (Fig. 10) has been devised for theexperimental assessment of the control methodology. Theexperimental setup is a hardware in the loop (HIL) platform,which is comprised of a centrifugal compressor, manifolds,control valves, a dSPACE, sensors, etc. The centrifugal com-pressor introduced in section III has a maximum speed of260,000 rpm. A fast butterfly valve is used for the pressureand surge control. The high-performance motor controller isimplemented by a DSP with the speed control frequency of15 kHz and current control frequency of 80 kHz, respectively.The mass flow and pressure closed-loop control strategies aswell as surge control methodology are implemented by thedSPACE at a lower frequency of 1 kHz.

B. Model validation

Model verification and validation are essential parts ofthe model development. Both the parameter estimation andmodel based controller design need an accurate model. Themathematical models presented in section III cannot giveidentical results to the real system because of the parametermismatches and model inaccuracies. By means of the outputcomparisons between the real system and the simulationmodel, the validity of the model is verified. The same inputs(ω* and θ) are given to the real system and simulation modelsimultaneously. Corresponding outputs are shown in Fig. 11.The maximum errors of mass flow and pressure ratio betweenthe real system and the simulation are less than 0.8 g/s and0.03 bar respectively.

The output differences are mainly because of the inaccura-cies in the measurement, such as valve position, compressor



7

Motor

controller

Sensors

(pressure &

flow meters)Air filter

Motorized

Compressor

Cooler (Fan)

Valve

dSPACE

Valve

controller

Fig. 10. Photograph of the air management test bench

0 2 4 6 8 10 121

1.1

1.2

1.3

1.4

1.5

1.6

Time (s)

Pre

ssur

e ra

tio (

−)

real systemsimulation

(a) pressure ratio response

0 2 4 6 8 10 12

5

10

15

Time (s)

Mas

s flo

w (

g/s)

real systemsimulation

(b) mass flow response

Fig. 11. Model validation in terms of outputs verification

speed, mass flow, and pressure, etc.. At the same time, thediscrepancies of the system parameters, motor inertia andmanifold volume for instance, also contribute to the mismatch.The experimental results have shown that the simulation modelbasically matches with the real system.

C. Reference track

In the fuel cell system, the mass flow and pressure refer-ences are calculated according to the load demands. Fast massflow response is a fundamental requirement to avoid fuel celloxygen starvation. For the purpose of operating at the optimaloperating points, the pressure also need to be regulated as themass flow changes. The centrifugal compressor map reveals

0 5 10 15 20 25 301

1.1

1.2

1.3

1.4

1.5

1.6

Time (s)

Pre

ssur

e ra

tio (

−)

measurementreference

(a) pressure response

0 5 10 15 20 25 30

5

10

15

Time (s)

Mas

s flo

w (

g/s)



Fig. 12. Tracking characteristics of pressure and mass flow

that the mass flow and pressure are coupled, which means thatas one of the two variables changes the other also changes.In this paper, two decentralized PI controllers are designed tocontrol the mass flow and pressure. The experimental results(Fig. 12) show that the mass flow response time is 4 s at thestarting stage, which is larger than in the situation of keepingthe pressure constant. This is mainly because the increase ofpressure prolongs the mass flow response time. It is worthnoting that the sudden changes of pressure induced inversemass flow varieties (Fig. 12 at 8 s, 15 s, 18.5 s respectively).However, sudden deviations of mass flow hardly influenced thepressure (Fig. 12 at 9.5 s, 19 s and Fig. 13 at 12 s) as a resultof the faster response of pressure than mass flow. In practicalapplications, the sudden large change of pressure should beavoided during the operation.

D. Surge prevention

In the start-up stage, due to the faster response of pressure, itis likely to lead the compressor into the surge region if there isno restriction to it. Two reference limiters have been describedin section IV to prevent the compressor surge. The latter isthe improved version of the former, in terms of avoiding theoscillations of the pressure and mass flow along the controlsurge line. Fig. 13(a) demonstrates that the reference limitercan effectively prevent the compressor going into the surgeregion. However, as mentioned in section IV, it results theoscillations of mass flow and pressure during the start-up stage,which are shown in Fig. 13(b) and Fig. 13(c) respectively.Those oscillations will result in the degradation of the fuel cellperformance. The pressure oscillations lead to the vibrationsof the output voltage of the fuel cell stack. Moreover, in



8

0 2 4 6 8 10 12 14 151

1.1

1.2

1.3

1.4

1.5

Mass flow (g/s)

Pre

ssur

e ra

tio (

−)

trajectorycontrol surge line

(a) Compressor operating trajectory

0 5 10 15 20 25 301

1.1

1.2

1.3

1.4

1.5

Time (s)

Pre

ssur

e ra

tio (

−)


(b) pressure response

0 5 10 15 20 25 300

5

10

15

Time (s)

Mas

s flo

w (

g/s)


(c) mass flow response

Fig. 13. Oscillations caused by the reference limiter, i.e., equation (22) and(23)

severe cases it may damage the stack membrane. The massflow oscillations may cause the fuel cell oxygen starvation,which can shorten the life time of fuel cell stack. Fig. 14,which is the trajectory plot of Fig. 12, gives the experimentalresults under the improved reference limiter. It shows thatthe oscillations along the control surge line are eliminated.However, the overshoot of the PI control also leaded to a smallpressure vibration (Fig. 12 at 3 s).

This phenomenon can be avoided by adding a lower limiterto the valve angle θ. In the following experiment, a valveposition limiter (θ ≥ π/60) is added, which makes the pressurerespond slower. Meanwhile, a slower mass flow response isperformed by reselecting PI parameters. Experimental results(Fig. 15) show that sacrificing of response time gives a bettersurge control result in return. The trajectory even did nottouch the control surge line. Moreover, the sudden reductionof mass flow (at 15 s, 22 s) did not result compressor surge.The tradeoff between the response time and the surge controlperformance should be made according to practical applica-

0 2 4 6 8 10 12 14 161

1.1

1.2

1.3

1.4

1.5

Mass flow (g/s)

Pre

ssur

e ra

tio (

−)

measurement control surge line

Fig. 14. Surge prevention as the results of the improved reference limiter (itis the trajectory of Fig. 12)

0 2 4 6 8 10 12 14 161

1.1

1.2

1.3

1.4

1.5

Mass flow (g/s)P

ress

ure

ratio

(−

)

trajectorycontrol surge line

(a) Compressor operating trajectory

5 10 15 20 25 30

5

10

15

Time (s)

Mas

s flo

w (

g/s)



0 5 10 15 20 25 301

1.1

1.2

1.3

1.4

1.5

1.6

Time (s)

Pre

ssur

e ra

tio (

−)


(c) pressure response

Fig. 15. Surge prevention after adding an angle limiter

tions.

VI. CONCLUSION

This paper presents the design and experimental validationof an ultra high speed centrifugal compressor controller for theair management of PEMFCs in automotive applications. The



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reason of using an ultra high speed centrifugal compressoris that it can dramatically reduce the size of the air man-agement system, which is a fundamental requirement for fuelcell systems in automotive applications. The compressor mapmodel is developed based on neural network and validatedexperimentally. The main drawbacks of centrifugal compressorfor fuel cell applications lie in the difficulty of pressure control,as well as the surge constraint which significantly affects thesafety of the whole system. Through the analysis of the RGAcharacteristic of the system, two decentralized PI controllersare developed to control the mass flow and pressure. Thedifficulty of pressure control is overcome as the result of theutilization of a fast butterfly valve with a PI controller. Areference limiter is proposed to deal with the surge constraint.

An experimental setup is established for the validation ofthe control system. Experimental results have shown thatthe mathematical model corresponds to the real system. Themass flow and pressure ratio have a correct and fast trackingproperty. Meanwhile, the operation trajectory is controlled inthe right region of the surge boundary. It should be noticedthat the valve angle limiter can be deemed as an adjustablevariable to balance the effectiveness of surge control and theresponse time.

ACKNOWLEDGMENT

The authors gratefully acknowledge the contributions ofChristof Zwyssig and Daniel Krahenbuhl from Celeroton,who lead the compressor design team. The authors dedicatethis paper to the memory of their friend and coauthor, Dr.B.Blunier, formerly an Associate Professor with the Universityof Technology of Belfort-Montbeliard, who passed away onFebruary 23, 2012.

REFERENCES

[1] B. Blunier and A. Miraoui, “Proton exchange membrane fuel cell airmanagement in automotive applications,” J. Fuel Cell Sci. Technol.,vol. 7, no. 041007, 2010.

[2] A. Accetta, M. Cirrincione, G. Marsala, M. Pucci, and G. Vitale, “PEMfuel cell system model predictive control and real-time operation on apower emulator,” in Proc. IEEE ECCE, 2010, pp. 1610–1616.

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[4] A. Vahidi, A. Stefanopoulou, and H. Peng, “Model predictive controlfor starvation prevention in a hybrid fuel cell system,” in Proc. Amer.Control Conf., vol. 1, 2004, pp. 834–839.

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[6] B. Blunier, G. Cirrincione, Y. Herve, and A. Miraoui, “A new analyticaland dynamical model of a scroll compressor with experimental valida-tion,” Int. J. Refrigeration, vol. 32, no. 5, pp. 874–891, 2009.

[7] B. Blunier, M. Pucci, G. Cirrincione, and A. Miraoui, “A scrollcompressor with a high-performance induction motor drive for the airmanagement of a pemfc system for automotive applications,” IEEETrans. Ind. Appl., vol. 44, no. 6, pp. 1966–1976, 2008.

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[12] D. Zhao, D. Krahenbuhl, B. Blunier, C. Zwyssig, M. Dou, and A. Mi-raoui, “Design and control of an ultra high speed turbo compressor forthe air management of fuel cell systems,” in Proc. IEEE ITEC, 2012,pp. 1–6.

[13] J. Sun and I. Kolmanovsky, “Load governor for fuel cell oxygenstarvation protection: A robust nonlinear reference governor approach,”IEEE Trans. Control Syst. Technol., vol. 13, no. 6, pp. 911–920, 2005.

[14] B. Blunier and A. Miraoui, “Air management in PEM fuel cells: State-of-the-art and prospectives,” in Proc. Elect. Mach. Power Electron. Conf.,2007, pp. 245–254.

[15] D. Krahenbuhl, C. Zwyssig, H. Weser, and J. Kolar, “A miniature 500000-r/min electrically driven turbocompressor,” IEEE Trans. Ind. Appl.,vol. 46, no. 6, pp. 2459–2466, 2010.

[16] M. Nored, K. Brun, and R. Kurz, “Development of a guideline for thedesign of surge control systems.” ASME, 2008, pp. 9–13.

[17] J. Gravdahl and O. Egeland, “Compressor surge control using a close-coupled valve and backstepping,” in Proc. Amer. Control Conf., vol. 2,1997, pp. 982–986.

[18] A. Vahidi, I. Kolmanovsky, and A. Stefanopoulou, “Constraint manage-ment in fuel cells: A fast reference governor approach,” in Proc. Amer.Control Conf., 2005, pp. 3865–3870.

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[21] C. Zwyssig, S. D. Round, and J. W. Kolar, “An ultrahigh-speed, lowpower electrical drive system,” IEEE Trans. Ind. Electron., vol. 55, no. 2,pp. 577–585, 2008.

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Dongdong Zhao (S’12) received the B.Eng degreein 2008 at Northwestern Polytechnical University(NPU), Xi’an, China. He was then a graduate studentat NPU until 2010. He is currently working towardPh.D. degree at the University of Technology ofBelfort-Montbeliard, 90010 Belfort, France.

His research interests include air compressor con-trol, fuel cell modeling and power electronics.

Benjamin Blunier (S’07-M’08) received the M.Sc.and Ph.D. degrees electrical engineering from theUniversity of Technology of Belfort-Montbeliard(UTBM), 90010 Belfort, France, in 2004 and 2007respectively.

He studied fuel cell system modeling and partic-ularly air management and control for hybrid andelectric vehicles. He was an Associate Professor atUTBM utile his death on February 23, 2012. Hisresearch interests include fuel cell systems, electric,hybrid, and plug-in hybrid vehicles, and intelligent

energy management in smart grids and microgrids.



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Fei Gao (S’09-M’11) received the Master’s andDoctor’s degree in electrical engineering from theUniversity of Technology of Belfort-Montbeliard(UTBM), 90010 Belfort, France, in 2007 and 2010respectively.

Since 2011, he has been an Associate Professor atthe UTBM. His research interests include fuel cells,renewable energy, smart grid technology, real-timeoriented system modeling, and hardware-in-the-loopapplications.

Manfeng Dou (M’08) received the Master’s degreeand Doctor’s degree in electrical engineering fromNorthwestern Polytechnical University (NPU), X-i’an, China, in 1991 and 1998 respectively. His iscurrently a professor at NPU. And he is the vicedirector of Institute of REPM Electric Machine andControl Technology, NPU.

His research interests include electrical machinedesign, analysis of electromagnetic field, motioncontrol technology, and intelligent control. He gotthe Second Prize of National invention, China, in

1993, and the Second Prize of National Defense Science and TechnologyProgress Award, China, in 2007. He also got the Youth Science Award ofShaanxi Province, China, in 2004.

Abdellatif Miraoui (M’07-SM’09) was born inMorocco in 1962. He received the M.Sc.degree fromHaute Alsace University, Colmar-Mulhouse, France,in 1988, and the Ph.D. degree and the Habilitation toSupervise Research from the University of Franche-Comte, France, in 1992 and 1999 respectively.

He is the President of Cadi Ayyad University,Marrakech, Morocco. He has been a Full Professorof electrical engineering (electrical machines andenergy) at the University of Technology of Belfort-Montbeliard (UTBM), Belfort, France, since 2000.

His special interests include fuel cell energy, energy management in trans-portation, and design and optimization of electrical propulsions/tractions.

Prof.Miraoui is the Editor of the International Journal on ElectricalEngineering Transportation. He is a Doctor Honoris Causa of the TechnicalUniversity of Cluj-Napoca, Romania. He received the high distinction fromthe Ministry of Higher Education and Research of France of ”Chevalier dansl’Ordre des Palmes Academiques” in 2007. He was also distinguished by theUniversity of Brasov, Romania, as an Honorary Professor.

Control of an Ultrahigh-Speed Centrifugal Compressor for the Air Management of Fuel Cell Systems

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