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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 25, NO. 3, SEPTEMBER 2010 909
Analysis of Differential FlatnessBased Controlfor a Fuel Cell Hybrid Power Source
Phatiphat Thounthong, Member, IEEE, Serge Pierfederici, and Bernard Davat, Member, IEEE
AbstractThis paper presents an innovative control law for distributed dc generation supplied by a fuel cell (FC) (main source)and supercapacitor (auxiliary source). This kind of system is amulticonverter structure and exhibits nonlinear behavior. The operation of a multiconverter structure can lead to interactions between the controls of the converters if they are designed separately. Typically, interactions between converters are studied usingimpedance criteria to investigate the stability of cascaded systems.In this paper, a nonlinear control algorithm based on the flatnessproperties of the system is proposed.Flatness providesa convenientframework for meeting a number of performance specifications forthe hybrid power source. Using the flatness property, we proposesimple solutions to hybrid energy management and stabilization
problems. The design controller parameters are autonomous ofthe operating point; moreover, interactions between converters aretaken into account by the controllers, and high dynamics in disturbance rejection is achieved. To validate the proposed method,a hardware system is realized with analog circuits, and digital estimation is accomplished with a dSPACE controller. Experimentalresults with smallscale devices (a polymer electrolyte membraneFC of 1200 W, 46 A and a supercapacitor module of 100 F, 500 A,and 32 V) in a laboratory corroborate the excellent control schemeduring a motordrive cycle.
Index TermsConverters, current control, electric vehicles,energy management, flatnessbased control, fuel cells (FCs),supercapacitor.
I. INTRODUCTION
RENEWABLE energy sources [such as wind turbines, pho
tovoltaics, and fuel cells (FCs)] are expected to provide a
higher proportion of the worlds energy demand in the near fu
ture. FCs, in particular, are anticipated to play a significant role
Manuscript received October 30, 2009; revised April 5, 2010 and May 16,2010; accepted June 6, 2010. Date of current version August 20, 2010. Thiswork was supportedin part bya ResearchProgramin cooperationwith theThaiFrench Innovation Institute, King Mongkuts University of Technology NorthBangkok, and the Institut National Polytechniquede Lorraine, Nancy Universityunder the FrancoThai on Higher Education and Research Joint Project (20092010), in part by the French National Center for Scientific Research (CNRS)and the Nancy Research Group in Electrical Engineering (GREEN UMR 7037),and in part by the Thailand Research Fund (TRF) under Grant MRG5180348.Paper no. TEC004642009.
P. Thounthong is with the Department of Teacher Training in ElectricalEngineering and the Renewable Energy Research Centre, King MongkutsUniversity of Technology North Bangkok, Bangkok 10800, Thailand (email:[email protected]; [email protected]).
S. Pierfederici and B. Davat are with the Groupe de Rechercheen Electrotechnique et Electronique de Nancy, Institut National Polytechnique de Lorraine, Nancy University, 54510 Nancy, France (email:[email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEC.2010.2053037
in helping to meet the demands of power quality and reliability
of distributed power generation [1], [2].
It is believed that FC vehicles could revolutionize the auto
mobile industry by replacing internal combustion engine (ICE)
technology [3]. As reported in [4], for vehicle applications, the
total efficiency of an ICE based on a propulsion system and
FC vehicle comprises the welltotank efficiency and the tank
towheel efficiency. Overall, the FC vehicle is more efficient
than the ICE vehicle. The welltowheel efficiencies are 21.7
and 13.8% for FC and ICE vehicles, respectively. For hydro
gen manufacture, there are many ways to produce hydrogen,
particular from wind turbines and photovoltaic cells [5].According to recent works on FC characteristics [6][9],
the specific properties of FCs that result in a delayed out
put power response are related to processing time through
subsidiary equipments, and slow internal electrochemical and
thermodynamic characteristics. Therefore, in order to supply
electric power to fluctuating loads via the hybrid system of the
FC, an electric energy storage system is needed to compensate
the gap between the output from the FC and the load, in addition
to collaborative load sharing. At the moment, based on present
storage device technology, the supercapacitor (or ultracapaci
tor) storage device has received wide attention [10], [11] as an
auxiliary power source.The primary difference between batteries and supercapaci
tors is that the former store energy in the bulk of chemical
reactants capable of generating charge, whereas the latter store
energy directly as surface charge. Battery discharge rate and,
therefore, power performance is limited by reaction kinetics
as well as mass transport, while such limitations do not ap
ply to supercapacitors constructed with two activated carbon
electrodes, thereby allowing exceptionally high power capa
bility during both charge and discharge [12]. In addition, the
highly reversible electrostatic charge storage mechanism in su
percapacitors does not lead to the volume changes observed in
batteries with electrochemical transformations of active masses.
This volume change limits the lifetime cycle of batteries usu
ally to several hundred cycles, whereas supercapacitors have
demonstrated from hundreds of thousands to many millions of
fullcharge/discharge cycles [10].
Previous research works have shown that hybridization of
FC vehicles with batteries [13], [14], supercapacitors (ultra
capacitors) [15], [16], and battery/supercapacitors [17], [18],
provides cost, performance, and operational improvements, as
well as fuel economy benefits that are attractive and should
be considered. As reported in [19], an FC/supercapacitor hy
brid source has better performance than an FC/battery source,
because the supercapacitor can more effectively assist the FC
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to meet the transient power demand, and highcurrent charges
and discharges from batteries will also have a reduced lifetime.
Even better, hybrid source in a FC/battery/supercapacitor com
bination has been presented in [18]. A main improvement of the
FC/battery/supercapacitor vehicle is the increase in the battery
lifetime due to reduction of highcurrent charges and discharges.
However, there are still some aspects of control methods
to be studied, particularly in the area of dynamics, robust
ness, stability, and efficiency. Recent work on controlling a
FC/supercapacitor hybrid power plant is reported in [16], where
a linear control using PI compensator was proposed for dc
link stabilization. Design controller parameters based on linear
methods require a linear approximation, where this is dependent
on the operating point. Because the switching model of the hy
brid power plant is nonlinear, it is natural to apply modelbased
nonlinear control strategies that directly compensate for system
nonlinearity without requiring a linear approximation [20].
Differential flatness theory (nonlinear approach) was first in
troduced by Fliess et al. [21]. This allowed an alternate repre
sentation of the system, where trajectory planning and nonlinearcontroller design is clearcut. These ideas have been used lately
in a variety of nonlinear systems across various engineering
disciplines including: control of a highspeed linear axis driven
by pneumatic muscle actuators [22], control of cathode pressure
and oxygen excess ratio of a proton exchange membrane (PEM)
fuel cell system [23], steering control of a twolevel quantum
system [24], reactive power and dc voltage tracking control of
a threephase voltage source converter [25], control of open
channel flow in an irrigation canal [26], current control for three
phase threewire boost converters [27], design of a guidance al
gorithm for the hypersonic phase of a liftingbody vehicle [28],
and control of a space robot with arbitrarily oriented joint axesand two momentum wheels at the base [29].
In this paper, we present an innovative control approach called
differential flatness to manage energy in the proposed system.
This paper is focused on a special control strategy and control
law. This method enables the management of transient power
demand, power peaks, and regenerative braking, particularly in
future FC vehicle applications, in light of FC and supercapacitor
constraints. It will provide a new contribution to the field of the
multisource system. The general structure of the studied system,
the new control algorithm of the hybrid source, realization of the
experimental bench, and experimental validation are presented
in the following sections.
II. FC HYBRID POWER SOURCE
A. Proposed Hybrid Structure
Lowvoltage, highcurrent (power) converters are needed
because of the electrical characteristics of FCs and superca
pacitors. A classical boost converter is often used as an FC con
verter [30], [31], and a classical twoquadrant (bidirectional)
converter is often used as a supercapacitor or battery con
verter [32]. However, the classical converters will be limited
when the power increases or at higher stepup ratios. As such,
the use of parallel power converters (multiphase converters in
parallel) with interleaving may offer better performance [33].
In the interleaving method, the converter modules all operate
at the same switching frequency. Their switching waveforms are
displaced in phase with respect to one another by 2/Nradiansover the switching period, withNbeing the number of converters
working in parallel. The interleaved converter can benefit both
high current and high power density designs. It is ideal for dc
bus converters and merchant power applications because the
reduced input ripple current and reduced output capacitor ripple
current lessen the electrical stress on the dc capacitors [33].
Fig. 1 depicts the proposed hybrid source structure. The FC
converter combines fourphase parallel boost converters with
interleaving, and the supercapacitor converter employs four
phase parallel bidirectional converters with interleaving. These
latter two converters are in the highcurrent and lowvoltage
sections. In order to obtain a higher utility voltage level, a three
level boost converter can be used as a highvoltage section.
The use of a highvoltage section converter leads to better ef
ficiency of the global conversion structure due to the use of
MOSFET/Schottky diode technology rather than insulated gate
bipolar transistor (IGBT)/ultrafast diode technology [34].Constraints in operating the threelevel boost converter are
to regulate the input current iLoad , the dcbus output vOu t andto ensure the balance of voltages across capacitors C1 and C2 .It is beyond the scope of this paper to present the threelevel
boost converter. For more details may be found in [34]. Thus,
the following presentation will detail only with the lowvoltage
and highcurrent section.
For safety and high dynamics, the FC and supercapacitor
converters are typically controlled primarily by inner current
regulation loops. The current controls of these converters, as
illustrated in Fig. 2, are similar to the basic current control
of parallel converters. These controls can be easily realizedwith linear (PI) or nonlinear (sliding mode) current controllers
[35]. The dynamics of the current regulation loops are also
supposed to be much faster than those of the outer control loops
[36]. These current control loops are supplied by two reference
signals: the supercapacitor current reference iSCREF and the FCcurrent reference iFCREF generated by the energy managementalgorithm presented hereafter.
B. ReducedOrder Model of FC/Supercapacitor Converters
We suppose that the FC and supercapacitor currents follow
their reference values completely. Thus,
iFC = iFCREF =pFCvFC
=pFCREF
vFC(1)
iSC = iSCREF =pSCvSC
=pSCREF
vSC. (2)
A reducedorder model [37] of the studied power converters
is shown in Fig. 3. Now, the FC generator and the supercapacitor
storage device function as controlled current sources. We con
sider here that there are only static losses in these converters, and
rFC and rSC represent static losses in the FC and supercapacitor
converters, respectively.

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Fig. 1. Proposed distributed generation system supplied by fuel cell and supercapacitor, where pL o a d (= vB u s iL o a d ), vB u s , and iL o a d are the load power, thedcbus voltage, and the dcbus load current, respectively.pFC (= vFC iFC ), vFC , and iFC are the FC power, voltage, and current, respectively.pSC (= vSC iS C ),vSC , and iS C are the supercapacitor power, voltage, and current, respectively. pFC o and pS C o are the output powers to the dc link from the converters of FC andsupercapacitor, respectively.
The dcbus capacitive energy yBu s , and the supercapacitive
energy ySC can be written as follows:
yBu s =1
2CB us v
2Bu s (3)
ySC =1
2CSC v
2SC . (4)
The totalelectrostatic energy yT stored in the dcbus capacitorCB us and the supercapacitor CSC can also be written as follows:
yT =1
2CBu sv
2Bu s +
1
2CSC v
2SC . (5)
The dcbus capacitive energy yBu s is given versuspFC o ,pSC o ,and pLoad by the following differential equation:
yB us = pFC o +pSC o pLoad (6)
where
pFC o = pFC rFC
pFCvFC
2(7)
pSC o = pSC rSC
pSCvSC
2(8)
pLoad = vB us iLoad = 2yB usCBu s iLoad (9)
pSC = vSC iSC =
2ySCCSC
iSC . (10)
III. CONTROL OF A HYBRID POWER SOURCE
A. Literature Review: Control of a Hybrid Power Source
The energy management of multipower sources has been
studied recently: for example, by Feroldi et al. [38], who studied
the control (based on the efficiency map) of a FC/supercapacitor
hybrid powersource for vehicle applications; by Jiang et al. [39],
who studied the control (based on adaptive control with state
machine estimation) of a FC/battery hybrid power source; byLi and Liu [40], who studied the control (using a fuzzy power
control algorithm) of a FC/battery hybrid power source; and
by Thounthong et al., whose work concerned a regulated dcbus
voltage FC/supercapacitor hybrid source (based on a basic linear
controller operated by setting controller parameters that depend
on a defined operating point) [16], a regulated dcbus voltage
FC/battery/supercapacitor hybrid source (based on a basic linear
controller operated by setting controller parameters that depend
on a defined operating point) [18] and an unregulated dcbus
voltage FC/battery hybrid source (based on the battery state
ofcharge) [14]. Nevertheless, in these structures, there are still
some aspects about the control laws that remain open to study,

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Fig. 2. Current control loops of the proposed FC/supercapacitor converters.
Fig. 3. Reducedorder model of the studied power converters.
Fig. 4. Concept of control system based on the flatness principle, where yis the output variable, yR E F is the output set point, and u is the control inputvariable.
particularly in the area of dynamics, robustness, stability, and
efficiency.
B. Brief Theory of Differential Flatness
The theory of differential flatness consists of a parameteriza
tion of the trajectories of a system by one of its outputs y, called
the flat output, and its derivatives. Here, we consider generalnonlinear systems of the form
x = f(x,u) (11)
x = [x1 , x2 , . . . xn ]T ,x n (12)
u = [u1 , u2 , . . . um ]T ,u m (13)
where x is the state variable, u is the vector of input (control)
variables, and (n, m) N.
According to Fliess et al. [21], [41], if the state variable x can
be parameterized by outputy and its derivatives, an autonomous
dynamical system, (i.e., (11) with time removed) is said to bedifferentially flat and admits the flat output y
y = [y1 , y2 , . . . , ym ]T ; y m (14)
with
y = (x, u, u , . . . , u() ) (15)
such that the state variable and control variable can be written
as follows:
x = (y, y , . . . , y() ) (16)
u = (y, y , . . . , y(+ 1) ) (17)
where and are the finite numbers of derivative. As depictedin Fig. 4, nonlinear flat systems are equivalent to linear con
trollable systems. Therefore, a dynamical system is naturally
differentially flat if it is equivalent to a system without dynam
ics, i.e., a static system [22], [23]. The aforementioned equations
mean that there exists a quantity y that summarizes the behav
ior of the whole system via the mappings and . Clearly, theadvantage of the differential flatness approach is that the trajec
tories of the system, i.e., (x, u) are straightforwardly estimated
by the trajectories ofy and its derivatives without integrating
any differential equation [29], [42].

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C. Proposed Differential FlatnessBased Control Hybrid
Source
In the proposed system depicted in Fig. 1, there are two
voltage variables or two energy variables to be regulated.
1) The dcbus energy yB us is the most important variable.2) The supercapacitor storage energy ySC is of secondary
importance.Therefore, based on the previous literature referenced earlier,
we propose to utilize the supercapacitors, the fastest energy
source of the proposed system, to supply the energy for the dc
bus [16], [18]. Hence, the FC (as the slowest dynamic device)
functions to supply the energy to both the dcbus capacitor CBu sand the supercapacitors CSC to keep them charged.
The flat outputy = [y1 , y2 ]T , control variableu = [u1 , u2 ]
T ,
and state variable x = [x1 , x2 ]T are defined as follows:
y =
yBu s
yT
, u =
pSCREF
pFCREF
, x =
vBu s
vSC
.
(18)
From (3) and (5), the state variables x can be written as
follows:
x1 =
2y1
CBu s= 1 (y1 ) (19)
x2 =
2(y2 y1 )
CSC= 2 (y1 , y2 ) . (20)
From (6), the control variables u can be calculated from the
flat output y and its time derivatives (inverse dynamics, see
Fig. 4)
u1 = 2pSCMax11y1 +(2y1 /CBu s )iLoad pFC o
pSCMax
= 1 (y1 , y1 ) = pSCREF (21)
u2 = 2pF CMax
1
1
y2 +
(2y1 /CBu s )iLoadpF CMax
= 2 (y1 , y2 ) = pFCREF (22)
where
pSCMax =
v2SC4rSC , pF CMax =
v2FC4rFC . (23)
In this case, pSCMax and pF CMax are the limited maximumpower of the supercapacitor and FC sources, respectively.
Thus, it is apparent that x1 = 1 (y1 ), x2 = 2 (y1 , y2 ),u1 = 1 (y1 , y1 ), and u2 = 2 (y1 , y2 ) correspond with (16)and (17). Consequently, the proposed reducedorder system can
be considered as a flat system.
D. Control Law and Stability
For dcbus energy regulation, a desired reference trajectory
for the dcbus energy is represented by y1REF . A lineariz
ing feedback control law that performs exponential asymptotic
tracking of the trajectory is given by the following expres
sion [20], [27]:
(y1 y1REF )+ K11 (y1 y1REF )+ K12
(y1 y1REF )d= 0
(24)
where the set of controller parameters (K11 , K12 ) is chosen, so
that the roots of the closedloop characteristic polynomial, inthe complex variable s, is a Hurwitz polynomial
p (s) = s2 + 1 s1 + 0 . (25)
Obviously, the tracking error e1 = y1 y1REF satisfies
e1 + K11 e1 + K12 e1 = 0. (26)
The optimum choice of the design controller parameters
is obtained by matching the characteristic polynomial p(s)
to a desired characteristic polynomial, with prespecified root
locations.
We may set as the desired characteristic polynomial
p (s) = s2 + 2n s + 2n (27)
K11 = 2n (28)
K12 = 2n (29)
where and n are the desired dominant damping ratio andnatural frequency.
It is noticeable that the control system is stable for K11 ,K12 > 0 (, n > 0). However, based on the power electronicconstant switching frequency S and cascade control structure,the outer control loop (here, the dcbus energy control) must
operate at a cutoff frequency E C (the cutoff frequencyof the supercapacitor power loop) S [43]. Once the flatoutputs are stabilized, the whole system is stable because all the
variables of the system are expressed in terms of the flat outputs
via (19)(23).
The control law of the dcbus energy loop detailed earlier is
portrayed in Fig. 5. The dcbus energy control law generates
a supercapacitor power reference pSCREF . This signal is thendivided by the measured supercapacitor voltage vSC and limited to maintain the supercapacitor voltage within the interval
[minimum VSCMi n , maximum VSCMax ] by limiting the supercapacitor charging current or discharging current, as presented in
the block superC current limitation function [16]. This yields
supercapacitor current reference iSCREF .
For total energy regulation (or supercapacitor energy regulation), the desired reference trajectory for the total energy is
represented by y2REF . Because the supercapacitor has an enormous energy storage capacity, and because the supercapacitor
energy is defined as a slower dynamic variable than the dc
bus energy variable, the total energy control law is defined as
follows:
(y2 y2REF ) + K21 (y2 y2REF ) = 0. (30)
Fig. 6 depicts the total energy control loop. The total energy
control law generatesthe FC powerreferencepFCREF .Itmustberestricted to an interval with maximum pF CMax (corresponding
to a rated power of the FC) and minimum pFCMin (set to 0 W)

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Fig. 5. Control law of the dcbus energy regulation for FC/supercapacitor hybrid source.
Fig. 6. Control law of the total energy regulation (charging supercapacitor) for FC/supercapacitor hybrid source.
as well as be limited in dynamics; these limitations ensure safe
operation of the FC with respect to the constraints that are
associated with the FC (i.e., the prevention of an FC stack from
undergoing fuel starvation [7]). Here, the secondorder delay is
selected as the fuel cell power dynamic limitation.
The proposed control presents a solution of how to avoid fuel
starvation, which allows the FC system to operate at high effi
ciency. In effect, the fuel flow varies depending on the power
demand, rather than being fixed to a constant fuel flow at a maxi
mum value(the FC alwayshas sufficientfuel flow).Nonetheless,
the operating system by fixing the fuel flow to a constant fuel
flow at a maximum value has low efficiency because fuel flow
(known as the power input of this generator) is always constant
at the maximum value [7].
IV. EXPERIMENTAL VALIDATION
A. Test Bench Description
In order to authenticate the proposed control algorithm and
control laws, a smallscale test bench of the hybrid system was
implemented in our laboratory, as presented in Fig. 7. The FC
system used in this effort was a PEMFC system (1.2 kW, 46 A;
Ballard Power Systems Company), as illustrated in Fig. 8. It was
supplied using pure hydrogen of regulated pressure at 10 bars
from bottles under a pressure of 150 bars and with clean and dry
air from a compressor. The supercapacitor module (100 F, 32 V;
Maxwell Technologies Company) was obtained by means of 12
BCAP1200 cells (capacitance: 1200 F and maximum voltage:
2.7 V) connected in series, as shown in Fig. 9.
Fig. 7. Hybrid source test bench.
The FC converter (1.2 kW) and the supercapacitor converter
(4 kW) (see Fig. 1) were both realized in the laboratory. The con
verter parameters and semiconductor components are detailed
in Table I.
B. Control Description
Measurements of the FC current iFC , the supercapacitor current iSC , the load current iLoad , the dcbus voltage vBu s , the FCvoltage vFC , and the supercapacitor voltage vSC were carried
out by means of zeroflux Hall effect sensors.

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Fig. 8. Test bench of PEM fuel cell system of 1200 W, 46 A.
Fig. 9. Test bench of supercapacitor module of 100 F, 32 V.
TABLE ICONVERTER PARAMETERS AND SEMICONDUCTOR DEVICES
The FC and supercapacitor current regulation loops were
realized using analog circuits to function at a high band
width. Parameters associated with the dcbus energy regula
tion loop and the total energy regulation loop can be seen in
Tables II and III, respectively. The FC power dynamic delay
is shown in Table III. This value has been experimentally de
TABLE IIDCBUS ENERGY CONTROL LOOP PARAMETERS
TABLE IIITOTAL ENERGY CONTROL LOOP PARAMETERS
termined as having the highest power slope of our FC sys
tem, where no fuel starvation occurs. It must be noted that,
for the smalltest bench, the FC maximum power pF CMax wasset at 600 W; in fact, the rated FC power considered here is
1200 W. Moreover, these two energy control loops, which
generated current references iFCREF and iSCREF , were imple
mented in the realtime card dSPACE DS1104 using MATLABSimulink at a sampling frequency of 25 kHz.
C. Experimental Results
The experimental tests were carried out by connecting a dc
link loaded by a traction motor that was coupled with a small
inertia flywheel andfrictionload. Fig. 10 presents thewaveforms
that were obtained duringthe motor drive cycle, andshow thedc
bus voltage, the FC voltage, the load power, the supercapacitor
power, the FC power, the supercapacitor current, the FC current,
and the supercapacitor voltage [or the supercapacitor stateof
charge (SOC)].
The initial state was in noload power, and the storage devicewas fully charged, i.e., vSC = 25 V; as a result, both the FCand supercapacitor powers were zero. At t = 10 s, the tractionmotor speed accelerated to its final speed of 800 r/min; syn
chronously, the final FC power increased with a limited slope to
its limited maximum power of 600 W. Thus, the supercapacitor,
which supplies most of the power that is required during motor
acceleration, remained in a discharged state after the start of the
motor because the steadystate load power (friction load) was
greater than the FClimited maximum power.
Afterward, at t= 50 s, the motor speed decelerated to a stopwith a peak load power of about 200 W. The supercapacitor
was deeply charged, demonstrating the three phases. First, the

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Fig. 10. Hybrid source response during motor drive cycle.

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Fig. 11. Setting controllers by choosing the cutoff frequency in frequencyspace, where S is the constant switching frequency of the supercapacitorconverter of 25 kHz (157 080 rads1 ), P is the cutoff frequency of the supercapacitor power loop of 450 rads1 , and E is the cutoff frequency of theclosedloop dcbus energy.
supercapacitor recovers the energy that is supplied to the dc bus
by the FC (600 W) and the traction motor. Second, the superca
pacitor is charged only by the FC. Third, the supercapacitor isnearly fully charged, which then reduces the charging current.
After this, both the FC and supercapacitor powers reduce to zero
when vSC reaches vSCREF of 25 V.To demonstrate dynamic regulation of the dcbus energy
(voltage) at different nonlinear controller parameters (see
Fig. 11), the oscilloscope waveforms in Fig. 12 show the dc
bus voltage dynamics (representing the flat output y1 ) to the
large load power demanded (disturbance) from 0 to 600 W,
whereas the dc bus was loaded with an electronic load. The
oscilloscope screens show the dcbus voltage (the state variable
x1 , representing the flat output y1 ), the supercapacitor voltage
(the state variable x2 ), the load power, and the supercapacitorpower (the control input variable u1 ).The cutoff frequency (P ) of the supercapacitor power loop
was 450 rads1 (equivalent as a firstorder delay with a time
constant TP of 2.2 ms, determined from experimentation). Thecutoff frequency (E) of the closedloop dcbus energy mustthen be lower than the cutoff frequency (P ) of the supercapacitor power loop, so that the system is stable.
The FC power dynamics were purposely limited (see Fig. 10),
forcing the supercapacitor to supply the transient load power
demand. As depicted in Fig. 12(a), the nonlinear controller gains
used were K11 = 71 rads1 and K12 = 2500 rad2 s
2 , so that
the system damping ratio was equal to 0.707 and the natural
frequency n was equal to 50 rads1 . As a result, the cutofffrequency (E1 ) of the closedloop dcbus energy was equal to50 rads1 . As depicted in Fig. 12(b), the nonlinear controller
gains used were K11 = 141 rads1 and K12 = 10000 rad
2 s2 ,
so that the system damping ratio was equal to 0.707 and thenatural frequency n was equal to 100 rads
1 . As a result,
the cutoff frequency (E2 ) of the closedloop dcbus energywas equal to 100 rads1 . Finally, as depicted in Fig. 12(c),
the nonlinear controller gains used were K11 = 354 rads1
and K12 = 62 500 rad2 s2 , so that the system damping ratio
was equal to 0.707 and the natural frequency n was equalto 250 rads1 . As a result, the cutoff frequency (E3 ) of the
closedloop dcbus energy was equal to 250 rads1
. Although
Fig. 12. Comparison of dcbus voltage regulation (dclink stabilization) ofhybrid power plant during large load step at different controller parameters. (a) K11 = 71 rads
1 and K12 = 2500 rad2 s2 ( = 0.707; n =
50 rads1 ). (b) K11 = 141 rads1 and K12 = 10 000 rad
2 s2 ( = 0.707;n = 100 rads
1 ), (c) K11 = 354 rads1 and K12 = 62 500 rad
2 s2 ( =
0.707; n = 250 rads
1
).

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the dynamic response of the control system can be improved
relative to that shown in the figures by increasing the cutoff
frequency, this improvement comes at the outflow of reduced
boundary stability, as illustrated in Fig. 12(c), in which the
cutoff frequency (250 rads1 ) is closed to P (450 rads1 ).
As presented in Fig. 12(b), the controller parameters at the
cutoff frequency (E2 ) of 100 rads1 (E = P/4.5) show
good stability and optimum response (no oscillation and short
settling time) of the dcbus voltage regulation to its desired
reference of 60 V.
Note that there are some losses (static and dynamic losses)
in the supercapacitor converter (see Figs. 1 and 3), because
the implemented converters are hardswitching converters, then,
the power difference between the supercapacitor and the load
powers (for example, during 100 to 200 ms) can be observed.
To improve the converter efficiency, softswitching converters
may be effective solutions for future work.
The flatnessbased control is modelbased (see the inverse
dynamics detailed in Figs. 5 and 6). As a result, it may have
some sensitivity to errors in the model parameters [see (21)and (22)]. To substantiate its robustness and dynamic regulation
of the dcbus energy (or voltage), the flatnessbased control
was tested with the exact model parameters (rFC = 0.14 andrSC = 0.10 ) and for the case of lossless parameters (rFC =0.0 and rSC = 0.0 ). Comparisons (robustness) betweenthe accurate parameters and the error parameters are given in
Fig. 13. The oscilloscope generated waveforms obtained during
the large load step from 0 to around 800 W and showed the dc
bus voltage (representing the flat output y1 ), the supercapacitor
voltage, the load power (disturbance), the supercapacitor power
(the control input variable u1 ). The FC power dynamics were
intentionally limited (see Fig. 10), forcing the supercapacitor tomeet the transient load power demand. Similar waveforms are
seen in Fig. 13(a) and (b).
The dcbus voltage (dclink stabilization) is minimally influ
enced by the large step in load power. Undoubtedly, the perfor
mance of the control system is hardly affected by the error con
sidered in the model parameters. It is then possible to conclude
that the nonlinear differential flatnessbased approach provides
an absolutely robust controller in this application.
D. Performance Comparison Between Nonlinear Control
Based on Flatness and Classical Linear Control
To compare the performance of the flatnessbased control,a traditional linear control method presented in [16] was also
implemented on the hybrid test stand. A dcbus energy reference
was represented by yBusREF(=y1REF ). A linear feedback PIcontrol law is given by the following expression:
pSCREF = KP (yBusREF yBu s )+ KI
t0
(yBusREF yBu s )d
(31)
where KP and KI are the set of controller parameters.Because the supercapacitor current loop is much faster than
the dclink voltage loop [so that it can be considered as a pure
unity gain, see (6)], the openloop transfer function associated
Fig. 13. Comparison of dcbus voltage regulation (dclink stabilization) ofhybrid power plant during large load step. (a) Exact model (rFC = 0.14 andrS C = 0.10 ). (b) Error model (robustness) (rFC = 0.0 and rS C = 0.0 ).
with the dclink voltage regulation can be written as follows:
yBu s (s)
yBusREF (s)=
PI Controller KP +
KIs
EB u s /p S C1s
pS C /pSC R E F 1TPs + 1
(32)
where TP is the time constant of an equivalent firstorder delayof the supercapacitor power regulation loop (or the supercapaci
tor current regulation loop). The linear control law of the dclink
stabilization detailed earlier is portrayed in Fig. 14; it is similar
to the nonlinear control law (see Fig. 5), where the PI controller
also generates a supercapacitor power reference pSCREF . Themain difference between nonlinear control based on the flatness
property and classical linear control is that the inverse dynamic
equation, known as the flatness property (see (21) and Fig. 5),
appears in the nonlinear control.

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Fig. 14. Control law of the dcbus energy regulation based on PI control.
Fig. 15. Comparison of the flatnessbased control law with a linear PI controllaw during a large load step.
Finally, in order to give a reasonable comparison between themethods, the parameters of the linear controller KP and KIwere tuned to obtain the best possible performance. This result
was compared to the flatnessbased control. In this case, KP =252WJ1 and KI = 42000W(Js)
1 , so that the desired phase
margin was 30. IfKP = 124 WJ1 and KI = 3968 W(Js)
1 ,
the desired phase margin (PM) was 60. Fig. 15 shows exper
imental results obtained for both controllers during the large
load step. The flatnessbased control shows good stability and
optimum response of the dcbus voltage regulation to its desired
reference of 60 V. Although dynamic response of the linear con
trol law could be improved relative to that shown in the figures,
this enhancement comes at the expense of a reduced stabilitymargin. From these results, we conclude that flatnessbased con
trol provides better performance than the classical PI controller.
V. CONCLUSION
A new control approach for a distributed dc generation system
supplied by a hybrid source that uses supercapacitors as a fast
auxiliary source, in association with a PEMFC as the main
source, has been proposed. The reducedorder model of the
FC/supercapacitor power plant is flat. A trajectory planning
algorithm that allows for energy (voltage) regulation in finite
time has also been presented. Theoretically, the flatnessbased
control shows better performance than a classical controller (PI
or PID controllers) for transitions between equilibrium points,
particularly in a nonlinear system.
Experimental results with a smallscale hybrid test bench
in the laboratory have authenticated the excellent closedloop
performance of this system. The robustness of the proposed
control was demonstrated by test bench results.
ACKNOWLEDGMENT
The authors would like to thank S. Lekapat, who is incharge
of the process of the FrancoThai on Higher Education and
Research Joint Project year: 20092010.
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Phatiphat Thounthong (M09) received the B.S.and M.E. degrees in electrical engineering from KingMongkuts Institute of Technology North Bangkok(KMITNB), Bangkok, Thailand, in 1996 and 2001,respectively, and the Ph.D. degree in electrical engineering from the Institut National Polytechnique deLorraine (INPL), Nancy Universite, NancyLorraine,France, in 2005.
From 1997 to 1998, he was an Electrical Engineerwith the E.R. Metal Works Ltd. (EKARAT Group),Thailand. From 1998 to 2002, he was an Assistant
Lecturer with KMITNB. Since 2008, he has been an Assistant Professor and theDirector of the Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkuts University of Technology NorthBangkok (KMUTNB), Bangkok, Thailand, where he is also the Head of the Renewable Energy Research Laboratory (sponsored by KMUTNB and the FrenchEmbassy in Bangkok). He is also an Invited Assistant Professor at INPL. He isthe author or coauthor of more than 50 journal and conference papers, as wellas a book entitled Fuel Cell Energy Source for Electric Vehicle Applications(New York: Nova Science, 2008). He has also contributed for Recent Advancesin Supercapacitors (Kerala: Transworld Research Network, 2006), Progress inFuel Cell Research (New York: Nova Science, 2007), and Polymer Electrolyte
Membrane Fuel Cells and Electrocatalysts (New York: Nova Science, 2009).His current research interests include power electronics, electric drives, andelectrical devices (fuel cells, batteries, and supercapacitors).
Serge Pierfederici received the Engineer degreein electrical engineering from Ecole NationaleSuperieure en Electricite e t Mecanique, NancyLorraine, France, in 1994, and the Ph.D. degreein electrical engineering and the Habilitation aDiriger des Recherches (HDR) degree from the Institut National Polytechnique de Lorraine (INPL),Nancy Universite, NancyLorraine, in 1998and 2007,respectively.
Since 1999, he has been an Associate Professorat INPL. His current research interests include power
electronics, stability study of distributed power system, and the control of multisources and multiload systems.
Bernard Davat (M89) received the Engineer degree in electrical engineering fromEcole Nationale Superieure dElectrotechnique,dElectronique,dInformatique, dHydrauliqueet desTelecommunications, Toulouse, France, in 1975, andthe Ph.D. and Docteur dEtat degrees in electrical engineering from Institut National Polytechniquede Toulouse (INPT), Toulouse, in 1978 and 1984,respectively.
From 1980 to 1988, he wasa Researcher at FrenchNational Center for Scientific Research, Laboratoire
dElectrotechnique et dElectronique Industrielle. Since 1988, he has been aProfessor at Institut National Polytechnique de Lorraine, Nancy Universite,NancyLorraine, France. His current research interests include power electronics, drives, and new electrical devices (fuel cell and supercapacitor).