Multivariable Robust Control of a Proton Exchange Membrane Fuel Cell System

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fuel cell system

Fu-Cheng Wang

∗

, Hsuan-Tsung Chen, Yee-Pien Yang, Jia-Yush Yen

Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan

Received 10 September 2007; received in revised form 15 November 2007; accepted 15 November 2007 Available online 23 November 2007

Abstract

This paper applies multivariable robust control strategies to a proton exchange membrane fuel cell (PEMFC) system. From the system point of view, a PEMFC can be modeled as a two-input-two-output system, where the inputs are air and hydrogen flow rates and the outputs are cell voltage and current. By fixing the output resistance, we aimed to control the cell voltage output by regulating the air and hydrogen flow rates. Due to the nonlinear characteristics of this system, multivariable robust controllers were designed to provide robust performance and to reduce the hydrogen consumption of this system. The study was carried out in three parts. Firstly, the PEMFC system was modeled as multivariable transfer function matrices using identification techniques, with the un-modeled dynamics treated as system uncertainties and disturbances. Secondly, robust control algorithms were utilized to design multivariable H_∞controllers to deal with system uncertainty and performance requirements. Finally, the designed robust controllers were implemented to control the air and hydrogen flow rates. From the experimental results, multivariable robust control is shown to provide steady output responses and significantly reduce hydrogen consumption.

Keywords: Proton exchange membrane fuel cell; Multivariable control; Robust control; System identification

1. Introduction

In recent years, alternative energy resources have gained more and more attention due to the greenhouse effect and the decreas-ing levels of fossil fuel. Among them, the proton exchange membrane fuel cell (PEMFC) is an important candidate for replacing traditional fuel because of its favorable characteris-tics, including low operation temperature, fast power response, high power density, low noise pollution, high system efficiency and environmental friendliness. Until recently, PEMFC has been applied to many systems such as vehicles, boats, etc.[1,2]. For most of the applications, batteries and dc/dc converters were uti-lized to provide steady output voltages. However, the use of those peripheral components can decrease the efficiency of the fuel cell system. On the other hand, traditional control methodolo-gies such as process control were frequently applied to PEMFC.

∗_{Corresponding author. Tel.: +886 2 33662680; fax: +886 2 23631755.}

E-mail addresses:[email protected](F.-C. Wang),[email protected] (H.-T. Chen),[email protected](Y.-P. Yang),[email protected] (J.-Y. Yen).

Nevertheless, these control methods cannot provide good sys-tem performance and may cause instability due to the nonlinear characteristics of the fuel cell system. Therefore, in this paper we consider the closed-loop structures of the PEMFC system, and apply robust control strategies to improve system stability and performance.

Forrai et al. [3] applied system identification methods to model a PEMFC system as a circuit consisting of inner resis-tors and a capacitor. Kazim and Lund [4] performed a basic parametric study of a PEMFC system, and showed that the sys-tem performance can be improved at lower cell sys-temperature and higher cell pressure with a higher air stoichiometric ratio. Wang et al.[5]discussed a distributed generation system and designed a controller to maintain the power delivered from the fuel cell system to the utility grid. The simulation results showed that the designed proportional-integral (PI) controller could maintain system stability even with some system faults. Woo and Benziger

[6]designed a proportional-integral-derivative (PID) controller to regulate the hydrogen flow rate and tuned the oxygen flow at a ratio of 1.3:2 (O2:H2) to obtain optimal performance.

Vega-Leal et al. [7] developed a multi-input–single-output (MISO) system to control the output current. They designed a

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forward controller to adjust the airflow rate, and a proportional controller to regulate temperature so that the net power is opti-mized. Methekar et al.[8]considered a multi-input-multi-output (MIMO) system with inputs of hydrogen and coolant and out-puts of power density and temperature, and proposed two PID control strategies. The simulation results showed that the ratio control strategy achieved a faster response than the MIMO con-trol strategy. Rodatz et al.[9]illustrated a dynamic model of air supply for a PEMFC system. They designed a linear-quadratic-Gaussian (LQG) controller to decouple the pressure trace from the mass flow trace, which provided better performance than PI control. Di Domenico et al.[10]extended this idea to create a multi-variable LQG controller, designed to tune the excess air ratio while tracking the optimal pressurization to maximize sys-tem efficiency for transient loads. Sedghisigarchi and Feliachi

[11]designed an H_∞controller to regulate the cell voltage under small load variations. From the simulations, the output voltage offset was kept below 5% by controlling the hydrogen flow rate. Many studies have utilized hybrid systems to improve overall system performance. In those systems, fuel cell was regarded as the main power source, which was combined with other auxil-iary power sources to provide steady output power. Thounthong et al.[12]integrated a fuel cell and super-capacitors for electric vehicles. They aimed to control the transient power through PID control of the super-capacitors, while the fuel cell operated at a steady rate. Lee et al.[13]designed a hybrid system for a vehi-cle equipped with a fuel cell and a battery. The system power was supplied by the fuel cell at low loadings and by the battery at high loadings when the output voltage of fuel cell stack was too low. Jurado and Saenz[14]developed an adaptive controller for a fuel-cell micro-turbine hybrid power plant. Taking into account the system variation and disturbances, they found that the controller, designed at a fixed operating point, could stabi-lize the system under different operating conditions. For some applications, the dc/dc converters were designed to increase sys-tem efficiency. Wai et al. [15]employed the voltage-clamped and soft-switching techniques to design a dc/dc converter. The experimental results illustrated that the converter can achieve more than 95% efficiency for a 250 W PEMFC system. Zenith and Skogestad[16]utilized sliding mode control to adjust the duty cycle of a rapid dc/dc converter to control the output volt-age. Jiang et al.[17]developed a system consisting of a fuel cell, a battery and a dc/dc converter. By adjusting the duty cycle of the converter, they found that the battery could be charged by the fuel cell through either the maximum power strategy or the maximum efficiency strategy.

Because a steady power source is important for electrical equipment, in this paper robust control methodologies are uti-lized to guarantee a steady voltage or current supply when the operating conditions change. Robust control is well known for its capability in dealing with system uncertainties and distur-bances[18–20]. Wang et al.[21–23] applied robust control to a single-input-single-output (SISO) PEMFC system to achieve steady voltage output by regulating the oxygen flow rate. The experimental results illustrated that robust controllers can cope with system perturbations and achieve splendid performance. Furthermore, the robust control can also replace the dc/dc

con-verter and broaden the applications. This paper extends H_∞ control strategies to a multi-input fuel-cell system, where the proposed multivariable robust controllers can provide steady voltage and reduce hydrogen consumption by regulating the air and the hydrogen flow rates simultaneously. The experimen-tal results show that the designed MISO robust controllers are better than the SISO controller in terms of hydrogen consump-tion and energy dissipaconsump-tion. This paper is arranged as follows: in Section2, fuel-cell dynamics is described and modeled as a MIMO system. The Pulse Width Modulation (PWM) theory is also introduced and applied to control the hydrogen valve. In Section3, we utilize robust control strategies to design multi-variable H_∞controllers. In Section4, the designed controllers are implemented to verify their performance. Finally, we draw some conclusions in Section5.

2. Materials and methods

In this section, fuel cell dynamics is described and modeled as a MIMO system using identification techniques. Those system matrices will then be used for the controller designs in Section

3.

2.1. System description

The fuel-cell system considered in this paper was designed and manufactured by Chung Shan Institute of Science and Tech-nology (CSIST) and integrated by DELTA ElectronicsTM. The inputs of the system are hydrogen and air while the outputs are cell voltage and current. The system consists of 15 cells with an active area of 50 cm2on each. The maximum efficiency of the fuel cell stack is 37% (Lower Heating Value, LHV) under dry H2/air and humidification-free conditions[22].

The dynamics of the fuel-cell system is non-linear and time-varying in that it is influenced by many factors, including the diffusion dynamic, the Nernst equation, proton concentration dynamics and cathode kinetics as follows:

diffusion equation : Rohm= Rref+ αT(T − Tref), (1)

Nernst equation : E = Eref+

dE. dT (T − Tref) +kRT 2F ln(PH2P 1/2 O2 ), (2)

proton concentration dynamics :

u _−∂C H+ ∂t _∂C H+ ∂t + CH+ τH+ = 1+ αH+j3 τH+ , (3) cathodic kinetics : η = b ln p10[H+]0 p1[H+] 1+ jr j0Ar , (4) as shown inFig. 1 [24].

From the system point of view, the physics-based model of

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Fig. 1. Dynamics of the PEMFC system[24].

Fig. 2. The block diagram of the fuel cell system[22].

Fig. 2, with the following relation[25]:

Icell= T1(s)Nair+ T3(s)NH2, (5)

Vcell= T2(s)Nair+ T4(s)NH2− RIcell, (6)

in which T1(s)∼ T4(s) represent the transfer functions of the

sys-tem. It is noted that the dynamics of the linearized model of(5)

and(6)depends on the operating conditions. For example, when the current load varies from 2 to 6 A, the output voltage decreases significantly from 11 to 7.5 V using the on-board controller, as illustrated in Fig. 3. Therefore, robust control algorithms are applied to achieve steady outputs even when the operating con-ditions change. By fixing the output resistance, we can either control the cell voltage or current output by regulating the air (Nair) and the hydrogen (NH2) flow rates. Since most electrical

equipment requires constant voltage supply, in this paper we aim to control the cell voltage output.

2.2. System identiﬁcation

In order to describe the transfer functions of(5)and(6), we measured the input and output signals of the fuel-cell system,

Fig. 3. Voltage variations when the current loading is changed.

Fig. 4. The MISO PEMFC system for system identifications.

and utilized subspace system identification methods to estimate the models in state-space form, as presented in the following:

xt+1= Axt+ But+ νt

yt = Cxt+ Dut+ υt , (7)

in whichu_t∈ Rmandy_t∈ Rl are the input and output signals, whilext∈ Rnrepresents the state andνt∈ Rn, υt∈ Rl are zero mean white Gaussian noise vector sequences. By applying the numerical algorithms for subspace state space system identi-fication (N4SID), the linear model of (7) can be derived by the low-rank approximation of a matrix obtained from a set of component-wise least squares support vector machines regres-sion problems[26].

For the experiments, a chirp signal and a pseudorandom, binary signal (PRBS) were generated to control the air pump and the hydrogen valve of the PEMFC system, respectively, as shown in Fig. 4. Both the frequencies of the chirp signal and PRBS were set at 0.01–5 Hz (see Fig. 5(a)). We set the current loadings as 2 A, 3 A and 4 A, and measured the out-put voltage responses, as illustrated in Fig. 5(b). In order to

Table 1

Transfer functions at the operation points

2 A 3 A 4 A 1 G11= _{0.00202z−0.001598} z2_{−1.954z+0.9555} 0.000505z−0.0003996_z2_{−1.954z+0.9555} G21= _{0.001935z−0.00153} z2_{−1.971z+0.973} 0.0004837z−0.0003824_z2_{−1.971z+0.973} G31= _{0.001603z−0.001052} z2_{−1.934z+0.9373} 0.0004z−0.0002629_z2_{−1.934z+0.9373} 2 G12= _{0.00156z−0.001158} z2_{−1.976z+0.9771} 0.0003901z−0.0002896_z2_{−1.976z+0.9771} G22= _{0.001919z−0.001483} z2_{−1.974z+0.9753} 0.0004798z−0.0003708_z2_{−1.974z+0.9753} G32= _{0.001774z−0.001231} z2_{−1.932z+0.9354} 0.0004435z−0.0003077_z2_{−1.932z+0.9354} 3 G13= _{0.0006934z−0.000162} z2_{−1.942z+0.9457} 0.0001733z−0.0000405_z2_{−1.942z+0.9457} G23= _{0.00154z−0.000985} z2_{−1.948z+0.95} 0.0003851z−0.0002462_z2_{−1.948z+0.95} G33= _{0.001483z−0.0009106} z2_{−1.918z+0.9208} 0.0003707z−0.0002277_z2_{−1.918z+0.9208}

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Fig. 5. The input and output signals of the system (with 3 A load): (a) the input signals and (b) the output voltage responses.

take system variation into account, we repeated the experi-ments three times at each operating condition, and employed the aforementioned identification techniques to obtain the cor-responding transfer functions illustrated in Table 1. Those transfer functions will be utilized for robust controller design in Section3.

2.3. Pulse Width Modulation theory

To control the hydrogen valve, the PWM theory is employed. In recent years, the combination of PWM and fast-switch valves has been widely applied in many control fields, such as position control of pneumatic actuators[27]. PWM is a modulation

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Fig. 7. Illustration of Small Gain Theorem.

nique which utilizes a carry function to generate variable-width pulses in order to represent the amplitude of an input signal. As illustrated inFig. 6, given the input signal and carry function, a comparator is utilized to compare the magnitudes of these two signals to generate the modulated signal. When the input signal is greater than the carry signal, the modulated signal is set to be “high”. Otherwise, it is set to be “low”. InFig. 6(b), the period of the modulated signal is the same as the period of the carry signal, Tc. Furthermore, the duty ratioτ of the modulated signal

is defined as

τ = Ton

Tc , (8)

in which Ton is the operating time. In applying PWM to

con-trol the hydrogen valve of the fuel-cell system, more hydrogen is supplied whenτ is increased. In general, the frequency and amplitude of the carry signal must be higher than those of the input signals. To control hydrogen flow, we employed a 2/2-way MAC 35A-AAA-DAA-1BA valve with a switch frequency of about 1 kHz and a maximum power consumption of 5.4 W[28]. For the experiments, we utilized a chirp signal from 0.01–5 Hz, and a carry function with a frequency of 10 Hz and maximum amplitude of 1 V. Using the comparator, a PRBS signal, such as

Fig. 5(a), was generated to control the hydrogen valve.

3. Theory and calculation

In this section, the robust control algorithms are introduced, and applied to design H_∞controllers to provide the maximum stability bound for the fuel cell system. The resulting controllers are then implemented with PWM to verify the effect by experi-mentation in Section4.

Theorem 1 (Small Gain Theorem [20]). Suppose M∈ RH_∞

and letγ > 0, then the interconnected system shown inFig. 7,

whereωi represent the input signals and ei the error signals,

is well posed and internally stable for all(s) ∈ RH_∞with (a)

∞≤ 1/γ if and only if M(s)∞≤ γ; (b) ∞< 1/γ if and

only ifM(s)_∞<γ, where G_∞is the∞ norm of system G.

Suppose that a nominal plant G0 can be expressed as

G0= M−1N, where (1) M, N∈ RH∞ and (2) MM*+ NN*= I,

∀ω. This is called a normalised left coprime factorisation of

G0. Furthermore, suppose that a perturbed system G can be

Fig. 8. Feedback structure of the perturbed plant Gwith a controller K.

expressed as

G = (M + M)−1(N + _N), (9) with [M,N]∞<ε, M, N∈ RH∞. Considering a

con-troller K with the block structure of Fig. 8 where zi and ω

are corresponding input and output signals of the systems, the system transfer functions can be simplified as follows:

z1 z2 = K I (I − GK)−1M−1ω = K I (I − GK)−1[I G]ω, (10)

as shown inFig. 9. Therefore, fromTheorem 1, the closed-loop system remains internally stable for all[M,N]∞<ε if and

only if K I (I − G K)−1[I G] ∞ ≤ 1_ε. (11)

Thus we can define the stability margin of the system in following:

Deﬁnition 1 (Stability Margin[29]). The stability margin b(G, K) of the closed-loop system is defined as follows:

b(G, K) ≡ K I (I − GK)−1[I G] −1 ∞ . (12)

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Hence, from Theorem 1 the closed-loop system is internally stable for all[M,N]∞<ε if and only if b(G, K) ≥ ε.

It is further noted that the coprime factorisation of a system is not unique. That is, there is more than one expression for G0

or G. Therefore, the gap between two systems G0and Gcan

be defined as

Deﬁnition 2 (Gap Metric [20]). The smallest value of

[M,N]∞ which perturbs G0 into G, is called the gap

between G0and G, and is denoted asδ(G0, G).

3.1. Selection of the nominal plant

From the definitions, b(G, K) gives the radius (in terms of gap metric) of the largest ball of plants stabilized by the controller K. Therefore, the goal of the controller design is to derive a suitable controller K from a nominal plant G0, such that all perturbed

plants Gi located inside the gapδ(G0, Gi) <ε will satisfy b(G,

K)≥ ε and the closed-loop system will remain internally stable.

The selection of the nominal plants G0(s) was based on the

calculation of gaps between the nominal plants and the perturbed plants, such that the maximum gap is minimized as

min

G0

max

Gi δ(G0, Gi). (13)

Considering the system transfer function matrices inTable 1, the gaps between all plants are illustrated inTable 2. Therefore,

G23 was selected as the nominal plant because the maximum

gap between G23and other plants is 0.2449, which is the

mini-mum of all systems. The maximini-mum gap can be regarded as the maximum perturbation of the system due to the changes of oper-ating conditions, such as temperature, humidification and power loads.

3.2. Robust controller synthesis

The design procedures of the robust controller are illustrated as follows[30]:

(1) Loop shaping design: as shown inFig. 10(a), the nominal plant G is shaped by a pre-compensator W1 and a

post-Fig. 10. The design procedures of robust controllers.

compensator W2to form a shaped plant Gs= W2GW1.

(2) Robust stabilization estimate: the maximum stability margin

bmaxis defined as follows:

bmax(Gs, K) inf K stablizing K I (I−G_sK)−1[I G_s] −1 ∞ , (14) where Ms, Ns are the normalized left coprime

factor-ization of Gs, i.e. such that G_s= M_s−1N_s. If bmax(Gs,

K) 1, then we must return to step (1) and modify W1 and W2. Finally, we can select an ε ≤ bmax(Gs, K)

and synthesize a stabilizing controller K∞, which

satis-fies K∞ I (I − G_sK_∞)−1[I G_s] −1 ∞ ≥ ε, as shown in Fig. 10(b).

(3) The designed controller K_∞is then multiplied by the weight functions, such that K = W1K_∞W2is implemented to control

the system G, as illustrated inFig. 10(c).

Table 2

Gaps of the plants

G11 G12 G13 G21 G22 G23 G31 G32 G33 G11 0 0.2127 0.1346 0.1278 0.3054 0.0751 0.078 0.0966 0.0956 G12 0.2127 0 0.3395 0.2098 0.2137 0.1649 0.2858 0.3034 0.3044 G13 0.1346 0.3395 0 0.2068 0.4254 0.1932 0.0585 0.039 0.0488 G21 0.1278 0.2098 0.2068 0 0.3522 0.1327 0.161 0.1785 0.1922 G22 0.3054 0.2137 0.4254 0.3522 0 0.2449 0.3736 0.3902 0.3844 G23 0.0751 0.1649 0.1932 0.1327 0.2449 0 0.1366 0.1551 0.1522 G31 0.078 0.2858 0.0585 0.161 0.3736 0.1366 0 0.0195 0.0341 G32 0.0966 0.3034 0.039 0.1785 0.3902 0.1551 0.0195 0 0.0263 G33 0.0956 0.3044 0.0488 0.1922 0.3844 0.1522 0.0341 0.0263 0 Max 0.3054 0.3395 0.4254 0.3522 0.4254 0.2449 0.3736 0.3902 0.3844

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Fig. 11. The control structure in Matlab/Simulink.

For the first design, we employed G23(z):

G23(z)= 0.00154z−0.000985 z2_{−1.948z+0.95} 0.0003851z−0.0002462 z2_{− 1.948z+0.95} , (15)

and a constant weighting function:

W1(z) = 3 0 0 3 . (16)

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The optimal (in terms of the stability bound) H_∞controller K23(z) was designed as K23(z) = ⎡ ⎢ ⎣ −0.5769z + 0.5586 z − 0.9183 −0.1442z + 0.1397 z − 0.9183 ⎤ ⎥ ⎦ , (17)

which gives a stability bound of b(G23W1, K23) = 0.8595. The

stability bound is much larger than the maximal gap (0.2449) of the systems. Therefore, the controller can easily stabilize the sys-tem even with plant perturbations. Implemented with W1K23(z),

the experimental results showed a significant steady-state error in the voltage output. This is because the current design empha-sized on stability rather than performance. Therefore, to improve system performance, we need to add integrals in the weighting functions to eliminate the steady-state error[31,chapter 9].

For the second design, the following weighting function

W1(z) = ⎡ ⎢ ⎣ z − 0.99 z − 1 0 0 0.006 z − 1 ⎤ ⎥ ⎦ , (18)

was utilized to eliminate the steady-state errors of the output responses. Following the procedures, a H_∞ robust controller

was designed as K23 (z) = ⎡ ⎢ ⎢ ⎣ −0.8446z2_{+ 1.647z − 0.804} z2_{− 1.941z + 0.9422} −0.08869z2_{+ 0.1728z − 0.08427} z2_{− 1.941z + 0.9422} ⎤ ⎥ ⎥ ⎦ , (19) with a stability bound of b(G23W1, K23 )= 0.7622, which is

still greater than the maximum gap (0.2449) of the systems, but less than the previous design (0.8595). However, the inte-gral inW₁(z) guaranteed a zero steady-state error in the output responses. Therefore, the choice of weighting functions can be regarded as a compromise between system performance and sta-bility, such that the designed controllerK₂₃ (z) can achieve robust performance for the fuel cell system.

4. Results and discussion

In order to implement the controllers, MatlabTM was employed with a data-acquisition (DAQ) card to control the PEMFC system. The control structure in Matlab/Simulink is illustrated inFig. 11.

Implemented with W1K23(z) and the voltage command set at

9.5 V, the output voltage responses are shown inFig. 12. Firstly, the voltage output was about 6.6 V with some perturbation when the water was purged. Secondly, it is as expected that the sys-tem achieved excellent stability but poor performance, with a root-mean-square (RMS) error of about 2.8 V. Furthermore, we

Fig. 13. The comparison of voltage responses and control signals using the SISO and MISO controllers: (a) 2 A load, (b) 3 A load, (c) 4 A load and (d) 2 A→ 3 A → 4 A load.

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Fig. 14. The voltage responses and control signals, with settings of 7 V→ 8 V → 9 V → 8 V → 7 V: (a) 3 A load, (b) 4 A load, (c) 5 A load and (d) 6 A load.

note that for the SISO system[22], the hydrogen consumption was set as 1.2 liter-per-minute (LPM) in order to achieve sys-tem stability and performance. Using the proposed multivariable controller, the hydrogen consumption can be reduced to about 0.6 LPM.

To eliminate the steady-state error,W₁K₂₃(z) was designed and implemented. The experimental results are shown in

Figs. 13 and 14. InFig. 13, we set the output voltage at 9.5 V, with the fixed current settings 2 A, 3 A and 4 A in (a), (b) and (c), respectively, and a varied current loading of 2 A→ 3 A → 4 A in (d). The corresponding output voltage and hydrogen consump-tion are compared with the SISO study in Ref.[22]. First of all, the MISO and SISO robust controllers achieved similar voltage responses. On the other hand, the hydrogen consumption was

significantly reduced by the multivariable robust controller. For quantitative comparison, Table 3illustrates the RMS error of the output voltage and the average duty ratio of the hydrogen valve calculated fromFig. 13. It is noted that the hydrogen con-sumption was reduced to about 20–30%, as compared to the SISO controller (seeAppendix Afor experimental verification). That is, the hydrogen consumption was regulated according to the current loads to avoid waste of fuel. To conclude, the designed controller has not only achieved robust performance for the closed-loop system, but also exhibits reduced hydrogen consumption.

In Fig. 14, we set the voltage command as 7 V→ 8 V → 9 V → 8 V → 7 V, with current loads of 3 A, 4 A, 5 A and 6 A, respectively. Firstly, the controller

demon-Table 3

Statistic data fromFig. 13

2 A (a) 3 A (b) 4 A (c) 2 A→ 3 A → 4 A (d)

20 s→ 300 s 20 s→ 300 s 20 s→ 300 s 20 s→ 100 s 100 s→ 200 s 200 s→ 300 s MISO

RMS error 0.0504 0.0366 0.0365 0.0142 0.0361 0.0371

Average air pump voltage (V) 2.5953 3.1921 3.7702 2.3692 3.1905 3.7959

Average hydrogen flow rate (LPM) 0.24 0.294 0.36 0.237 0.3046 0.3556

SISO

RMS error 0.023 0.038 0.033 0.029 0.063 0.049

Average air pump voltage (V) 2.06 3.425 3.2 2.33 2.74 3.78

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Table 4

Statistic data fromFig. 14(with settings of 7 V→ 8 V → 9 V → 8 V → 7 V)

7 V 8 V 9 V 8 V 7 V 20 s→ 100 s 100 s→ 200 s 200 s→ 300 s 300 s→ 400 s 400 s→ 500 s RMS error 3 A 0.0144 0.0501 0.0533 0.0894 0.0818 4 A 0.0177 0.0506 0.0494 0.0924 0.0772 5 A 0.0146 0.0489 0.0658 0.116 0.0683 6 A 0.0227 0.0507 0.0772 0.1024 0.0641

Average air pump voltage (V)

3 A 2.5403 2.7581 3.0499 2.5599 2.2531

4 A 2.8444 2.9217 3.3226 2.9188 2.6826

5 A 3.1441 3.2974 4.9313 3.222 3.0157

6 A 3.4375 3.8177 5.6203 3.7858 3.6014

Average hydrogen flow rate (LPM)

3 A 0.237 0.2376 0.2424 0.2376 0.2376

4 A 0.237 0.2376 0.3091 0.2381 0.2376

5 A 0.237 0.3517 0.4564 0.311 0.2376

6 A 0.3556 0.3564 0.4716 0.3574 0.3558

Fig. 15. Dissipated power of the hydrogen valve. (a) Valve current measurement and (b) valve power measurement.

strated excellent tracking ability with the voltage command. Furthermore, the statistic data fromFig. 14is shown inTable 4, where the hydrogen consumption was significantly reduced from 1.2 LPM to about 0.24–0.47 LPM. And more hydrogen was supplied to the system when the power load was increased.

5. Conclusion

In this paper, multivariable robust controllers have been designed and implemented on a PEMFC system. At first, the dynamics of the PEMFC was described and modeled as a MIMO system. By fixing the output resistance, we have succeeded in controlling the output voltage by

regu-Table 5

Integrated flow with various duty ratios

Duty ratio (%) Liter

20 8 30 11 40 14 50 18 60 23 70 27 80 32 90 36

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lating the hydrogen and airflow rates through the designed controllers. The experimental results showed that using a suit-able weighting function, the proposed multivarisuit-able robust controller not only achieved robust performance, but also sig-nificantly reduced the hydrogen consumption of the PEMFC system.

Acknowledgments

The authors would like to thank Delta ElectronicsTM and CSIST for providing the portable PEMFC system studied in this paper.

Appendix A

A couple of experiments were designed to verify the reduc-tion of hydrogen consumpreduc-tion and energy dissipareduc-tion. For the first experiment, we aimed to show that hydrogen consumption could be evaluated by the duty ratio of the PWM signal. Setting the inlet flow rate to 8 LPM with duration of 5 min, we applied control signals with various duty ratios to the hydrogen valve and measured the flow rates with a digital flow meter SMC-PF2A710

[32]. The results inTable 5illustrated that the hydrogen con-sumption can be evaluated by the duty ratio of the PWM signal. Furthermore, we applied the measured hydrogen control signals inFig. 13to control the hydrogen valve. Given the inlet flow of 8 LPM, the expected flow was calculated and compared with the measured flow, as shown inTable 6. The results showed that the consumed gas flow was as expected, with little difference because the flow meter can only give integer readings.

For the second experiment, we verified that the energy dis-sipation of the hydrogen valve is reduced by the proposed multivariable robust controller. Using a current sensor (Hall sen-sor), we measured the operating current and power consumption of the hydrogen valve as shown inFig. 15. It is illustrated that the energy dissipation of the MISO system is less than the SISO sys-tem (where the valve was fully open and hydrogen was supplied in a constant rate). From the above experiments, the proposed multivariable robust controller can really reduce both hydrogen consumption and energy dissipation.

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