Hydrogen circulation system model predictive control for polymer electrolyte membrane fuel cell-based electric vehicle application

international journal of hydrogen energy xxx (xxxx) xxx

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Hydrogen circulation system model predictive control for polymer electrolyte membrane fuel cellbased electric vehicle application Hongwen He a, Shengwei Quan a, Ya-Xiong Wang a,b,* a b

National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350108, China

highlights
A switched MPC strategy is proposed to regulate hydrogen circulating of the PEMFC.
A control-oriented model of the hydrogen circulation system of PEMFC is formulated.
The switched MPC strategy is designed based on piecewise linearized models.
The performance of the proposed MPC is verified via typical operating conditions.

article info

abstract

Article history:

Polymer electrolyte membrane fuel cell (PEMFC) is one of the promising solutions over-

Received 19 September 2019

coming future energy crisis and environment pollution in the automotive industry. How-

Received in revised form

ever, PEMFC is vulnerable to the circulation of hydrogen mass flow rate and pressure,

21 November 2019

which may cause the degradation of the PEMFC's anode components and reduction of

Accepted 12 December 2019

output performance over time. Thus, the control of the hydrogen supply system draws

Available online xxx

attention currently and is critical for the durability and stability of the PEMFC system. In this study, a model predictive control (MPC) approach for hydrogen circulation system is

Keywords:

developed to regulate the hydrogen flow circulating. A model of the hydrogen supply

Polymer electrolyte membrane fuel

system that contains a flow control valve, a supply manifold, a return manifold and a

cell (PEMFC)

hydrogen circulating pump is firstly developed to describe the behavior of the hydrogen

Hydrogen circulation system

mass flow dynamics in the PEMFC. Subsequently, a hydrogen circulating pump MPC

Switched model predictive control

scheme is designed based on the piecewise linearized model of hydrogen circulation as

(MPC) scheme

well as the switched MPC controllers. By predicting the pressure of the return manifold and

Fuel cell electric vehicles

the angle velocity of the pump, the proposed MPC approach can manipulate the hydrogen circulating pump to achieve efficient and stable operation of the PEMFC. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

* Corresponding author. National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing 100081, China. E-mail addresses: [email protected], [email protected] (Y.-X. Wang). https://doi.org/10.1016/j.ijhydene.2019.12.147 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: He H et al., Hydrogen circulation system model predictive control for polymer electrolyte membrane fuel cellbased electric vehicle application, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.147

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Introduction Energy shortage, air pollution, greenhouse effect and other environmental problems have affected every country in the world. Guaranteeing the sustainable development of human society has become one of the major issues. A variety of new energy vehicles have emerged, and these changes in the field of automotive industry are in line with the trend of sustainable development. Many high performance energy system technologies have prospect in electric vehicles, such as high energy density Lithium-selenium batteries, eco-friendly rechargeable metal batteries and hydrogen fuel cells [1e3]. Fuel cell electric vehicles, with the pollution-free and high efficiency, have attracted attention of many countries and been an important direction for the development of new energy vehicles [4,5]. Among many types of fuel cells and other potential batteries, polymer electrolyte membrane fuel cell (PEMFC) generates electricity by electrochemical reaction between oxygen and hydrogen, with the advantages of great commercial prospects, high energy conversion efficiency, good start-up performance, and low temperature, which is generally considered as the most potential candidate for fuel cell electric vehicle application [6e9]. Hydrogen is normally supplied from a high-pressure hydrogen tank and incompletely consumed in the anode of PEMFC. There is still a part of hydrogen that has not been reacted in time and is drained, which results in hydrogen waste degrading the efficiency of the system. To improve the utilization efficiency of hydrogen in PEMFC, the unreacted hydrogen recycling is necessary. Hydrogen circulating pump is widely used to circulate the hydrogen from the anode and re-import it into the gas supply manifold in front of the anode of PEMFC [10,11]. Anode hydrogen supply system is an important component of the fuel cell, which regulates the hydrogen mass flow rate and pressure of anode to ensure the efficient and stable operation of the fuel cell. During the fuel cell electric vehicle driving process, the demand of hydrogen mass flow rate under different working conditions is also different. Excessive or insufficient hydrogen supply leads to changes in the output efficiency and capacity of the PEMFC, which may seriously result in a rapid decrease in remaining useful lifetime of the PEMFC [12,13]. Due to the influence of anode gas pressure and inlet mass flow rate on the output characteristics of the PEMFC, it is necessary to control the anode hydrogen supply system to meet the complex energy requirements of fuel cell electric vehicles. Many researchers have proposed many different kinds of PEMFC anode supply system model and various hydrogen supply strategies to regulate the key parameters such as pressure and hydrogen excess ratio. Ye et al. [14] developed a Mamdani fuzzy controller to regulate the anode hydrogen pressure of a hydrogen/ejector assembly. He et al. [15] proposed an anode hydrogen supply system with hydrogen circulating pump and ejector in parallel, and designed a state feedback control and PI control to keep the anode pressure and hydrogen ratio of the supply system in constant. Migliardini et al. [16] designed an anode supply system with two operative modes which are dead-end and recirculation modes to

ensure the efficient and stable performance of PEMFC during the whole operation phases. Hong et al. [17] proposed a multiple input multiple output (MIMO) nonlinear state feedback controller to maintain the hydrogen concentration in the anode based on an observer. In addition, many studies have developed various control methods on the balance-of-plant (BOP) of PEMFC such as cathode oxygen supply system. Wang et al. [18] designed an air flow control method based on model predictive control (MPC) to prevent starvation that might occur in PEMFC. Liu et al. [19] introduced a second-order sliding mode method of the oxygen excess ratio to maximize the net power of PEMFC. Rakhtala et al. [20] proposed a feedback linearization control system with a gap metric analysis to regulate the excess ratio of oxygen avoiding the starvation in PEMFC which has certain resistance to interference. Han et al. [21] proposed an oxygen excess ratio robust control system based on the model reference adaptive control method which can improve the efficiency of the air compressor under parameter uncertainties. At present, the modeling and control of hydrogen supply system mostly focus on the anode pressure and purge. Output mass flow rates of the hydrogen circulating pump affect the hydrogen excess ratio in the PEMFC's anode. Thereby, the regulation of hydrogen circulation is asked to be implemented in the varied operation conditions of fuel cell electric vehicles. In this paper, a hydrogen supply system of a 100 kW PEMFC consisting of a hydrogen circulating pump to circulate the unreacted hydrogen is presented. The hydrogen circulating pump control scheme based on MPC is designed, which has the advantages of good control performance and strong robustness that effectively deal with the disturbance injections and the constrained optimization problems. The purge valve is intermittently opened during the operation of the PEMFC to ensure the hydrogen concentration in the anode. The effect of hydrogen purge on the output flow of hydrogen circulating pump in the anode hydrogen supply system is discussed. The rest of the paper is organized as follows. In Section Modeling of hydrogen supply system , the model of hydrogen supply system in PEMFC is developed. Hydrogen pump MPC controller design and implementation are introduced in Section MPC design and implementation. Section Results and discussion describes the results and discussion of implementation of MPC. Finally, the conclusion is drawn in Section Conclusion.

Modeling of hydrogen supply system Hydrogen supply system of PEMFC as shown in Fig. 1 is a complicated nonlinear system consisting of a hydrogen tank, a supply manifold, a return manifold, a flow control valve, an anode channel and a hydrogen circulating pump [22e24]. The return manifold and the hydrogen circulating pump are the main components of the hydrogen circulation system. Assuming that there is no liquid water with inflow and outflow, and the temperature is constant in the manifold, and the gases in the model are regarded as ideal gases, and the variation of anode mixed gas is described by the ideal gas state equation.

Please cite this article as: He H et al., Hydrogen circulation system model predictive control for polymer electrolyte membrane fuel cellbased electric vehicle application, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.147

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where uv is the control voltage of the flow control valve. Wv,full is the output flow rate when the valve is fully open.

Anode channel Anode channel of PEMFC is approximately regarded as isothermal, and there is no leakage of hydrogen between anode and cathode. The mass flow rate of hydrogen in the anode channel is calculated by  dpH2 ;an RH2 Tan
¼ WH2 ;an;in  WH2 ;an;out  WH2 ;rt dt Van

Fig. 1 e Structural diagram of the hydrogen supply system.

(4)

where WH2,an,in is the mass flow rate of hydrogen entering the anode channel, WH2,an,out is the mass flow rate of hydrogen flowing out the anode channel. Since the pressure difference between the anode and cathode is limited to a certain value, the pressure of anode tracks the pressure of cathode which can be described as a quadratic function of fuel cell current. WH2,rt is the reaction rate of hydrogen mass in the anode, which is described by

Supply manifold and return manifold The supply manifold is a pipeline connecting the flow control valve, hydrogen circulating pump and anode of the PEMFC. The gases flowing into the supply manifold include the gas flowing through the flow control valve and the gas flowing back from the hydrogen circulating pump. The return manifold connects the anode channel and the hydrogen circulating pump, which redirects the unreacted hydrogen of the fuel cell anode into the supply manifold through hydrogen circulating pump. The dynamics of the mixed gas in the manifold can be described as follow  dpm Rg Tm
¼ Wm;in  Wm;out dt Vm

(1)

where Wm,in is the mass flow rate of hydrogen into the manifold, Wm,out is the mass flow rate of hydrogen out of the manifold. When the gas in the return manifold is stable, the mass flow rate of gas flowing through the manifold can be described as an equation of the pressure difference between the outlet and the inlet [25]   Wrm ¼ krm prm;out  prm;in

(2)

where krm is the return manifold coefficient. The pressure of return manifold inlet is equal to the pressure of anode.

Flow control valve The valve area of the flow control valve is variable, and its steady-state characteristics can be described as a linear equation controlled by voltage signal whose value is 0e1. Under the steady state, the output mass flow rate of the flow control valve and the hydrogen mass flow rate consumed in the anode channel should be balanced, so the drive voltage signal of the flow control valve can be described as a linear function of the current as formulated in below [25] Wv ¼ uv Wv; full

(3)

WH2 ;rt ¼ Nc

Ist MH2 2F

(5)

where Nc is the number of the single cells, Ist is the current of PEMFC and F is the Faraday's constant. Hydrogen enters into the anode of PEMFC after humidification to maintain the gas humidity in the anode channel. The diffusion rate of water vapor from the anode to the cathode in the anode channel is denoted by Wv;ts ¼ anet Nc

Ist MH2 O F

(6)

where anet is the water transport coefficient which is denoting by the membrane parameters and water content in the PEMFC anode [25]. When the humidity of the mixed gas is in the anode and remains constant under the stable working condition, the partial pressure of the water vapor in the mixed gas can be calculated by the humidity and the saturation pressure of water vapor [22,26]. Consequently, the mass fraction of hydrogen in the mixed gas of PEMFC anode and return manifold can be calculated.

Purge valve The purge valve is mounted on the fuel cell return manifold and discharges excess water and nitrogen diffused from the cathode by periodic opening and closing which is set to maintain the hydrogen concentration and remove liquid water in the anode. The opening frequency of the purge valve is related to the current. When the current is large, the water that penetrates from the cathode to the anode increases, which may cause water flooding [27,28]. It is necessary to increase the opening frequency of purge valve while under large current operation. The mass flow rate of the exhaust gas of the purge valve can be calculated by [15] Wpv ¼ kpv Fpv ðPan  Patm Þ

(7)

where kpv is the flow coefficients of the purge valve, Fpv is the on-off state of the purge valve (1 denots ON and 0 denots OFF), Patm is the standard atmospheric pressure.

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Hydrogen circulating pump

Table 1 e The main parameters for PEMFC model. Parameters

The hydrogen circulating pump collects unreacted hydrogen from the anode channel and inputs it into the supply manifold according to a certain hydrogen circulation ratio to reuse hydrogen. The model of hydrogen circulating pump can be divided into fan characteristics and motor model. The fan characteristics exhibit the relation of flow rate, efficiency, gas pressure ratio and impeller speed. The motor model expresses the motor speed under a certain driving voltage [29,30]. The fan characteristics offer the static features and the variable values in non-standard conditions according to the fan map as well as the working environment of the circulating pump. The mass flow rate and angle velocity of hydrogen circulating pump in non-standard conditions can be described by the temperature and pressure ratio between the reference and the return manifold. Thus, the scaled flow rate of the hydrogen circulating pump is defined by [15] F¼

Wpc . 2 rrm dpu Upu p 4

(8)

where rrm is the mixed gas density of hydrogen and water in the return manifold, Upu is the tip velocity of the rotating blade of the hydrogen circulating pump, and dpu is the diameter of the blade of the pump. The motor model of hydrogen circulating pump [15] can reveal the angle velocity of circulating pump under a certain driving voltage  dupu 1
¼ tpm  tpu Jpu dt 3 2  gg;rm 1 cp;rm Tm 6 Psm gg;rm 7 tpu ¼  15Wpu 4 uc hc Prm  kt
tpm ¼ hpm upu  kv upu Rpm

(9)

(10)

Temperature in manifolds Tm Temperature in anode Tan Volume of manifolds Vm Volume of anode Van The coefficient of return manifold krm Full mass flow rate of flow control valve Wv,full Number of single cells Nc Flow coefficient of purge valve kpv Standard atmospheric pressure Patm Diameter of pump rotating blade dpu Rotational inertia of pump Jpu Angular velocity coefficient of motor kt Voltage coefficient of motor kv Resistance of motor Rpm Efficiency of motor hpm

In this Section, a control scheme based on MPC is designed to regulate the output mass flow rate of hydrogen circulating pump. Due to the wide operating range of the 100 kW PEMFC, the nonlinear hydrogen circulation system plant is approximated by the Taylor expansion at the selected operation points to obtain the piecewise linear models. Accordingly, the switched MPC controller is developed based on the linearized model to achieve the mass flow rate tracking under the varied operation conditions [31,32].

e e Pa m kg$m2 N$mA1 V$(rad/s)1 ohm e

381 5  109 1.01325  105 0.15 2.6  103 0.15 0.15 0.82 0.9

The model of the hydrogen circulating pump is a nonlinear system which is difficult to be directly used to design the mass flow rate controller. Thus, the nonlinear plant is linearized to develop the MPC controller. Due to the wide operation ranges of PEMFC, these nonlinear equations (1) and (9), are linearized by Taylor expansion at two operating points. The current of the rated operating point is 350 A, and the pressure of the return manifold is 1.72  105 Pa and the angle velocity of the pump is 1133 rad/s. Another operating point is chosen at a lower current (150 A) to consider the low power response demands, the pressure of the return manifold is 1.90  105 Pa and the angle velocity of the pump is 498 rad/s. After linearization, the continuous-time state space model is described as follow

(11)

MPC design and implementation

Values 353 353 4  103 5  103 2  107 2  103

Piecewise linearization of the plant



where Jpu is the rotational inertia of the hydrogen circulating pump, tpm is the driving torque, tpu is the resistance torque, hc is the efficiency of the pump which can be calculated by fitting the experimental data. kt, Rpm, hpm, kv are the performance parameters of the motor, upu is the driving voltage of the hydrogen circulating pump. The output flow of hydrogen circulating pump under a certain driving voltage can be calculated by equation (8). Table 1 shows the main parameters of the 100 kW PEMFC model in this study.

Units K K m3 m3 e kg/s

_ ¼ Ac XðtÞ þ Bcu UðtÞ þ Bcd dðtÞ þ Bcw WðtÞ XðtÞ YðtÞ ¼ CXðtÞ þ D

(12)

where 8

T > X ¼ Prp ; upu > < Y ¼ Wpu > > : U ¼ upu d ¼ Ist

(13)

where X is the state vector of the hydrogen circulating pump model which consists of the pressure of the return manifold and the angle velocity of the pump, Y is the controlled output variable which is the output mass flow rate of the hydrogen circulating pump, U is the control input variable which is the driving voltage of the hydrogen circulating pump, d is the measured disturbance, W is the unmeasured disturbance, and Ac, Bcu, Bcd, Bcw, C, D are the matrices of the state space model. Then, transforming the continuous-time state space model into the incremental form to facilitate the description of predictive equation, the system can be rewrite as 

DXðk þ 1Þ ¼ Ad DXðkÞ þ Bdu DUðkÞ þ Bdd DdðkÞ þ Bdw DWðkÞ YðkÞ ¼ CDXðkÞ þ Yðk  1Þ

(14)

To compare the response accuracy between a linear model and a nonlinear model, three current conditions are set which

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are 300A, 350A and 400A. The comparison results can be seen in Fig. 2 which shows the error between the two types of models. When the current is far from the linearization operating point, a certain error is shown rather than the equal state at the rated operating point. Furthermore, the response speed is different between the linear model and the nonlinear model, and the errors are acceptable.

MPC controller design The principle of MPC can be summarized as: the optimization problem is refreshed and solved with the latest measured value at each sampling time, then the optimal control sequence is applied to the plant, and reciprocating the above steps [33]. Thus, the implementation process of MPC can be divided into three parts: predicting the behavior of system, solving the optimization problem and applying the optimal control sequence to the system. For the hydrogen circulation system, a switched MPC scheme is proposed since the operation range is wide.

Predictive equation and solving the optimization problem The predictive equation for the future p-step of the system is obtained by the incremental state equation Yp ðk þ 1jkÞ ¼ SX DXðkÞ þ EYðkÞ þ SU DUm ðkÞ þ Sd DdðkÞ

(15)

where Yp(kþ1|k) is a column vector composed of the future pstep controlled output variable which are calculated at time k, and DUm(k) is the m-step control input column vector. p is defined as the prediction horizon and m is the control horizon, resulting in the control performance. SX, E, SU, Sd are the matrices of the predictive equation. The objective function of the MPC represents the performance requirements of the hydrogen circulating pump system. The fast following of the controlled output variable to a reference input and the limited variation in control action are crucial issues of MPC designing [34,35]. Thus, the objective function is expressed as follows [18] J¼

p m    X X   GY;i ðYðk þ ijkÞ  rðk þ iÞÞ 2 þ GU;i ðDUðk þ i  1ÞÞ2 i¼1

i¼1

(16)

Fig. 2 e Nonlinear and linear model response comparison.

5

where r(k) is the reference output, GY,i is the weighting factor of the output error and GU,i is the weighting factor of the control increment. The values of the weighting factor represent the expectation of the system. By adjusting the values of the weighting factor, the control process of MPC can be changed to achieve the expected control effect. Combining with the prediction equations, the optimization problem can be transferred from a minimum problem to an extreme value problem. Solving the extreme value problem, the optimal control sequence at time k can be obtained. Then, the MPC controller outputs the optimal control sequence to the model of hydrogen circulating pump and recalculates the optimal control sequence at time kþ1.

Switched MPC According to equation (5), the hydrogen mass flow rate consumed in the anode is directly related to the current. In this study, the hydrogen excess ratio is fixed at 1.5 and the mass flow rate of the circulating hydrogen can be regarded as a function of the current, which indicates that the variation of circulating hydrogen mass flow rate and current are consistent. A switched MPC scheme is designed to control the mass low rate of the circulating hydrogen to regulate the hydrogen excess ratio. Due to the error between the linear model and the nonlinear model, two linearized MPC controllers are designed in order to cover the entire current range of PEMFC [36,37]. In the low-power case, the operation point is selected at 150 A, and the MPC with linearized model works well when the current is less than 250 A. For high-power requirement of PEMFC, the rate current 350A is selected as the expansion working point, and the MPC exhibits a good control performance. The switched MPC strategy scheme is shown in Fig. 3. In this control scheme, the stack current value is judged at first. Then, the suitable MPC controller is applied to regulate the mass flow rate of the hydrogen circulating pump. When the current fluctuates around the threshold current I0, the control variable output by the switched MPC scheme may also fluctuate due to the frequent switching between two MPC controllers. In order to ensure the stability of the switched MPC scheme, a switching strategy at the threshold current is designed. A buffer is set to 2b around the threshold current. When the current is larger than I0 þ b, the high-power MPC is applied to regulate the hydrogen supply system. When the current is less than I0 - b, the low-power MPC is applied to regulate the hydrogen supply system. If the current is in the buffer which is larger than I0 þ b but less than I0 - b, the slope of the current is calculated and judged. If the current is in the upper butter [I0, I0 þ b] and the current slope is larger than a small positive value ε, the current is increasing and the highpower MPC is still applied. If the current is in the upper butter [I0, I0 þ b] and the current slope is less than a small positive value ε, the current may decrease below the threshold so the low-power MPC is applied. Similarly, if the current is in the lower butter [I0-b, I0] and the current slope is less than a small positive value ε, the current is decreasing and the low-power MPC is still applied. If the current is in the lower butter [I0-b, I0] and the current slope is larger than a small positive value ε, the current may increase over the threshold I0 so the highpower MPC is applied. Therefore, a switching strategy by

Please cite this article as: He H et al., Hydrogen circulation system model predictive control for polymer electrolyte membrane fuel cellbased electric vehicle application, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.147

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Fig. 3 e Switched MPC scheme. comparing the operation current with the threshold current is designed and the suitable MPC can be applied to the nonlinear circulation plant. The switching strategy can avoid current fluctuations at the threshold current which can be described as follow, 8 MpcðFH ðX;Y;U;dÞÞ ;ðIst ðkÞ  I0 þ bÞ > > >   > > Ist ðkÞ  Ist ðk  iÞ > > > >ε ∪ I  I ðkÞ > iDt > > >   > > > I st ðkÞ  Ist ðk  iÞ > > >ε ∪ I0  b < iDt Upu ¼ > MpcðFL ðX;Y;U;dÞÞ ;ðIst ðkÞ  I0  bÞ > > > >   > > Ist ðkÞ  Ist ðk  iÞ > >  ε ∪ I  b 0 st 0 > > iDt > > >   > > > Ist ðkÞ  Ist ðk  iÞ > : ε ∪ I0  Ist ðkÞ
shown in Fig. 4, a current condition which steps from 150 A to 350 A is applied into the switched MPC scheme to compare the control effects between the two MPCs. The certain errors are shown in Fig. 4 (a) and (b) of the driving voltage and the pump

(17)

Here, the Mpc is the optimal control action function of MPC which is transformed into a solution of quadratic programming problem. The FH(X,Y,U,d) is the state equation of the high-power plant and FL(X,Y,U,d) is the low-power state equation which determining the output control action of MPC. The threshold I0 is set to 250, the b is set to 5 and the ε is set to 0.1. The switching effect depends on the size of i and Dt.

Results and discussion Simulation analysis of the proposed hydrogen circulation control system under the operation condition variation is demonstrated in this Section. The stack current is regarded as a disturbance of the hydrogen circulation control system. As

Fig. 4 e Control results under constant stack current conditions: (a) Control voltage of the two MPCs; (b) Mass flow rate responses.

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mass flow rate which shows the rationality of switched MPC scheme. A proportional-integral (PI) controller which is widely used in industrial processes is designed to compare with the proposed MPC scheme to validate the efficacy. Fig. 5 shows the

Fig. 5 e Control results under varied step current condition: (a) Startup performance; (b) Step change in stack current; (c) Control voltage; (d) Mass flow rate of hydrogen circulating pump.

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control results of the switched MPC and the PI controller under startup condition and a varied step current condition. PI has a high overshoot and is with long time to approach the reference values. Compare with the PI controller, MPC controller can make an accurate tracking control of the circulating hydrogen when the stack current changes. From the enlargement of Fig. 5(a), (c) and (d), the good control performance of MPC on the circulating hydrogen mass flow rate and the rapid response of the driving voltage can be found. PI controller cannot eliminate the steady-state errors of the tracking control since the hydrogen circulation displays a strong nonlinearity. In Fig. 6, a current operating condition is customized based on a 100 kW PEMFC bus operation condition to simulate and verify the control effects of the switched MPC scheme. The maximum current of the PEMFC is 400 A and the maximum driving voltage of the hydrogen circulating pump is 250 V. The driving voltage and the pump output hydrogen under the type of current have a certain fluctuation when the current is at 250A due to the switch between the two MPC. Moreover, when

Fig. 6 e Control results under customer defined operation condition: (a) Current profile; (b) Control voltage; (c) Mass flow rate of hydrogen circulating pump.

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anode channel which effects on the circulating hydrogen is also considered in the system modelling. The dynamic model of hydrogen supply system is then carried out. Moreover, a switched MPC approach is proposed to regulate the hydrogen circulation based on the piecewise linearized model. Two linearization models are constructed according to the current threshold of the PEMFC that divides the operation range into the low-power case and high-power case. Then the switched MPC scheme is hereby designed through the piecewise linear models, predictions, and optimizations. Finally, a hydrogen circulation control simulation test is implemented by a varied PEMFC operation profile step changing in the stack current in order to validate the proposed MPC method. The comparative results between the proposed MPC and PI controller indicate that the proposed MPC exhibits a better control performance with rapid response and good tracking accuracy even under the disturbance variations. The proposed MPC approach has a prospect in regulating the hydrogen supply system for PEMFC vehicle application. In the future work, a multiple-input and multiple-output MPC controller may be designed and applied into the hydrogen supply system which can regulate the both hydrogen excess ratio and the anode pressure through the flow control valve and the circulating pump. Also, the anode control may be collaborated with the cathode control via the combined management of hydrogen and oxygen. Fig. 7 e Purge valve effects: (a) Mass flow rate of hydrogen circulating pump; (b) Purge valve control signal.

Acknowledgements the current and the reference mass flow rate are far from the two linearized models used for MPC, the control result has an error due to incomplete matching between the nonlinear system and the linear controller. These errors of MPC are within the allowable range. Furthermore, when the purge valve is open, the pressure of anode obviously decrease if the flow control valve operates at a constant angle, which may affect the pump output hydrogen flow. Meanwhile, the pressure of anode is required to track the pressure of cathode to maintain the pressure difference in the actual work process. The output hydrogen flow rate of flow control valve should appropriate change to make up for the exhausted hydrogen. This process may cause some fluctuations in the pressure of the anode which affects the pressure ratio of the input and output of the hydrogen circulating pump and further affect the circulation flow according to equations (12) and (17). Thus, the control effect of hydrogen circulating pump depends on fluctuations in anode pressure when the purge valve is open (see Fig. 7).

Conclusion In this study, a switched MPC scheme is proposed for regulating a hydrogen circulation system of a 100 kW PEMFC. The main contributions of this work are summarized as follows. First, the relation of mass flow rate between the flow control valve and the hydrogen circulating pump under the steady state is discussed in detail. The change of water vapor in the

This work was supported by the National Key R&D Program of China (Grant No. 2018YFB0105500), the Natural Science Foundation of Fujian Province of China (Grant No. 2017J01690), and the Qishan Scholar Program in Fuzhou University (Grant No. XRC-1643).

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Please cite this article as: He H et al., Hydrogen circulation system model predictive control for polymer electrolyte membrane fuel cellbased electric vehicle application, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.147

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Please cite this article as: He H et al., Hydrogen circulation system model predictive control for polymer electrolyte membrane fuel cellbased electric vehicle application, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.147