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Oxygen Excess Ratio Control of PEM Fuel Cell Based on Self-adaptive Fuzzy PID⁎
5th IFAC Conference on 5th IFAC Conference on Engine Powertrain Simulation and online Modeling 5th IFACand Conference onControl, Available at www.sciencedirect.com Engine Powertrain Simulation and Modeling 5th IFACand Conference onControl, Changchun, China, September September 20-22, 2018 and Modeling Engine and Powertrain Control,20-22, Simulation Changchun, China, 2018 Engine and Powertrain Control, Simulation and Modeling Changchun, China, September 20-22, 2018 Changchun, China, September 20-22, 2018
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IFAC PapersOnLine 51-31 (2018) 15–20
Oxygen Excess Ratio Control of PEM Fuel Oxygen Excess Ratio Control of PEM Fuel Oxygen Excess Ratio Control of PEM Fuel ⋆⋆ Oxygen Excess Ratio Control of PEM Fuel Cell Based on Self-adaptive Fuzzy PID Cell Based on Self-adaptive Fuzzy PID ⋆⋆ Cell on Self-adaptive Fuzzy PID Cell Based Based on Self-adaptive Fuzzy PID ∗∗ ∗∗∗ ∗,∗∗ ∗,∗∗
∗∗ Xiaolei Yu ∗∗∗ ∗,∗∗ Chen Hong ∗,∗∗ ∗,∗∗ Zhang Ma Yan ∗,∗∗ Zhang Fan Fan ∗∗ Xiaolei Yu ∗∗∗ ∗∗∗ Ma Yan ∗,∗∗ Chen Hong ∗,∗∗ Zhang Fan ∗∗ ∗∗ Xiaolei Yu ∗∗∗ Ma Yan ∗,∗∗ Chen Hong ∗,∗∗ Xiaolei Yu Ma Yan Chen Hong ∗ Zhang Fan ∗ ∗ State Key Laboratory of Automotive Simulation and Control, Jilin ∗ State Key Laboratory of Automotive Simulation and Control, Jilin Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun China (e-mail: ∗ State University, Changchunof130025, 130025, China (e-mail: [email protected]). [email protected]). State Key Laboratory Automotive Simulation and Control, Jilin University, Changchun 130025, China (e-mail: [email protected]). (e-mail:[email protected]) (e-mail:[email protected]) 130025, China (e-mail: [email protected]). ∗∗University, Changchun (e-mail:[email protected]) ∗∗ Department of of Control Control Science Science and and Engineering, Engineering, Jilin Jilin University University ∗∗ Department (e-mail:[email protected]) ∗∗ of Control Science and Engineering, Jilin University (Campus NanLing), Changchun 130025, China ∗∗ Department (Campus NanLing), Changchun 130025, China Department of Control Science and Engineering, Jilin University (Campus NanLing), Changchun 130025, China (e-mail:[email protected]) (e-mail:[email protected]) (Campus NanLing), Changchun 130025, China ∗∗∗ (e-mail:[email protected]) ∗∗∗ College of Physics, Jilin University, Changchun 130012, China ∗∗∗ Jilin University, Changchun 130012, China (e-mail:[email protected]) ∗∗∗ College of Physics, Jilin University, Changchun 130012, China (e-mail:[email protected]) ∗∗∗ College of Physics, (e-mail:[email protected]) College of Physics, Jilin University, Changchun 130012, China (e-mail:[email protected]) (e-mail:[email protected]) Abstract: Abstract: Oxygen Oxygen excess excess ratio ratio is is closely closely related related to to the the output output efficiency efficiency and and service service life life of of Abstract: Oxygen excess ratio (PEM) is closely related to theTo output efficiency andbehaviors service life of the proton exchange membrane fuel cell system. simulate dynamic of air the proton exchange membrane (PEM) fuel cell system. To simulate dynamic behaviors of air Abstract: Oxygen model excess ratio is closely related tois the output efficiency andbehaviors service life of the proton exchange membrane (PEM) fuel cell system. To simulate dynamic of air flow, a fourth-order of PEM fuel cell system established. Then, a self-adaptive fuzzy flow, aa fourth-order model of PEM fuel cell system is established. Then, aa self-adaptive fuzzy the proton exchange membrane (PEM) fuel cell system. To simulate dynamic behaviors of air flow, fourth-order model of PEM fuel cell system is established. Then, self-adaptive fuzzy PID (SFPID) controller is proposed to regulate the excess ratio through its PID (SFPID) controller is of proposed to cell regulate theis oxygen oxygen excess ratioa on-line on-line through its flow, a fourth-order model PEM fuel system established. Then, self-adaptive fuzzy PID (SFPID) controller is proposed tocurrent regulate the oxygen ratio on-line through its adaptive characteristic. Under different disturbances, aaexcess comparison of proposed SFPID adaptive characteristic. Under different current disturbances, comparison of proposed SFPID PID (SFPID) controller is proposed tofeedforward, regulate thePID, oxygen ratio on-line through its adaptive characteristic. Under different current disturbances, aexcess comparison of proposed SFPID with several control topologies such as and PID plus feedforward (PID-FF) with several control topologies such as feedforward, PID, andaPID plus feedforward (PID-FF) adaptive characteristic. Under different current disturbances, comparison of proposed SFPID with several control topologies such as feedforward, PID, and PID plusMoreover, feedforward (PID-FF) is carried out to the of controller. the proposed is carried outcontrol to validate validate the advantages advantages of the the proposed proposed controller. the (PID-FF) proposed with several topologies such asthe feedforward, PID, and PIDratio. plusMoreover, feedforward is carried out to validate theto advantages of the proposed controller. Moreover, the proposed SFPID controller is applied track variable oxygen excess The simulation results SFPID controller is applied to track the variable oxygen excess ratio. The simulation results is carried out to validate the advantages of the proposed controller. Moreover, the proposed SFPID controller is applied to track the variable oxygen excess ratio. rapidly The simulation results display that the set-point value of oxygen excess ratio can be tracked and accurately, display that the set-point value of oxygen excess ratio can be tracked rapidly and accurately, SFPID controller isproposed applied to track the variable oxygen excess ratio. Theperformance. simulation results display that thethe set-point value of oxygen excess ratio can be tracked rapidly and accurately, and verify that SFPID controller has good dynamic response and verify that the proposed SFPID controller hasratio goodcan dynamic response performance. display that the set-point value of oxygen excess be tracked rapidly and accurately, and verify that the proposed SFPID controller has good dynamic response performance. and verify that the proposed SFPIDofcontroller goodHosting dynamic performance. © 2018, IFAC (International Federation Automatichas Control) by response Elsevier Ltd. All rights reserved. Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive fuzzy PID Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive fuzzy fuzzy PID PID controller controller Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive fuzzy PID controller controller 1. INTRODUCTION INTRODUCTION between 1. between cathode cathode and and anode anode with with aa fast fast electrical electrical valve, valve, 1. INTRODUCTION between cathode anode with a fast electrical valve, is controlled by aa and simple proportional control. Moreover, is controlled by simple proportional control. Moreover, 1. INTRODUCTION between cathode and anode with a fast electrical valve, is controlled by a simple proportional control. Moreover, since the degree of humidity and temperature cannot inThe ever-increasing severe problem of energy shortage the degree ofsimple humidity and temperature cannot inThe ever-increasing severe problem of energy shortage since is controlled by a proportional control. Moreover, The ever-increasing severe problem of energy shortage since the degree of humidity and temperature cannot increase or decrease rapidly, many researchers assumed that and environmental pollution has led to a constant exand environmental pollution has led to a constant excrease or decrease rapidly, many researchers assumed that since the degree ofrapidly, humidity andresearchers temperature cannot inThe environmental ever-increasing severe problem oftoenergy shortage and pollution has led a constant excrease or decrease many assumed that the fuel cell operates in a constant temperature condition. ploration toward new efficient and clean energy sources ploration toward new efficienthas andled clean energy sources the fuelorcell operates in a constant temperature condition. crease decrease rapidly, many researchers assumed that and environmental pollution to a constant exploration toward new efficient and clean energy sources the fuel cell operates in a constant temperature condition. Meanwhile, thermal thermal dynamic dynamic behavior behavior is is much much slower slower than than such as as solar, solar, wind, wind, geothermal geothermal and and hydrogen. hydrogen. Fuel Fuel cell, cell, Meanwhile, such fuel cell operates in a constant temperature condition. ploration toward efficient and energy sources such geothermal andclean hydrogen. cell, the Meanwhile, thermal dynamic behavior is much slower than air flow dynamic behavior, which is one of the reasons as a as newsolar, typewind, of new power generation device thatFuel directly as a new type of power generation device that directly air flow dynamic behavior, which is one of the reasons thermal dynamic change behavior is much slower than such as solar, wind, geothermal and device hydrogen. Fuel cell, Meanwhile, as a new type of power generation that directly air flow dynamic behavior, which is one of the reasons that the small temperature is neglected. For the and continuously converts chemical energy into electric and continuously converts chemical device energy that into directly electric air that the small temperature change is neglected. For the flow dynamic behavior, which is one of the reasons as a new type of power generation that the small temperature change is neglected. For the and continuously converts chemical energy into electric air supply subsystem, owing to the slow air flow dynamic energy, is a substitute for clean energy production durenergy, is a substitute for clean air supply subsystem, owing change to the slow air flow dynamic energy production durthat the small temperature is neglected. For the and continuously converts chemical energy into electric energy, is a substitute for air supply subsystem, owing to the slow air flow dynamic clean energy production durbehavior of the compressor and the air supply manifolds, ing recent recent decades decades (Grujicic (Grujicic et et al. al. (2004)). (2004)). Particularly, Particularly, behavior of the compressor and the air supply manifolds, ing air supply subsystem, owing to the slow air flow dynamic energy, is a substitute for clean energy production during recent decades (Grujicic(PEM) et al. (2004)). of the compressor and the air supply manifolds, when the current suddenly, it cause proton exchange membrane (PEM) fuel cell cell Particularly, can produce produce behavior proton exchange membrane fuel can when theofload load current changes changes suddenly, it may may cause behavior the compressor and the air supply manifolds, ing recent decades (Grujicic et al.zero (2004)). Particularly, proton exchange membrane (PEM) fuel cell can produce when the load current changes suddenly, it may cause oxygen starvation in the cathode if proper oxygen is not electricity, heat, water and almost pollution emission electricity, heat, water and almost zero pollution emission oxygen starvation in the cathode if proper oxygen is not when the load current changes suddenly, it may cause proton exchange membrane (PEM) fuel cell can produce oxygen starvation in the cathode if proper oxygen is not electricity, heat, water and almost zero pollution emission delivered enough. Oxygen starvation may cause low power from oxidant and hydrogen which can be produced from from oxidant andwater hydrogen which zero can pollution be produced from oxygen deliveredstarvation enough. Oxygen starvation may cause low power in the cathode if proper oxygen is not electricity, heat, and almost emission from oxidant and hydrogen which can be produced from delivered enough. Oxygen starvation may cause low power generation, membrane degradation, and even affecting the a wide variety of energy sources (Tong et al. (2017); Daud generation, membrane degradation, and even affecting the afrom wideoxidant varietyand of energy sources (Tong etbeal.produced (2017); Daud delivered enough. Oxygen starvation may cause low power hydrogen which can from aet variety of energy sources (Tong et al. (2017); Daud generation, membrane degradation, and even affecting the working life of the stack (Deng et al. (2017)). To avoid etwide al. (2017)). In fact, it is widely applied and developing in al. (2017)). In fact, it is widely applied and developing in working life of the stack (Deng et al. (2017)). To avoid generation, membrane degradation, and even affecting the a wide variety ofoffact, energy sources (Tong etand al. (2017); Daud et al. (2017)). In it is widely applied developing in working life of the stack (Deng et al. (2017)). To avoid these problems, the regulation of air flow or oxygen excess portable power mobile electronics, hybrid electric vehiportable power offact, mobile electronics, hybrid electric vehithese problems, the regulation of air flow or oxygen excess working life of the stack (Deng et al. (2017)). To avoid et al. (2017)). In it is widely applied and developing in these problems, the regulation of air flow or oxygen excess portable power of mobile electronics, hybrid electric vehinecessary. Furthermore, the oxygen excess ratio is cles (HEVs), (HEVs), fuel fuel cell cell electric electric vehicles vehicles (FCEVs) (FCEVs) and and other other ratio cles ratio is is necessary. excess ratio is problems, theFurthermore, regulation ofthe air oxygen flowoforPEM oxygen excess portable ofadvantages mobile electronics, hybrid electric vehi- these cles (HEVs), fuel cell electric (FCEVs) and safety other ratio is necessary. Furthermore, the oxygen excess ratio is of great significance on the efficiency fuel cell, fields duepower to its its ofvehicles high efficiency, efficiency, high safety of great significance on the efficiency of PEM fuel cell, fields due to advantages of high high ratio is necessary. Furthermore, the oxygen excess ratio is cles (HEVs), fuel cell electric vehicles (FCEVs) and other fields due to its advantages of high efficiency, high safety of great significance on the efficiency of PEM fuel cell, also reflecting the net power of PEM fuel cell system. factors, high power density, low operation temperature and factors, high power density, low operation temperature and also reflecting the net power of PEMoffuel cellfuel system. of great significance on the efficiency PEM cell, fields due to its advantages of high efficiency, high safety factors, high power density, low operation temperature and also reflecting the netoxygen power excess of PEM fuel cell focus system. Therefore, regulating ratio is the of low pollution pollution (Nonobe (2017)). low (Nonobe (2017)). Therefore, regulating ratio is of reflecting the netoxygen power excess of PEM fuel cell focus system. factors, high power density, low operation temperature and also Therefore, regulating oxygen excess ratio is the the focus of low pollution (Nonobe (2017)). work in this paper. work in this paper. Therefore, regulating oxygen excess ratio is the focus of Generally, a PEM fuel cell system consists of four main low pollution (Nonobe (2017)). Generally, a PEM fuel cell system consists of four main work in this paper. Generally, a PEM fuel cell system consists of four main A large number of studies have been proposed on the work in this paper. subsystems: the hydrogen supply subsystem, air supply subsystems: the hydrogen supply A large number of studies have been proposed on the Generally, ahumidity PEM fuel celltemperature systemsubsystem, consists of air foursupply main subsystems: the hydrogen supply subsystem, air supply large strategies number ofof studies have cell beenair on the control PEM supply subsystem, and management sub- A control PEM fuel fuel airproposed supply system. system. subsystem, humidity and temperature management subA large strategies number ofof studies have cell been proposed on conthe subsystems: the hydrogen supply subsystem, air supply subsystem, humidity and temperature management subcontrol strategies of PEM fuel cell air supply system. (Pukrushpan et al. (2016)) proposed different control system (Talj et al. (2011)). The schematic diagram of et al. of (2016)) proposed different control consystem (Taljhumidity et al. (2011)). The schematic diagramsubof (Pukrushpan control strategies PEM fuel cell air supply system. subsystem, and temperature management system (Talj al. (2011)). The schematic of (Pukrushpan et feedback al. (2016)) proposed different control nonconfigurations and design based on PEM fuel fuel celletsystem system is illustrated illustrated in Fig. Fig. 1. 1.diagram Hydrogen PEM cell is in Hydrogen and design baseddifferent on ninth-order ninth-order non(Pukrushpan et feedback al.as(2016)) proposed controllinear consystemfuel (Talj etsystem al.that (2011)). The the schematic diagram of figurations PEM cell is illustrated in Fig. 1. Hydrogen figurations and feedback design based on ninth-order nonlinear model such static or dynamic feedforward, supply subsystem minimizes pressure difference supply subsystem that isminimizes theinpressure linear modeland such as static or dynamic feedforward, linear difference figurations feedback design based on ninth-order nonPEM fuel cell system illustrated Fig. 1. Hydrogen supply subsystem that minimizes the pressure difference linear model such as static or dynamic feedforward, linear quadratic regulator regulator (LQR) (LQR) and and feedback feedback with with integral integral concon⋆ This work is supported by the National Nature Science Founquadratic linear model such as(LQR) static and oremployed dynamic linear supply subsystem that by minimizes the Nature pressure difference ⋆ This work is supported the National Science Founquadratic regulator feedbackaafeedforward, with integral control. (Matraji et al. (2013)) robust nonlinear ⋆ dation of China No. 61520106008, the National Key Science Research and trol. (Matraji et al. (2013)) employed robust nonlinear This work is supported by the National Nature Founquadratic regulator (LQR) and feedback with integral con⋆ dation of China No. 61520106008, the National Key Science Research and This work is supported by the National Nature Fountrol. (Matraji et al. (2013)) employed a robust nonlinear second order sliding mode controller (SMC) in cascaded Development Program of and the dation of China No. 61520106008, the National Key and second order sliding mode controller (SMC) in cascaded Development Program of China China 2017YFB0102800 2017YFB0102800 and Research the industrial industrial trol. (Matraji et al. (2013)) employed a robust nonlinear dation of China No. 61520106008, the National Key Research and second order sliding mode controller (SMC) in cascaded structure which is on sub-optimal algorithm to innovation special funds Jilin 2017YFB0102800 Province 2018C035-2. Development Program ofof China and the industrial structure which is based based sub-optimal to innovation special funds Jilin 2017YFB0102800 Province 2018C035-2. second order sliding mode on controller (SMC)algorithm in cascaded Development Program ofof China and the industrial structure which is based on sub-optimal algorithm to innovation special funds of Jilin Province 2018C035-2. structure which is based on sub-optimal algorithm to innovation special funds of Jilin Province 2018C035-2. 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Copyright © under 2018 IFAC 15 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 15 Copyright © 2018 IFAC 15 10.1016/j.ifacol.2018.10.004 Copyright © 2018 IFAC 15
IFAC E-CoSM 2018 16 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
where x1 and x2 are the cathode side oxygen partial pressure pO2 and nitrogen partial pressure pN2 , respectively. x3 is the angular speed wcp of motor compressor, x4 is the pressure psm of air supply manifold.
The fourth-order state-space model is derived based on the electrochemical, thermodynamic and fluid flow principles, and the state-space equations are as follows:
x˙ 1 = c1 (−x1 − x2 + x4 − c2 ) −
Fig. 1. Schematic diagram of PEM fuel cell system maintain optimum net power output by regulating the oxygen excess ratio in its operating range. (Kim (2010)) designed time delay control (TDC) to control the air flow to improve dynamic performance. Recently, model predictive control (MPC) is proposed to avoid oxygen starvation during load current changes (Wang and Kim (2014); Yu et al. (2008)). (Damour et al. (2014)) proposed the neural model-based self-tuning PID controller as an excellent candidate to address the oxygen excess ratio regulation issue. The diverse control strategies mentioned above have different degrees of performance in the regulation of oxygen excess ratio.
x˙ 2 = c8 (−x1 − x2 + x4 − c2 ) − x˙ 3 = −c9 x3 −
c10 x3
[
[(
x4 c11
)c12
c3 x2 W (x1 , x2 ) . c 4 x 1 + c5 x 2 + c 6
(3)
] − 1 y3 (x3 , x4 ) + c13 u. (4)
)c ]] x4 12 x˙ 4 = c14 1 + c15 −1 c11 · [y3 (x3 , x4 ) − c16 (−x1 − x2 + x4 − c2 )] .
[(
(5)
The total flow rate function W (x1 , x2 ) at the cathode exit is as follows:
In this paper, the study is focused on the design and verification performance of a self-adaptive fuzzy PID (SFPID) controller to keep the proper excess oxygen rate for preventing oxygen starvation at various stack currents. The proposed SFPID controller is benefited for adjusting the parameters of PID controller due to its adaptive characteristic. Accordingly, a control-oriented fourth-order model of PEM fuel cell air supply system is constructed to implement the SFPID control and validate control performance, which is a nonlinear dynamic model proposed by (Suh (2006)). In addition, the SFPID controller is applied to solve the control problem of oxygen excess ratio regulation in PEM fuel cell system.
)c18 c11 W (x1 , x2 ) = c17 (x1 + x2 + c2 ) x1 + x2 + c2 √ )c12 ( (6) c11 c11 · 1− , for > c19 x1 + x2 + c2 x 1 + x 2 + c2 (
and W (x1 , x2 ) = c20 (x1 + x2 + c2 ) , for
The remainder of this paper is organized as follows. The Section 2 presents the mathematical model of the PEM fuel cell air supply system and control problem. The PIDFF and SFPID controllers are designed in the Section 3. The Section 4 is simulation and discussion results. Finally, conclusion is provided in the Section 5.
c11 ≤ c19 x1 + x2 + c2 (7)
The motor compressor voltage vcm is an control input u, and the stack current Ist is considered as a measurable disturbance input d. The constants ci (1 ≤ i ≤ 24) are summarized in Appendix A. The equation (2) − (5) can be written in a compact state space form which is
2. PEM FUEL CELL MODEL DEVELOPMENT 2.1 Mathematical Model
x˙ = f (x) + gu u + gξ d.
An integrated fuel cell system model that consists of stacks of single fuel cells is composed of motor compressor, air supply manifolds, humidifier, cooler and electrical valve. The classical PEM fuel cell dynamic model for control is established by (Pukrushpan (2003)), which is a ninthorder dynamic model. However, it is not suitable for controller design due to the complexity of its model. In this paper, a fourth-order model of PEM fuel cell system is adopted under some assumptions (Suh (2006)), which could suitably present the dynamic behaviors of air flow.
T
(8) T
y = [y1 , y2 , y3 ] = [y1 (x1 , x2 ) , x4 , y3 (x3 , x4 )] .
(9)
where x is the system state variable. f is a continuous vector function representing the dynamics of the fuel cell system. gu and gξ , represent the gain distribution vectors of input and disturbance, respectively. y is the system output, including the stack voltage y1 , air supply manifold pressure y2 , and compressor flow y3 . 2.2 Control Problem
The state variable, x is x = [x1 , x2 , x3 , x4 ]T .
c3 x1 W (x1 , x2 ) − c7 d. c 4 x1 + c 5 x2 + c 6 (2)
The two variables of net power and oxygen excess ratio are considered as control performance of the fuel cell
(1) 16
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
3.1 PID-FF Controller
Feedforward control is a compensation for disturbances, which is often used for disturbances with large variations. A feedforward controller must be attached with a feedback controller to ensure that the steady-state offset value is zero. Feedback control has good control performance in many applications, but the main drawback of feedback control is time delay. Besides, the conventional PID controller is widely used in the industrial process control owing to its simple structure and good robustness for both linear and nonlinear system. In this paper, PID plus feedforward controller is adopted to avoid these disadvantages, and the structure of PID-FF is shown in Fig. 3.
O
Fig. 2. The relation between the oxygen excess ratio and net power for different stack currents system. The net power is defined as the difference between stack power generation and parasitic power consumption. The majority of the parasitic power is caused by the air compressor. The oxygen excess ratio is defined as the ratio of consumed amount of oxygen supplied to amount of oxygen reacted. The net power and oxygen excess ratio indicate the efficiency and oxygen supply of fuel cell system, respectively, are important performance index of the system, which can be written as z1 z2
]
=
[
] y1 d − c21 u (u − c22 x3 ) c23 (x4 − x1 − x2 − c2 ) . c24 d
³
O
Fig. 3. Structure of the PID-FF controller 3.2 SFPID Controller The PID and fuzzy logic controllers with good robustness are benefited to use in nonlinear systems. However, for nonlinear system, the conventional PID cannot keep the system being a relative steady state, because the inner parameters of nonlinear system always vary with the operating state. Thus, a SFPID controller is developed to solve the nonlinear system in real time, which has adaptive characteristic compared to conventional PID controller. And the parameters of PID controller can be adjusted by using on-line fuzzy logic. The structure based on SFPID controller is shown in Fig. 4.
(10)
where z1 is net power pnet , z2 is oxygen excess ratio λO2 . For z2 < 1, even slightly higher than 1, oxygen starvation occurs. Oxygen starvation can lead to performance degradation, damage of membrane surface and the reduction of power generation. Also, if z2 is very high, the net power will be reduced due to the increase of the power consumption of the compressor.
Therefore, the main control objective for PEM fuel cell air supply system is regulating the oxygen excess ratio λO2 to prevent oxygen starvation and reduce the power consumed by compressor. The system net power under different stack currents and oxygen excess ratios is shown in Fig. 2. And Fig. 2 indicates that the maximum value of pnet is achieved when the oxygen excess ratio λO2 is between 1.9 and 2.5 for various stack currents. In this paper, in order to simplify, λO2 = 2 is considered as a desired target value to control for various disturbance conditions (Kunusch et al. (2009)). Moreover, the second scenario is to track the variable λO2 based on disturbance variations to achieve efficient power output.
³
O
Fig. 4. Structure of the SFPID controller In Fig. 4, the fuzzy logic consists of the fuzzifier, inference engine, rule base and defuzzifier, as shown in Fig. 5. There are two inputs of the oxygen excess ratio error e = ∆λO2 and derivation of error ∆e = d∆λO2 /dt and three output scaling factors are α, β and γ, corresponding to three outputs kp , ki and kd , respectively. Firstly, the two inputs of ∆λO2 and d∆λO2 /dt are normalized and converted into fuzzy variables by the fuzzifier.
3. CONTROLLER DESIGN In order to solve control problem in section 2.2, it is necessary to develop effective control method to rapidly regulate the oxygen excess ratio. In this paper, several control topologies based PEM fuel cell nonlinear dynamic model are designed to obtain the best control performance such as feedforward controller, PID controller, PID plus feedforward (PID-FF) controller, SFPID controller.
'O
z=
[
P
Fig. 5. Block diagram of the fuzzy logic 17
17
IFAC E-CoSM 2018 18 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
Stack Current (A)
'O
300 250 200 150 100
0
5
10
15 Time (s)
20
25
30
Fig. 7. Current profile for fuel cell stack 'O
245
d∆λO2 dt
5
10
PID−FF
15 Time (s)
20
SFPID
25
30
Oxygen Excess Ratio
2 Set−point FF
1.5
PID PID−FF SFPID
0
5
10
15 Time (s)
20
25
30
Fig. 9. Oxygen excess ratio for different control methods Oxygen Excess Ratio
2.2
Table 1. Fuzzy rules for SFPID
Small Medium Large
0
PID
2.5
The fuzzy logic rule is based on the knowledge and plenty of simulations, which contains 9 rules. The outputs of fuzzy logic for tuning the PID parameters are decided from related fuzzy inputs. And fuzzy rule table is listed in table 1. For instance, if ∆λO2 is large and d∆λO2 /dt is small, then kp is small, ki is large, and kd is small. Then the fuzzy inference engine transforms the fuzzy rule base into a fuzzy linguistic output. Finally, to obtain the available output variables, the centroid defuzzification method which has the characteristics of simplified calculation and smooth output control performance is chosen in this paper.
∆λO2 Medium SMS MMS LMS
FF
Fig. 8. Stack voltage variation for different control methods
Then the fuzzy variables are sent to the inference engine and processed with fuzzy rules. Finally, the results from inference engine are sent to the defuzzifier and converted to exact values (Ma et al. (2018)). The input and output are divided into fuzzy subsections. Among, the input is divided into large, medium and small, and the output is divided into large, medium and small. The triangular fuzzy membership function is chosen, shown in Fig. 6.
Small SMS MLM LLL
225 215
Fig. 6. Membership function of the fuzzy logic
k p , k i , kd
235
2 1.8 Set−point FF
1.6
PID PID−FF
1.4
Large SLS MMS LSS
2.1
SFPID
4
5
6 Time (s) (a)
7
Oxygen Excess Ratio
Stack Voltage (V)
2
1.8
Set−point FF PID PID−FF
1.6 14
SFPID
15
16 17 Time (s) (b)
Fig. 10. The magnified plot of oxygen excess ratio variations: (a) t = 5s (b) t = 15s under different stack current variation. A current-varying procedure from the fuel cell stack is shown in Fig. 7, and the current range changes from 130A to 300A in simulation. Fig. 8 shows that the response of the stack voltage variations is stable under different control methods. The performance of oxygen excess ratio regulation is illustrated in Fig. 9, and all the utilized control methods have an excellent dynamic tracking behavior in adjusting λO2 at the set-point value. More specifically, the magnified plot of oxygen excess ratio variations at t = 5s and t = 15s in Fig. 10 show that the proposed SFPID controller can reach the set-point faster than others and no overshoot, when stack current changes. Meanwhile, using SFPID control method, the steady state-error of system dynamic response
4. SIMULATION AND DISCUSSION RESULTS The SFPID controller is applied to the PEM fuel cell system nonlinear model. The numerical parameters used in the simulation are given in Appendix A. The main control objectives are: keeping λO2 constant at 2 to avoid oxygen starvation, and tracking variable λO2 to achieve the efficient system performance. 4.1 Constant Oxygen Excess Ratio Control To verify the simulation performance, the set-point value of λO2 is selected as constant 2 to avoid oxygen starvation 18
Stack Voltage (V)
2.5 2
5
1.5 Set−point SFPID
1 0.5
0
5
10
245
15 Time (s) (a)
20
25
30
235
4
3.76
x 10
3.74
4.5 3.72
6.5
7.5
8.5
9.5
0
5
10
15 Time (s) (b)
20
25
4.92 22
3.5
1.6 19
2
20
Constant Oxygen Excess Ratio Variable Oxygen Excess Ratio 0
5
10
15 Time (s)
20
25
30
voltage, respectively, which shows that the SFPID controller is able to accurately track the variable set-point value with constant disturbance. And the stack voltage changes smoothly, indicating that the dynamic output performance is good. Moreover, the change of stack current is adopted in the same as that of the first simulation to track the variable oxygen excess ratio, as shown in Fig. 7. The variation of oxygen excess ratio and stack voltage is illustrated in Fig. 12. The simulation results show that the proposed SFPID controller is appropriate and accurate for tracking variable set-point value with variable disturbance. Particularly, the settling time is less than 1s at t = 20s. The stack voltage variation is relatively large compared to the constant oxygen excess ratio control, but the dynamic response is stable. Based simulation on the results, the proposed SFPID controller has good performance in tracking the variable λO2 .
21
Set−point SFPID
1 0
5
10
15 Time (s) (a)
20
25
30
0
5
10
15 Time (s) (b)
20
25
30
235 225 215 205
24
Fig. 13. Comparison of net power for constant and variable λO2
1.5
245
23
30
1.75
2.5
x 10
4.93
2.5
215
4
4.94
4
3
Fig. 11. Tracking capability of the variable set-point value under constant stack current: (a) oxygen excess ratio; (b) stack voltage Oxygen Excess Ratio
x 10
225
205
Stack Voltage (V)
19
4
5.5
Net Power (W)
Oxygen Excess Ratio
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
To further explore the net power under the proposed SFPID controller on the PEM fuel cell system, the comparative result of net power for constant and variable λO2 is represented as Fig. 13. The stack current changes from 230A to 280A at t = 15s. From Fig. 13, when t > 15s, the net power for variable λO2 which is not optimal oxygen excess ratio, is greater than constant λO2 , and the performance is inconsistent with the former. That is because the relative large λO2 corresponds to larger net power when the stack current is relatively small, and it is opposite when the current increases. The result is also accord with the relationship shown in Fig. 2. Therefore, it is particularly important to adjust the oxygen excess ratio for PEM fuel cell air supply system in order to obtain good performance.
Fig. 12. Tracking capability of the variable set-point value under the change of stack current: (a) oxygen excess ratio; (b) stack voltage is small. The results mean that the proposed controller have some advantages in regulating oxygen excess ratio such as rapidity and accuracy over other methods under different stack currents. 4.2 Variable Oxygen Excess Ratio Control
5. CONCLUSION
In order to reduce parasitic power consumption and obtain efficient PEM fuel cell system performance, the variable oxygen excess ratio λO2 should be considered. Meanwhile, λO2 set-point value from 1.7 to 2 is derived according to stack current variation, as shown in Fig. 11. Certainly, the proposed SFPID controller is tested for tracking the variable λO2 .
In this paper, a reduced fourth-order model of PEM fuel cell is established to depict the air flow dynamic behavior of the air supply system. Then, a SFPID controller based on the control-oriented nonlinear model is proposed to regulate the oxygen excess ratio with on-line fuzzy logic. The different control topologies such as feedforward, PID, PIDFF, and SFPID are compared to validate the advantages of proposed controller when load current suddenly changed in the fuel cell stack. Besides, the proposed SFPID controller is tested for tracking the variable oxygen excess ratio, and the simulation results demonstrate that the proposed
Firstly, the regulation of λO2 with variable set-point value is implemented under the constant stack current which is set to 200A during the entire simulation, and the simulation results are illustrated in Fig. 11. Fig. 11 is revealed the variation of oxygen excess ratio and stack 19
IFAC E-CoSM 2018 20 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
controller is capable of excellent tracking performance in regulating the oxygen excess ratio with different current disturbances. As a future work, the optimal oxygen excess ratio control will be pursued, and the proposed controller will be tested and evaluated in the real PEM fuel cell system.
Transactions on Mechatronics, 19(3), 852–861. Yu, S., Chen, H., Zhang, D., and Guo, H. (2008). Model predictive control for oxygen starvation in air supply system of pem fuel cell. In Control Conference, 2008. CCC, 682–686. Appendix A. A SUMMARY OF PHYSICAL PARAMETERS FOR PEM FUEL CELL
REFERENCES Damour, C., Benne, M., Lebreton, C., Deseure, J., and Grondin-Perez, B. (2014). Real-time implementation of a neural model-based self-tuning pid strategy for oxygen stoichiometry control in pem fuel cell. International Journal of Hydrogen Energy, 39(24), 12819–12825. Daud, W.R.W., Rosli, R.E., Majlan, E.H., Hamid, S.A.A., and Mohamed, R. (2017). Pem fuel cell system control: A review. Renewable Energy, 113. Deng, H., Li, Q., and Chen, W. (2017). Research on hosm observer for oxygen excess ratio estimation of pemfc system. Zhongguo Dianji Gongcheng Xuebao/proceedings of the Chinese Society of Electrical Engineering, 37(17), 5058–5068. Grujicic, M., Chittajallu, K.M., Law, E.H., and Pukrushpan, J.T. (2004). Model-based control strategies in the dynamic interaction of air supply and fuel cell. Proceedings of the Institution of Mechanical Engineers.part A.journal of Power Energy, 218(7), 487–499. Kim, Y.B. (2010). Improving dynamic performance of proton-exchange membrane fuel cell system using time delay control. Journal of Power Sources, 195(19), 6329– 6341. Kunusch, C., Puleston, P.F., Mayosky, M.A., and Prat, M.S. (2009). Advances in hosm control design and implementation for pem fuel cell systems. IFAC Proceedings Volumes, 42(13), 709–716. Ma, Y., Duan, P., Sun, Y., and Chen, H. (2018). Equalization of lithium-ion battery pack based on fuzzy logic control in electric vehicle. IEEE Transactions on Industrial Electronics, 65(8), 6762–6771. Matraji, I., Laghrouche, S., Jemei, S., and Wack, M. (2013). Robust control of the pem fuel cell air-feed system via sub-optimal second order sliding mode. Applied Energy, 104(2), 945–957. Nonobe, Y. (2017). Development of the fuel cell vehicle mirai. Ieej Transactions on Electrical Electronic Engineering, 12(1), 5–9. Pukrushpan, J.T., Stefanopoulou, A.G., and Peng, H. (2016). Control of fuel cell breathing: Initial results on the oxygen starvation problem. Control Systems IEEE, 24(2), 30 – 46. Pukrushpan, J.T. (2003). Modeling and control of fuel cell systems and fuel processors. Dissertation Abstracts International, Volume: 64-02, Section: B, page: 0925.;Chairs: Anna Stefanopo, 18(3), 594–6. Suh, K.W. (2006). Modeling, analysis and control of fuel cell hybrid power systems. Talj, R., Ortega, R., and Astolfi, A. (2011). Passivity and robust pi control of the air supply system of a pem fuel cell model. Automatica, 47(12), 2554–2561. Tong, S., Fang, J., and Zhang, Y. (2017). Output tracking control of a hydrogen-air pem fuel cell. IEEE/CAA Journal of Automatica Sinica, 4(2), 273–279. Wang, Y.X. and Kim, Y.B. (2014). Real-time control for air excess ratio of a pem fuel cell system. IEEE/ASME
Table A.1. Parameters of PEM fuel cell model (x ) ¯
c1 =
RTst kca,in MO2 Vca ¯ st RT Vca
O2,atm
c2 = psat
1+watm
c3 = c 5 = M N2 c7 = c9 =
c 4 = M O2 c6 = Mv psat c8 =
c11 = patm ηcm kt Jcp Rcm 1 ηcp
c13 = c15 =
CD AT c17 = √ ¯
c19 = c21 =
(
RTst
2 γ+1 1 Rcm
(
¯ st kca,in 1−xO2,atm RT MN2 Vca 1+watm C T c10 = Jp ηatm cp cp c12 = γ−1 γ ¯ c14 = M RTatm a,atm Vsm
¯ st n RT 4FVca ηcm kt kv Jcp Rcm
√
)
c16 = kca,in 2γ γ−1
c18 =
γ ) γ−1
1
CD AT c20 = √ γ2 ¯ RTst
c22 = kv
xO
2,atm c23 = kca,in 1+w
atm
1 γ
(
c24 =
nMO2 4F
(
2 γ+1
γ+1 ) 2(γ−1)
)
Ma,atm = yO2 ,atm MO2 + 1 − yO2 ,atm MN2 xO2 ,atm =
yO ,atm MO2 2 Ma,atm
watm =
ϕatm psat Mv Ma,atm patm −ϕatm psat
Table A.2. Simulation parameters of PEM fuel cell system n ¯ R Patm Psat Tatm Tst ϕatm Cp γ MO 2 MN2 Mv Jcp kt Rcm kv ηcp ηcm Vsm Vca kca,in CD AT yO2 ,atm F
20
Number of cells in full-cell stack Universal gas constant Atmospheric pressure Saturation pressure Atmospheric temperature Stack temperature Average ambient air relative humidity Constant pressure Specific heat of air Ratio of specific heat of air Oxygen molar mass Nitrogen molar mass Vapour molar mass Compressor inertia Motor parameter Compressor motor resistance Motor parameter Motor mechanical efficiency Compressor efficiency Supply manifold volume Cathode volume Cathode inlet orifice constant Cathode outlet throttle discharge coefficient Cathode outlet throttle area Oxygen mole fraction Faraday constant
381 8.3145 J/mol/K 101325Pa 47076Pa 298K 353K 0.5 1004J/kg/K 1.4 32 × 10−3 kg/mol 28 × 10−3 kg/mol 18.02 × 10−3 kg/mol 5 × 10−5 kgm2 0.0225(Nm)/A 1.2Ω 0.0153V/(rad/s) 0.98% 0.8% 0.02m3 0.01m3 0.3629 × 10−5 kg/s/Pa 0.0124 0.002m3 0.21 96485C/mol
ScienceDirect
IFAC PapersOnLine 51-31 (2018) 15–20
Oxygen Excess Ratio Control of PEM Fuel Oxygen Excess Ratio Control of PEM Fuel Oxygen Excess Ratio Control of PEM Fuel ⋆⋆ Oxygen Excess Ratio Control of PEM Fuel Cell Based on Self-adaptive Fuzzy PID Cell Based on Self-adaptive Fuzzy PID ⋆⋆ Cell on Self-adaptive Fuzzy PID Cell Based Based on Self-adaptive Fuzzy PID ∗∗ ∗∗∗ ∗,∗∗ ∗,∗∗
∗∗ Xiaolei Yu ∗∗∗ ∗,∗∗ Chen Hong ∗,∗∗ ∗,∗∗ Zhang Ma Yan ∗,∗∗ Zhang Fan Fan ∗∗ Xiaolei Yu ∗∗∗ ∗∗∗ Ma Yan ∗,∗∗ Chen Hong ∗,∗∗ Zhang Fan ∗∗ ∗∗ Xiaolei Yu ∗∗∗ Ma Yan ∗,∗∗ Chen Hong ∗,∗∗ Xiaolei Yu Ma Yan Chen Hong ∗ Zhang Fan ∗ ∗ State Key Laboratory of Automotive Simulation and Control, Jilin ∗ State Key Laboratory of Automotive Simulation and Control, Jilin Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun China (e-mail: ∗ State University, Changchunof130025, 130025, China (e-mail: [email protected]). [email protected]). State Key Laboratory Automotive Simulation and Control, Jilin University, Changchun 130025, China (e-mail: [email protected]). (e-mail:[email protected]) (e-mail:[email protected]) 130025, China (e-mail: [email protected]). ∗∗University, Changchun (e-mail:[email protected]) ∗∗ Department of of Control Control Science Science and and Engineering, Engineering, Jilin Jilin University University ∗∗ Department (e-mail:[email protected]) ∗∗ of Control Science and Engineering, Jilin University (Campus NanLing), Changchun 130025, China ∗∗ Department (Campus NanLing), Changchun 130025, China Department of Control Science and Engineering, Jilin University (Campus NanLing), Changchun 130025, China (e-mail:[email protected]) (e-mail:[email protected]) (Campus NanLing), Changchun 130025, China ∗∗∗ (e-mail:[email protected]) ∗∗∗ College of Physics, Jilin University, Changchun 130012, China ∗∗∗ Jilin University, Changchun 130012, China (e-mail:[email protected]) ∗∗∗ College of Physics, Jilin University, Changchun 130012, China (e-mail:[email protected]) ∗∗∗ College of Physics, (e-mail:[email protected]) College of Physics, Jilin University, Changchun 130012, China (e-mail:[email protected]) (e-mail:[email protected]) Abstract: Abstract: Oxygen Oxygen excess excess ratio ratio is is closely closely related related to to the the output output efficiency efficiency and and service service life life of of Abstract: Oxygen excess ratio (PEM) is closely related to theTo output efficiency andbehaviors service life of the proton exchange membrane fuel cell system. simulate dynamic of air the proton exchange membrane (PEM) fuel cell system. To simulate dynamic behaviors of air Abstract: Oxygen model excess ratio is closely related tois the output efficiency andbehaviors service life of the proton exchange membrane (PEM) fuel cell system. To simulate dynamic of air flow, a fourth-order of PEM fuel cell system established. Then, a self-adaptive fuzzy flow, aa fourth-order model of PEM fuel cell system is established. Then, aa self-adaptive fuzzy the proton exchange membrane (PEM) fuel cell system. To simulate dynamic behaviors of air flow, fourth-order model of PEM fuel cell system is established. Then, self-adaptive fuzzy PID (SFPID) controller is proposed to regulate the excess ratio through its PID (SFPID) controller is of proposed to cell regulate theis oxygen oxygen excess ratioa on-line on-line through its flow, a fourth-order model PEM fuel system established. Then, self-adaptive fuzzy PID (SFPID) controller is proposed tocurrent regulate the oxygen ratio on-line through its adaptive characteristic. Under different disturbances, aaexcess comparison of proposed SFPID adaptive characteristic. Under different current disturbances, comparison of proposed SFPID PID (SFPID) controller is proposed tofeedforward, regulate thePID, oxygen ratio on-line through its adaptive characteristic. Under different current disturbances, aexcess comparison of proposed SFPID with several control topologies such as and PID plus feedforward (PID-FF) with several control topologies such as feedforward, PID, andaPID plus feedforward (PID-FF) adaptive characteristic. Under different current disturbances, comparison of proposed SFPID with several control topologies such as feedforward, PID, and PID plusMoreover, feedforward (PID-FF) is carried out to the of controller. the proposed is carried outcontrol to validate validate the advantages advantages of the the proposed proposed controller. the (PID-FF) proposed with several topologies such asthe feedforward, PID, and PIDratio. plusMoreover, feedforward is carried out to validate theto advantages of the proposed controller. Moreover, the proposed SFPID controller is applied track variable oxygen excess The simulation results SFPID controller is applied to track the variable oxygen excess ratio. The simulation results is carried out to validate the advantages of the proposed controller. Moreover, the proposed SFPID controller is applied to track the variable oxygen excess ratio. rapidly The simulation results display that the set-point value of oxygen excess ratio can be tracked and accurately, display that the set-point value of oxygen excess ratio can be tracked rapidly and accurately, SFPID controller isproposed applied to track the variable oxygen excess ratio. Theperformance. simulation results display that thethe set-point value of oxygen excess ratio can be tracked rapidly and accurately, and verify that SFPID controller has good dynamic response and verify that the proposed SFPID controller hasratio goodcan dynamic response performance. display that the set-point value of oxygen excess be tracked rapidly and accurately, and verify that the proposed SFPID controller has good dynamic response performance. and verify that the proposed SFPIDofcontroller goodHosting dynamic performance. © 2018, IFAC (International Federation Automatichas Control) by response Elsevier Ltd. All rights reserved. Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive fuzzy PID Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive fuzzy fuzzy PID PID controller controller Keywords: PEM fuel cell, Oxygen excess ratio, Feedforward, PID, Self-adaptive fuzzy PID controller controller 1. INTRODUCTION INTRODUCTION between 1. between cathode cathode and and anode anode with with aa fast fast electrical electrical valve, valve, 1. INTRODUCTION between cathode anode with a fast electrical valve, is controlled by aa and simple proportional control. Moreover, is controlled by simple proportional control. Moreover, 1. INTRODUCTION between cathode and anode with a fast electrical valve, is controlled by a simple proportional control. Moreover, since the degree of humidity and temperature cannot inThe ever-increasing severe problem of energy shortage the degree ofsimple humidity and temperature cannot inThe ever-increasing severe problem of energy shortage since is controlled by a proportional control. Moreover, The ever-increasing severe problem of energy shortage since the degree of humidity and temperature cannot increase or decrease rapidly, many researchers assumed that and environmental pollution has led to a constant exand environmental pollution has led to a constant excrease or decrease rapidly, many researchers assumed that since the degree ofrapidly, humidity andresearchers temperature cannot inThe environmental ever-increasing severe problem oftoenergy shortage and pollution has led a constant excrease or decrease many assumed that the fuel cell operates in a constant temperature condition. ploration toward new efficient and clean energy sources ploration toward new efficienthas andled clean energy sources the fuelorcell operates in a constant temperature condition. crease decrease rapidly, many researchers assumed that and environmental pollution to a constant exploration toward new efficient and clean energy sources the fuel cell operates in a constant temperature condition. Meanwhile, thermal thermal dynamic dynamic behavior behavior is is much much slower slower than than such as as solar, solar, wind, wind, geothermal geothermal and and hydrogen. hydrogen. Fuel Fuel cell, cell, Meanwhile, such fuel cell operates in a constant temperature condition. ploration toward efficient and energy sources such geothermal andclean hydrogen. cell, the Meanwhile, thermal dynamic behavior is much slower than air flow dynamic behavior, which is one of the reasons as a as newsolar, typewind, of new power generation device thatFuel directly as a new type of power generation device that directly air flow dynamic behavior, which is one of the reasons thermal dynamic change behavior is much slower than such as solar, wind, geothermal and device hydrogen. Fuel cell, Meanwhile, as a new type of power generation that directly air flow dynamic behavior, which is one of the reasons that the small temperature is neglected. For the and continuously converts chemical energy into electric and continuously converts chemical device energy that into directly electric air that the small temperature change is neglected. For the flow dynamic behavior, which is one of the reasons as a new type of power generation that the small temperature change is neglected. For the and continuously converts chemical energy into electric air supply subsystem, owing to the slow air flow dynamic energy, is a substitute for clean energy production durenergy, is a substitute for clean air supply subsystem, owing change to the slow air flow dynamic energy production durthat the small temperature is neglected. For the and continuously converts chemical energy into electric energy, is a substitute for air supply subsystem, owing to the slow air flow dynamic clean energy production durbehavior of the compressor and the air supply manifolds, ing recent recent decades decades (Grujicic (Grujicic et et al. al. (2004)). (2004)). Particularly, Particularly, behavior of the compressor and the air supply manifolds, ing air supply subsystem, owing to the slow air flow dynamic energy, is a substitute for clean energy production during recent decades (Grujicic(PEM) et al. (2004)). of the compressor and the air supply manifolds, when the current suddenly, it cause proton exchange membrane (PEM) fuel cell cell Particularly, can produce produce behavior proton exchange membrane fuel can when theofload load current changes changes suddenly, it may may cause behavior the compressor and the air supply manifolds, ing recent decades (Grujicic et al.zero (2004)). Particularly, proton exchange membrane (PEM) fuel cell can produce when the load current changes suddenly, it may cause oxygen starvation in the cathode if proper oxygen is not electricity, heat, water and almost pollution emission electricity, heat, water and almost zero pollution emission oxygen starvation in the cathode if proper oxygen is not when the load current changes suddenly, it may cause proton exchange membrane (PEM) fuel cell can produce oxygen starvation in the cathode if proper oxygen is not electricity, heat, water and almost zero pollution emission delivered enough. Oxygen starvation may cause low power from oxidant and hydrogen which can be produced from from oxidant andwater hydrogen which zero can pollution be produced from oxygen deliveredstarvation enough. Oxygen starvation may cause low power in the cathode if proper oxygen is not electricity, heat, and almost emission from oxidant and hydrogen which can be produced from delivered enough. Oxygen starvation may cause low power generation, membrane degradation, and even affecting the a wide variety of energy sources (Tong et al. (2017); Daud generation, membrane degradation, and even affecting the afrom wideoxidant varietyand of energy sources (Tong etbeal.produced (2017); Daud delivered enough. Oxygen starvation may cause low power hydrogen which can from aet variety of energy sources (Tong et al. (2017); Daud generation, membrane degradation, and even affecting the working life of the stack (Deng et al. (2017)). To avoid etwide al. (2017)). In fact, it is widely applied and developing in al. (2017)). In fact, it is widely applied and developing in working life of the stack (Deng et al. (2017)). To avoid generation, membrane degradation, and even affecting the a wide variety ofoffact, energy sources (Tong etand al. (2017); Daud et al. (2017)). In it is widely applied developing in working life of the stack (Deng et al. (2017)). To avoid these problems, the regulation of air flow or oxygen excess portable power mobile electronics, hybrid electric vehiportable power offact, mobile electronics, hybrid electric vehithese problems, the regulation of air flow or oxygen excess working life of the stack (Deng et al. (2017)). To avoid et al. (2017)). In it is widely applied and developing in these problems, the regulation of air flow or oxygen excess portable power of mobile electronics, hybrid electric vehinecessary. Furthermore, the oxygen excess ratio is cles (HEVs), (HEVs), fuel fuel cell cell electric electric vehicles vehicles (FCEVs) (FCEVs) and and other other ratio cles ratio is is necessary. excess ratio is problems, theFurthermore, regulation ofthe air oxygen flowoforPEM oxygen excess portable ofadvantages mobile electronics, hybrid electric vehi- these cles (HEVs), fuel cell electric (FCEVs) and safety other ratio is necessary. Furthermore, the oxygen excess ratio is of great significance on the efficiency fuel cell, fields duepower to its its ofvehicles high efficiency, efficiency, high safety of great significance on the efficiency of PEM fuel cell, fields due to advantages of high high ratio is necessary. Furthermore, the oxygen excess ratio is cles (HEVs), fuel cell electric vehicles (FCEVs) and other fields due to its advantages of high efficiency, high safety of great significance on the efficiency of PEM fuel cell, also reflecting the net power of PEM fuel cell system. factors, high power density, low operation temperature and factors, high power density, low operation temperature and also reflecting the net power of PEMoffuel cellfuel system. of great significance on the efficiency PEM cell, fields due to its advantages of high efficiency, high safety factors, high power density, low operation temperature and also reflecting the netoxygen power excess of PEM fuel cell focus system. Therefore, regulating ratio is the of low pollution pollution (Nonobe (2017)). low (Nonobe (2017)). Therefore, regulating ratio is of reflecting the netoxygen power excess of PEM fuel cell focus system. factors, high power density, low operation temperature and also Therefore, regulating oxygen excess ratio is the the focus of low pollution (Nonobe (2017)). work in this paper. work in this paper. Therefore, regulating oxygen excess ratio is the focus of Generally, a PEM fuel cell system consists of four main low pollution (Nonobe (2017)). Generally, a PEM fuel cell system consists of four main work in this paper. Generally, a PEM fuel cell system consists of four main A large number of studies have been proposed on the work in this paper. subsystems: the hydrogen supply subsystem, air supply subsystems: the hydrogen supply A large number of studies have been proposed on the Generally, ahumidity PEM fuel celltemperature systemsubsystem, consists of air foursupply main subsystems: the hydrogen supply subsystem, air supply large strategies number ofof studies have cell beenair on the control PEM supply subsystem, and management sub- A control PEM fuel fuel airproposed supply system. system. subsystem, humidity and temperature management subA large strategies number ofof studies have cell been proposed on conthe subsystems: the hydrogen supply subsystem, air supply subsystem, humidity and temperature management subcontrol strategies of PEM fuel cell air supply system. (Pukrushpan et al. (2016)) proposed different control system (Talj et al. (2011)). The schematic diagram of et al. of (2016)) proposed different control consystem (Taljhumidity et al. (2011)). The schematic diagramsubof (Pukrushpan control strategies PEM fuel cell air supply system. subsystem, and temperature management system (Talj al. (2011)). The schematic of (Pukrushpan et feedback al. (2016)) proposed different control nonconfigurations and design based on PEM fuel fuel celletsystem system is illustrated illustrated in Fig. Fig. 1. 1.diagram Hydrogen PEM cell is in Hydrogen and design baseddifferent on ninth-order ninth-order non(Pukrushpan et feedback al.as(2016)) proposed controllinear consystemfuel (Talj etsystem al.that (2011)). The the schematic diagram of figurations PEM cell is illustrated in Fig. 1. Hydrogen figurations and feedback design based on ninth-order nonlinear model such static or dynamic feedforward, supply subsystem minimizes pressure difference supply subsystem that isminimizes theinpressure linear modeland such as static or dynamic feedforward, linear difference figurations feedback design based on ninth-order nonPEM fuel cell system illustrated Fig. 1. Hydrogen supply subsystem that minimizes the pressure difference linear model such as static or dynamic feedforward, linear quadratic regulator regulator (LQR) (LQR) and and feedback feedback with with integral integral concon⋆ This work is supported by the National Nature Science Founquadratic linear model such as(LQR) static and oremployed dynamic linear supply subsystem that by minimizes the Nature pressure difference ⋆ This work is supported the National Science Founquadratic regulator feedbackaafeedforward, with integral control. (Matraji et al. (2013)) robust nonlinear ⋆ dation of China No. 61520106008, the National Key Science Research and trol. (Matraji et al. (2013)) employed robust nonlinear This work is supported by the National Nature Founquadratic regulator (LQR) and feedback with integral con⋆ dation of China No. 61520106008, the National Key Science Research and This work is supported by the National Nature Fountrol. (Matraji et al. (2013)) employed a robust nonlinear second order sliding mode controller (SMC) in cascaded Development Program of and the dation of China No. 61520106008, the National Key and second order sliding mode controller (SMC) in cascaded Development Program of China China 2017YFB0102800 2017YFB0102800 and Research the industrial industrial trol. (Matraji et al. (2013)) employed a robust nonlinear dation of China No. 61520106008, the National Key Research and second order sliding mode controller (SMC) in cascaded structure which is on sub-optimal algorithm to innovation special funds Jilin 2017YFB0102800 Province 2018C035-2. Development Program ofof China and the industrial structure which is based based sub-optimal to innovation special funds Jilin 2017YFB0102800 Province 2018C035-2. second order sliding mode on controller (SMC)algorithm in cascaded Development Program ofof China and the industrial structure which is based on sub-optimal algorithm to innovation special funds of Jilin Province 2018C035-2. structure which is based on sub-optimal algorithm to innovation special funds of Jilin Province 2018C035-2. 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Copyright © under 2018 IFAC 15 Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 15 Copyright © 2018 IFAC 15 10.1016/j.ifacol.2018.10.004 Copyright © 2018 IFAC 15
IFAC E-CoSM 2018 16 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
where x1 and x2 are the cathode side oxygen partial pressure pO2 and nitrogen partial pressure pN2 , respectively. x3 is the angular speed wcp of motor compressor, x4 is the pressure psm of air supply manifold.
The fourth-order state-space model is derived based on the electrochemical, thermodynamic and fluid flow principles, and the state-space equations are as follows:
x˙ 1 = c1 (−x1 − x2 + x4 − c2 ) −
Fig. 1. Schematic diagram of PEM fuel cell system maintain optimum net power output by regulating the oxygen excess ratio in its operating range. (Kim (2010)) designed time delay control (TDC) to control the air flow to improve dynamic performance. Recently, model predictive control (MPC) is proposed to avoid oxygen starvation during load current changes (Wang and Kim (2014); Yu et al. (2008)). (Damour et al. (2014)) proposed the neural model-based self-tuning PID controller as an excellent candidate to address the oxygen excess ratio regulation issue. The diverse control strategies mentioned above have different degrees of performance in the regulation of oxygen excess ratio.
x˙ 2 = c8 (−x1 − x2 + x4 − c2 ) − x˙ 3 = −c9 x3 −
c10 x3
[
[(
x4 c11
)c12
c3 x2 W (x1 , x2 ) . c 4 x 1 + c5 x 2 + c 6
(3)
] − 1 y3 (x3 , x4 ) + c13 u. (4)
)c ]] x4 12 x˙ 4 = c14 1 + c15 −1 c11 · [y3 (x3 , x4 ) − c16 (−x1 − x2 + x4 − c2 )] .
[(
(5)
The total flow rate function W (x1 , x2 ) at the cathode exit is as follows:
In this paper, the study is focused on the design and verification performance of a self-adaptive fuzzy PID (SFPID) controller to keep the proper excess oxygen rate for preventing oxygen starvation at various stack currents. The proposed SFPID controller is benefited for adjusting the parameters of PID controller due to its adaptive characteristic. Accordingly, a control-oriented fourth-order model of PEM fuel cell air supply system is constructed to implement the SFPID control and validate control performance, which is a nonlinear dynamic model proposed by (Suh (2006)). In addition, the SFPID controller is applied to solve the control problem of oxygen excess ratio regulation in PEM fuel cell system.
)c18 c11 W (x1 , x2 ) = c17 (x1 + x2 + c2 ) x1 + x2 + c2 √ )c12 ( (6) c11 c11 · 1− , for > c19 x1 + x2 + c2 x 1 + x 2 + c2 (
and W (x1 , x2 ) = c20 (x1 + x2 + c2 ) , for
The remainder of this paper is organized as follows. The Section 2 presents the mathematical model of the PEM fuel cell air supply system and control problem. The PIDFF and SFPID controllers are designed in the Section 3. The Section 4 is simulation and discussion results. Finally, conclusion is provided in the Section 5.
c11 ≤ c19 x1 + x2 + c2 (7)
The motor compressor voltage vcm is an control input u, and the stack current Ist is considered as a measurable disturbance input d. The constants ci (1 ≤ i ≤ 24) are summarized in Appendix A. The equation (2) − (5) can be written in a compact state space form which is
2. PEM FUEL CELL MODEL DEVELOPMENT 2.1 Mathematical Model
x˙ = f (x) + gu u + gξ d.
An integrated fuel cell system model that consists of stacks of single fuel cells is composed of motor compressor, air supply manifolds, humidifier, cooler and electrical valve. The classical PEM fuel cell dynamic model for control is established by (Pukrushpan (2003)), which is a ninthorder dynamic model. However, it is not suitable for controller design due to the complexity of its model. In this paper, a fourth-order model of PEM fuel cell system is adopted under some assumptions (Suh (2006)), which could suitably present the dynamic behaviors of air flow.
T
(8) T
y = [y1 , y2 , y3 ] = [y1 (x1 , x2 ) , x4 , y3 (x3 , x4 )] .
(9)
where x is the system state variable. f is a continuous vector function representing the dynamics of the fuel cell system. gu and gξ , represent the gain distribution vectors of input and disturbance, respectively. y is the system output, including the stack voltage y1 , air supply manifold pressure y2 , and compressor flow y3 . 2.2 Control Problem
The state variable, x is x = [x1 , x2 , x3 , x4 ]T .
c3 x1 W (x1 , x2 ) − c7 d. c 4 x1 + c 5 x2 + c 6 (2)
The two variables of net power and oxygen excess ratio are considered as control performance of the fuel cell
(1) 16
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
3.1 PID-FF Controller
Feedforward control is a compensation for disturbances, which is often used for disturbances with large variations. A feedforward controller must be attached with a feedback controller to ensure that the steady-state offset value is zero. Feedback control has good control performance in many applications, but the main drawback of feedback control is time delay. Besides, the conventional PID controller is widely used in the industrial process control owing to its simple structure and good robustness for both linear and nonlinear system. In this paper, PID plus feedforward controller is adopted to avoid these disadvantages, and the structure of PID-FF is shown in Fig. 3.
O
Fig. 2. The relation between the oxygen excess ratio and net power for different stack currents system. The net power is defined as the difference between stack power generation and parasitic power consumption. The majority of the parasitic power is caused by the air compressor. The oxygen excess ratio is defined as the ratio of consumed amount of oxygen supplied to amount of oxygen reacted. The net power and oxygen excess ratio indicate the efficiency and oxygen supply of fuel cell system, respectively, are important performance index of the system, which can be written as z1 z2
]
=
[
] y1 d − c21 u (u − c22 x3 ) c23 (x4 − x1 − x2 − c2 ) . c24 d
³
O
Fig. 3. Structure of the PID-FF controller 3.2 SFPID Controller The PID and fuzzy logic controllers with good robustness are benefited to use in nonlinear systems. However, for nonlinear system, the conventional PID cannot keep the system being a relative steady state, because the inner parameters of nonlinear system always vary with the operating state. Thus, a SFPID controller is developed to solve the nonlinear system in real time, which has adaptive characteristic compared to conventional PID controller. And the parameters of PID controller can be adjusted by using on-line fuzzy logic. The structure based on SFPID controller is shown in Fig. 4.
(10)
where z1 is net power pnet , z2 is oxygen excess ratio λO2 . For z2 < 1, even slightly higher than 1, oxygen starvation occurs. Oxygen starvation can lead to performance degradation, damage of membrane surface and the reduction of power generation. Also, if z2 is very high, the net power will be reduced due to the increase of the power consumption of the compressor.
Therefore, the main control objective for PEM fuel cell air supply system is regulating the oxygen excess ratio λO2 to prevent oxygen starvation and reduce the power consumed by compressor. The system net power under different stack currents and oxygen excess ratios is shown in Fig. 2. And Fig. 2 indicates that the maximum value of pnet is achieved when the oxygen excess ratio λO2 is between 1.9 and 2.5 for various stack currents. In this paper, in order to simplify, λO2 = 2 is considered as a desired target value to control for various disturbance conditions (Kunusch et al. (2009)). Moreover, the second scenario is to track the variable λO2 based on disturbance variations to achieve efficient power output.
³
O
Fig. 4. Structure of the SFPID controller In Fig. 4, the fuzzy logic consists of the fuzzifier, inference engine, rule base and defuzzifier, as shown in Fig. 5. There are two inputs of the oxygen excess ratio error e = ∆λO2 and derivation of error ∆e = d∆λO2 /dt and three output scaling factors are α, β and γ, corresponding to three outputs kp , ki and kd , respectively. Firstly, the two inputs of ∆λO2 and d∆λO2 /dt are normalized and converted into fuzzy variables by the fuzzifier.
3. CONTROLLER DESIGN In order to solve control problem in section 2.2, it is necessary to develop effective control method to rapidly regulate the oxygen excess ratio. In this paper, several control topologies based PEM fuel cell nonlinear dynamic model are designed to obtain the best control performance such as feedforward controller, PID controller, PID plus feedforward (PID-FF) controller, SFPID controller.
'O
z=
[
P
Fig. 5. Block diagram of the fuzzy logic 17
17
IFAC E-CoSM 2018 18 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
Stack Current (A)
'O
300 250 200 150 100
0
5
10
15 Time (s)
20
25
30
Fig. 7. Current profile for fuel cell stack 'O
245
d∆λO2 dt
5
10
PID−FF
15 Time (s)
20
SFPID
25
30
Oxygen Excess Ratio
2 Set−point FF
1.5
PID PID−FF SFPID
0
5
10
15 Time (s)
20
25
30
Fig. 9. Oxygen excess ratio for different control methods Oxygen Excess Ratio
2.2
Table 1. Fuzzy rules for SFPID
Small Medium Large
0
PID
2.5
The fuzzy logic rule is based on the knowledge and plenty of simulations, which contains 9 rules. The outputs of fuzzy logic for tuning the PID parameters are decided from related fuzzy inputs. And fuzzy rule table is listed in table 1. For instance, if ∆λO2 is large and d∆λO2 /dt is small, then kp is small, ki is large, and kd is small. Then the fuzzy inference engine transforms the fuzzy rule base into a fuzzy linguistic output. Finally, to obtain the available output variables, the centroid defuzzification method which has the characteristics of simplified calculation and smooth output control performance is chosen in this paper.
∆λO2 Medium SMS MMS LMS
FF
Fig. 8. Stack voltage variation for different control methods
Then the fuzzy variables are sent to the inference engine and processed with fuzzy rules. Finally, the results from inference engine are sent to the defuzzifier and converted to exact values (Ma et al. (2018)). The input and output are divided into fuzzy subsections. Among, the input is divided into large, medium and small, and the output is divided into large, medium and small. The triangular fuzzy membership function is chosen, shown in Fig. 6.
Small SMS MLM LLL
225 215
Fig. 6. Membership function of the fuzzy logic
k p , k i , kd
235
2 1.8 Set−point FF
1.6
PID PID−FF
1.4
Large SLS MMS LSS
2.1
SFPID
4
5
6 Time (s) (a)
7
Oxygen Excess Ratio
Stack Voltage (V)
2
1.8
Set−point FF PID PID−FF
1.6 14
SFPID
15
16 17 Time (s) (b)
Fig. 10. The magnified plot of oxygen excess ratio variations: (a) t = 5s (b) t = 15s under different stack current variation. A current-varying procedure from the fuel cell stack is shown in Fig. 7, and the current range changes from 130A to 300A in simulation. Fig. 8 shows that the response of the stack voltage variations is stable under different control methods. The performance of oxygen excess ratio regulation is illustrated in Fig. 9, and all the utilized control methods have an excellent dynamic tracking behavior in adjusting λO2 at the set-point value. More specifically, the magnified plot of oxygen excess ratio variations at t = 5s and t = 15s in Fig. 10 show that the proposed SFPID controller can reach the set-point faster than others and no overshoot, when stack current changes. Meanwhile, using SFPID control method, the steady state-error of system dynamic response
4. SIMULATION AND DISCUSSION RESULTS The SFPID controller is applied to the PEM fuel cell system nonlinear model. The numerical parameters used in the simulation are given in Appendix A. The main control objectives are: keeping λO2 constant at 2 to avoid oxygen starvation, and tracking variable λO2 to achieve the efficient system performance. 4.1 Constant Oxygen Excess Ratio Control To verify the simulation performance, the set-point value of λO2 is selected as constant 2 to avoid oxygen starvation 18
Stack Voltage (V)
2.5 2
5
1.5 Set−point SFPID
1 0.5
0
5
10
245
15 Time (s) (a)
20
25
30
235
4
3.76
x 10
3.74
4.5 3.72
6.5
7.5
8.5
9.5
0
5
10
15 Time (s) (b)
20
25
4.92 22
3.5
1.6 19
2
20
Constant Oxygen Excess Ratio Variable Oxygen Excess Ratio 0
5
10
15 Time (s)
20
25
30
voltage, respectively, which shows that the SFPID controller is able to accurately track the variable set-point value with constant disturbance. And the stack voltage changes smoothly, indicating that the dynamic output performance is good. Moreover, the change of stack current is adopted in the same as that of the first simulation to track the variable oxygen excess ratio, as shown in Fig. 7. The variation of oxygen excess ratio and stack voltage is illustrated in Fig. 12. The simulation results show that the proposed SFPID controller is appropriate and accurate for tracking variable set-point value with variable disturbance. Particularly, the settling time is less than 1s at t = 20s. The stack voltage variation is relatively large compared to the constant oxygen excess ratio control, but the dynamic response is stable. Based simulation on the results, the proposed SFPID controller has good performance in tracking the variable λO2 .
21
Set−point SFPID
1 0
5
10
15 Time (s) (a)
20
25
30
0
5
10
15 Time (s) (b)
20
25
30
235 225 215 205
24
Fig. 13. Comparison of net power for constant and variable λO2
1.5
245
23
30
1.75
2.5
x 10
4.93
2.5
215
4
4.94
4
3
Fig. 11. Tracking capability of the variable set-point value under constant stack current: (a) oxygen excess ratio; (b) stack voltage Oxygen Excess Ratio
x 10
225
205
Stack Voltage (V)
19
4
5.5
Net Power (W)
Oxygen Excess Ratio
IFAC E-CoSM 2018 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
To further explore the net power under the proposed SFPID controller on the PEM fuel cell system, the comparative result of net power for constant and variable λO2 is represented as Fig. 13. The stack current changes from 230A to 280A at t = 15s. From Fig. 13, when t > 15s, the net power for variable λO2 which is not optimal oxygen excess ratio, is greater than constant λO2 , and the performance is inconsistent with the former. That is because the relative large λO2 corresponds to larger net power when the stack current is relatively small, and it is opposite when the current increases. The result is also accord with the relationship shown in Fig. 2. Therefore, it is particularly important to adjust the oxygen excess ratio for PEM fuel cell air supply system in order to obtain good performance.
Fig. 12. Tracking capability of the variable set-point value under the change of stack current: (a) oxygen excess ratio; (b) stack voltage is small. The results mean that the proposed controller have some advantages in regulating oxygen excess ratio such as rapidity and accuracy over other methods under different stack currents. 4.2 Variable Oxygen Excess Ratio Control
5. CONCLUSION
In order to reduce parasitic power consumption and obtain efficient PEM fuel cell system performance, the variable oxygen excess ratio λO2 should be considered. Meanwhile, λO2 set-point value from 1.7 to 2 is derived according to stack current variation, as shown in Fig. 11. Certainly, the proposed SFPID controller is tested for tracking the variable λO2 .
In this paper, a reduced fourth-order model of PEM fuel cell is established to depict the air flow dynamic behavior of the air supply system. Then, a SFPID controller based on the control-oriented nonlinear model is proposed to regulate the oxygen excess ratio with on-line fuzzy logic. The different control topologies such as feedforward, PID, PIDFF, and SFPID are compared to validate the advantages of proposed controller when load current suddenly changed in the fuel cell stack. Besides, the proposed SFPID controller is tested for tracking the variable oxygen excess ratio, and the simulation results demonstrate that the proposed
Firstly, the regulation of λO2 with variable set-point value is implemented under the constant stack current which is set to 200A during the entire simulation, and the simulation results are illustrated in Fig. 11. Fig. 11 is revealed the variation of oxygen excess ratio and stack 19
IFAC E-CoSM 2018 20 Changchun, China, September 20-22, 2018 Zhang Fan et al. / IFAC PapersOnLine 51-31 (2018) 15–20
controller is capable of excellent tracking performance in regulating the oxygen excess ratio with different current disturbances. As a future work, the optimal oxygen excess ratio control will be pursued, and the proposed controller will be tested and evaluated in the real PEM fuel cell system.
Transactions on Mechatronics, 19(3), 852–861. Yu, S., Chen, H., Zhang, D., and Guo, H. (2008). Model predictive control for oxygen starvation in air supply system of pem fuel cell. In Control Conference, 2008. CCC, 682–686. Appendix A. A SUMMARY OF PHYSICAL PARAMETERS FOR PEM FUEL CELL
REFERENCES Damour, C., Benne, M., Lebreton, C., Deseure, J., and Grondin-Perez, B. (2014). Real-time implementation of a neural model-based self-tuning pid strategy for oxygen stoichiometry control in pem fuel cell. International Journal of Hydrogen Energy, 39(24), 12819–12825. Daud, W.R.W., Rosli, R.E., Majlan, E.H., Hamid, S.A.A., and Mohamed, R. (2017). Pem fuel cell system control: A review. Renewable Energy, 113. Deng, H., Li, Q., and Chen, W. (2017). Research on hosm observer for oxygen excess ratio estimation of pemfc system. Zhongguo Dianji Gongcheng Xuebao/proceedings of the Chinese Society of Electrical Engineering, 37(17), 5058–5068. Grujicic, M., Chittajallu, K.M., Law, E.H., and Pukrushpan, J.T. (2004). Model-based control strategies in the dynamic interaction of air supply and fuel cell. Proceedings of the Institution of Mechanical Engineers.part A.journal of Power Energy, 218(7), 487–499. Kim, Y.B. (2010). Improving dynamic performance of proton-exchange membrane fuel cell system using time delay control. Journal of Power Sources, 195(19), 6329– 6341. Kunusch, C., Puleston, P.F., Mayosky, M.A., and Prat, M.S. (2009). Advances in hosm control design and implementation for pem fuel cell systems. IFAC Proceedings Volumes, 42(13), 709–716. Ma, Y., Duan, P., Sun, Y., and Chen, H. (2018). Equalization of lithium-ion battery pack based on fuzzy logic control in electric vehicle. IEEE Transactions on Industrial Electronics, 65(8), 6762–6771. Matraji, I., Laghrouche, S., Jemei, S., and Wack, M. (2013). Robust control of the pem fuel cell air-feed system via sub-optimal second order sliding mode. Applied Energy, 104(2), 945–957. Nonobe, Y. (2017). Development of the fuel cell vehicle mirai. Ieej Transactions on Electrical Electronic Engineering, 12(1), 5–9. Pukrushpan, J.T., Stefanopoulou, A.G., and Peng, H. (2016). Control of fuel cell breathing: Initial results on the oxygen starvation problem. Control Systems IEEE, 24(2), 30 – 46. Pukrushpan, J.T. (2003). Modeling and control of fuel cell systems and fuel processors. Dissertation Abstracts International, Volume: 64-02, Section: B, page: 0925.;Chairs: Anna Stefanopo, 18(3), 594–6. Suh, K.W. (2006). Modeling, analysis and control of fuel cell hybrid power systems. Talj, R., Ortega, R., and Astolfi, A. (2011). Passivity and robust pi control of the air supply system of a pem fuel cell model. Automatica, 47(12), 2554–2561. Tong, S., Fang, J., and Zhang, Y. (2017). Output tracking control of a hydrogen-air pem fuel cell. IEEE/CAA Journal of Automatica Sinica, 4(2), 273–279. Wang, Y.X. and Kim, Y.B. (2014). Real-time control for air excess ratio of a pem fuel cell system. IEEE/ASME
Table A.1. Parameters of PEM fuel cell model (x ) ¯
c1 =
RTst kca,in MO2 Vca ¯ st RT Vca
O2,atm
c2 = psat
1+watm
c3 = c 5 = M N2 c7 = c9 =
c 4 = M O2 c6 = Mv psat c8 =
c11 = patm ηcm kt Jcp Rcm 1 ηcp
c13 = c15 =
CD AT c17 = √ ¯
c19 = c21 =
(
RTst
2 γ+1 1 Rcm
(
¯ st kca,in 1−xO2,atm RT MN2 Vca 1+watm C T c10 = Jp ηatm cp cp c12 = γ−1 γ ¯ c14 = M RTatm a,atm Vsm
¯ st n RT 4FVca ηcm kt kv Jcp Rcm
√
)
c16 = kca,in 2γ γ−1
c18 =
γ ) γ−1
1
CD AT c20 = √ γ2 ¯ RTst
c22 = kv
xO
2,atm c23 = kca,in 1+w
atm
1 γ
(
c24 =
nMO2 4F
(
2 γ+1
γ+1 ) 2(γ−1)
)
Ma,atm = yO2 ,atm MO2 + 1 − yO2 ,atm MN2 xO2 ,atm =
yO ,atm MO2 2 Ma,atm
watm =
ϕatm psat Mv Ma,atm patm −ϕatm psat
Table A.2. Simulation parameters of PEM fuel cell system n ¯ R Patm Psat Tatm Tst ϕatm Cp γ MO 2 MN2 Mv Jcp kt Rcm kv ηcp ηcm Vsm Vca kca,in CD AT yO2 ,atm F
20
Number of cells in full-cell stack Universal gas constant Atmospheric pressure Saturation pressure Atmospheric temperature Stack temperature Average ambient air relative humidity Constant pressure Specific heat of air Ratio of specific heat of air Oxygen molar mass Nitrogen molar mass Vapour molar mass Compressor inertia Motor parameter Compressor motor resistance Motor parameter Motor mechanical efficiency Compressor efficiency Supply manifold volume Cathode volume Cathode inlet orifice constant Cathode outlet throttle discharge coefficient Cathode outlet throttle area Oxygen mole fraction Faraday constant
381 8.3145 J/mol/K 101325Pa 47076Pa 298K 353K 0.5 1004J/kg/K 1.4 32 × 10−3 kg/mol 28 × 10−3 kg/mol 18.02 × 10−3 kg/mol 5 × 10−5 kgm2 0.0225(Nm)/A 1.2Ω 0.0153V/(rad/s) 0.98% 0.8% 0.02m3 0.01m3 0.3629 × 10−5 kg/s/Pa 0.0124 0.002m3 0.21 96485C/mol