Hybrid Adaptive Control for PEMFC Gas Pressure

This paper addresses the issues of nonlinearity and coupling between anode pressure and cathode pressure in proton exchange membrane fuel cell (PEMFC) gas supply systems. A fuzzy adaptive PI decoupling control strategy with an improved advanced genetic algorithm (AGA) is proposed. This AGA s utilized to optimize the PI parameters offline, and the fuzzy adaptive algorithm s used to adjust the PI parameters dynamically online to achieve the approximate decoupling control of the PEMFC gas supply system. According to the proposed dynamic model, the PEMFC gas supply system with the fuzzy–AGA–PI decoupling control method was simulated for comparison. The simulation results demonstrate that the proposed control system can reduce the pressure difference more efficiently with the classical control method under different load changes.


Introduction
The energy and environment crisis in the 21st century has given impetus to the emergence and development of renewable energy systems [1]. Increasing research and application of renewable energy has become an inevitable global trend. For example, the European Union (EU) set the goal of a low-carbon society in the early 2000s. Data for the EU and for individual EU members show that Germany and France have adopted investment incentives to promote renewable energy, while Denmark and Spain succeeded in structuring their renewable energy sectors [2]. Fuel cells (FC)-as highly efficient and environment-friendly power generating devices that directly convert chemical energy into electric energy-are high-tech devices that can provide a sustainable source of electrical power. The proton exchange membrane fuel cell (PEMFC) is the fifth generation of FCs, and considerable advances achieved in PEMFC technology have made it a promising clean energy technology. PEMFCs not only can complement solar energy, wind energy, and other renewable energy sources, but also have the advantages of low operation temperature and low environmental pollution, flexible use, etc. [3]. PEMFCs are suitable for portable power, hybrid electric vehicles, distributed power stations, and other applications. For example, in 2014, the automobile company Toyota launched Mirai, the first hydrogen fuel cell car, which performed well commercially. Mirai has excellent performance and zero pollution and marks a significant milestone in the technological progress of hydrogen fuel cell vehicles. In summary, PEMFCs have good prospects for commercial development.
Despite these successes, there remain many challenges, such as low safety and reliability, high cost, and short lifetime [4]. For example, the challenges of stability and safety have to be overcome for the popularization and application of PEMFCs. One important reason for these challenges is that the thin proton exchange membrane is subject to tremendous fluctuations in pressure difference between the anode and cathode due to variations in operating conditions and load changes in automotive applications [5]. Thus, it is necessary to strictly regulate gas pressures to protect the thin proton-exchange membrane and to avoid explosion hazards [6,7]. In the last few years, pressure difference control has been extensively studied. A nonlinear PEMFC gas supply system mathematic model was proposed and validated [8,9]. Based on this model, a control of pressure difference between the cathode and anode was proposed by applying a nonlinear control method based on feedback linearization. Imad et al. [10] proposed a second-order sliding mode multi-input, multi-output control based on a twisting algorithm to regulate the gas pressure on the anode and cathode sides of the PEMFC. Ebadighajari et al. [11] used a model predictive control approach to regulate the pressure difference. Li et al. [12] designed a nonlinear H∞ suboptimal output feedback controller and verified the disturbance rejection ability of the controller. Chen et al. [13] formulated a controller framework related to the common rail theory wherein input disturbances were rejected. An et al. [14] applied a generalized predictive control method to gas supply systems. Their control strategy was validated by comparison with the PID controller. Li et al. [15] studied the effect of pressure differences on the properties of a PEMFC stack and proposed a simple gas pressure control structure based on the PID controller.
However, most of these control methods require complex mathematical operations and are dependent on mathematic models. For better dynamic performance and adaptability to changeable operation conditions and frequent load variation, a model-independent and adaptive control strategy is necessary. This paper proposes a hybrid adaptive control strategy in which the advanced genetic algorithm (AGA) and fuzzy adaptive proportional-integral (PI) algorithm are combined to minimize the pressure differences between the supplied hydrogen and air. Therefore, PEMFC stack systems can be protected under complex operation conditions. The paper is organized as follows. Section 2 presents the PEMFC gas supply system model and a brief analysis. Section 3 presents the design procedure of the fuzzy-AGA-PI decoupling control in detail. Section 4 describes the evaluation of the performance of the proposed strategy for varied load changes as inputs and compares the strategy with the classical nonlinear control method. Finally, the conclusions are provided in Section 5.

PEMFC Gas Supply System Model
The common PEMFC gas supply system structure is shown in Figure 1. Pressurized oxygen (air) is provided to the humidifier for full humidification after regulation by a gas flow controller, and then it is transferred to the cathode channel of the PEMFC to participate in electrochemical reactions. The hydrogen supply route is similar to its oxygen counterpart, except that no compressor is needed for hydrogen given that it comes from a high-pressure hydrogen tank. To simplify the dynamic PEMFC model, the following assumptions were made.

1.
The gases are ideal.

2.
Regarding water management, liquid water stay in the fuel cell and will evaporate to both sides of PEMFC if the humidity become unsaturated [16].

3.
The PEMFC stack humidity and temperature are assumed constant because of the slow response time [17].

4.
Hydrogen is pure (99.99%), and the air contains a mixture of nitrogen and oxygen in a ratio of 2:8.

5.
The Nernst equation is applied.
According to the law of conservation of matter and the ideal gas equation, a PEMFC state equation in the anode can be derived as shown in (1) and (2) [8]: The PEMFC state equations of the cathode are given in (3)- (5): Further, the voltage of the PEMFC stack follows (6): where Classically, the water transient flow rate H 2 O c through a membrane is a function of the stack current and humidity. In this study, H 2 O c is the function of current only: H 2 Omem = C 1 Ifc because we assumed that the humidity is constant with a membrane-average water content.
The nomenclature is provided in Table 1.
The initial mole fractions of hydrogen, oxygen and nitrogen, respectively / Based on PEMFC state in Equations (1)- (8), H 2 in and O 2 in are the input variables; P H 2 and P O 2 are the output variables; and Ifc is the disturbance variable. The MIMO system can be described by Equation (9): In the presented model, which is based on Equations (1)-(8), the gas systems of the anode and cathode are coupled to obtain a complex system. In a PEMFC power generation system, the pressure and flow of the reaction gas in the PEMFC change with changes in the load [9]. To prevent damage to the membrane, the pressure difference should be minimized [18]. In addition, the performance of the PEMFC is a function of the gas pressure, which has a non-negligible influence on the FC performance [19]. Hence, it is desirable to adjust the partial pressures at the cathode and anode to stabilize at the set value, via an effective method, such as the decoupling control method, to avoid unwanted pressure fluctuation and reduce the pressure difference between the anode and the cathode when the PEMFC stack experiences large and frequent changes in the load.

Fuzzy-AGA-PI Decoupling Control Design
To achieve better decoupling control, an indirect decoupling algorithm was adopted, and the fuzzy subspace was decomposed based on the multivariable fuzzy rules. The fuzzy control algorithm is enforceable in a time-varying system or a pure hysteresis nonlinear system [20], including the complex PEMFC model, because it does not depend on the control object model. By combining the fuzzy adaptive algorithm with the AGA-PI control algorithm as done in the proposed feed-forward decoupling control system, the hydrogen gas pressure loop and oxygen gas pressure loop can be controlled to achieve the dynamic decoupling compensation of PI control parameters so that the coupled loops can be treated as two equivalent single loops. The hybrid adaptive fuzzy-AGA-PI decoupling control system of the PEMFC gas supply system is shown in Figure 2. First, the parameters of the PI controller were optimized by AGA. Then, the error e and the change in the error, ec, were the input variables for the fuzzy controller [19]. The fuzzy controller was run online to adaptively adjust K p0 and K p1 of the AGA-PI controller by outputs ∆K p and ∆K i , which obey the designed fuzzy rules.

AGA-PI Control Algorithm Design
First, an AGA was utilized to optimize the parameters of the PI controller offline and to improve the control performance of the pressure difference between p H 2 and p O 2 .
The traditional PID controller is still widely used in industrial process control because of its simple structure, strong handling ability, and great robustness. The PID controller has three parameters, Kp, Ki, and Kd. Kd is the differential of error with time, and it has a function of advanced control. Kd is not suitable for the PEMFC gas supply system because the pre-control will result in the abrupt change of pressure with changes in the load. Hence, PI control was chosen instead of PID control in this study.
The genetic algorithm (GA), which is a stochastic global search method based on the principle of natural selection and evolution, is frequently used in many engineering applications to find solutions to optimization problems. The heuristic search of GAs is based on the principle of survival of the fittest [21]. GAs start the optimization process with an initial random population. The objective function is the function responsible for assigning the fitness value to each member of the population. Individuals that represent better solutions are awarded higher fitness values, and thus, they survive for more generations. The successive generations of the population are created by the genetic operators reproduction, crossover, and mutation to yield better solutions to achieve the optimal solution to the problem. The above steps are repeated until the predetermined criteria are met. However, the traditional GA is likely to fall into local optimum solutions and cannot obtain globally optimal solutions [22]. In this study, the basic GA was improved to avoid the local optimum, and a simulated annealing algorithm was added to execute the local searching operation to obtain the advanced genetic algorithm (AGA) [23]. A flow chart of the proposed AGA control is shown in Figure 3. The main parameters defined in AGA control include the population size M, iteration number G, crossover probability Pc, and mutation probability Pm [24]. There is no theoretical definition for selecting the aforementioned parameters, although the empirical range of parameter settings has been reported by some researchers. Floudas et al. [25] studied the influence of parameters on the performance of GA systematically and proposed a set of widely applied standard parameters. Laoufi et al. [26] discussed the definition of parameters in detail and presented a general range of M, G, Pm, and Pc. The parameters chosen in this study were based on the cited publications and were combined with the simulation results. Thus, the following values were obtained: For realizing a better system dynamic response, the integral of time and squared errors (ITSE) should be minimized, i.e., the objective function is as shown in Equations (11): (11) where t is running time of the system and e(t) is the deviation between the input and the step response of a unit function response of the system. According to the presented optimization strategy and parameters settings, the AGA was programmed to optimize the parameters of the PI controller. After 100 generations of evolutionary search, the AGA converged, and the optimization result was obtained based on the model indicated by Equations (1)- (8). The results are as follows:

Fuzzy-AGA-PI Decoupling Control Design
The hybrid adaptive fuzzy-AGA-PI decoupling control is an improvement on the AGA-PI controller. It can realize adaptive control by adjusting the optimized PI parameters online with multifarious loading changes. The design process of the fuzzy controller involves three main steps: fuzzification, fuzzy inference, and defuzzification [27].
As shown in Figure 2, the input values of the fuzzy controller are e and ec, and the output values are ∆K p and ∆K i (see Equations (12)- (14)): where e is the absolute value of the difference between p x and p re f x ; x is H 2 or O 2 ; ec is the variation rate of e; K p0 and K i0 are the initial values of the parameters; and K p and K i are the parameters of AGA optimized PI controller changed by the fuzzy adaptive algorithm.
The adapted triangular membership function can be described as shown in Equations (15) [28]: where a, b, and c are the constants of the fuzzy domain. The ranges of inputs and outputs are defined according to the simulation outputs of the AGA-PI control system and experiments. These ranges are listed in Tables 2 and 3. The rule tables are provided in Tables 4 and 5. Seven membership functions are used for the inputs and outputs: negative big (NB), negative middle (NM), negative small (NS), zero (Z0), positive small (PS), positive middle (PM), and positive big (PB). The fuzzy rules are designed in accordance with the given PEMFC gas supply system, e.g., the surface values listed in Table 4 for the anode are shown in Figure 4. For the same control effect, the algorithm complexity of time and space are reduced by removing the fuzzy inferences on the negative part of e according to (12).

Simulation Results
The proposed hybrid adaptive fuzzy-PI decoupling control was tested by using MATLAB/Simulink. For simplicity, the fuel processor, water and heat management, and air The weighted averages method can be described as shown in (16): (16) where Z 0 is the numerical value, Z i is the membership value, and µ c (Z i ) is the fuzzy variable.

Simulation Results
The proposed hybrid adaptive fuzzy-PI decoupling control was tested by using MATLAB/Simulink. For simplicity, the fuel processor, water and heat management, and air compressor models were not considered in the simulation.
The aim of the controller is to minimize the pressure difference between the anode and cathode by maintaining the pressure at the set point. Because of the assumption that oxygen accounts for one-fifth of the air, the setpoint gas pressure of hydrogen and oxygen were maintained at 3 and 0.6 atm, respectively (1 atm = 0.1 MPa), under irregular load variations; thus, the pressure difference between the cathode and anode was minimized [8]. Experimental data reported by Hamelin et al. [29] were used for validating the presented dynamic PEMFC model. The nominal values of the simulation parameters are listed in Table 6. The response curves of the pressure in the anode and cathode corresponding to the load changes shown in Figure 5 are shown in Figures 6 and 7, respectively, corresponding to the fuzzy-AGA-PI control system and classical nonlinear control system. It is noteworthy that the output voltage improvement is not evident in Figure 6, due to the logarithm function between voltage and gas pressure, small pre factor (RT/2F), and fast response time. However, other simulation results in Figure 7a,b show that the proposed control strategy has a significantly better transient response than the classical nonlinear control; hence, the proposed strategy can maintain the gas pressure at an ideal value more efficiently as a whole.   Furthermore, five representative moments of changes in the load were selected for a detailed analysis. They are the start, the moments when the load decreases or increases slightly, and the moments when the load decreases or increases considerably. The moments are shown in Figures 8-10.   As shown in Figure 8, the fuzzy-AGA-PI adaptive control performs considerably better in terms of the wave stability of gas pressure in the gas supply system of the PEMFC when the PEMFC operation is started. The pressure difference is as high as 0.78 atm, which poses a safety risk for the proton exchange membrane [30]. However, the proposed control strategy reduces the gas pressure to less than 0.016 atm because of its adaptability and approximate decoupling. Figure 9 shows the responses of gas pressure difference when the load changes slightly. The fuzzy-AGA-PI control can reduce the overshoot to 45% and 50% compared to nonlinear control but needs a longer adjusting time. However, the fuzzy-AGA-PI control system can provide better protection against high pressure differences than possible with the nonlinear control system from the viewpoint of the application.
The fuzzy-AGA-PI control is still valid even under large changes in the load, e.g., increase and decrease by 4 Ω, as shown in Figure 9. The proposed control decreases the overshoot to 30% and 42% relative to the nonlinear control under two operation conditions and requires a shorter convergence time.
In conclusion, the simulation results show that the hybrid adaptive PI control system has better response characteristics than the classical nonlinear control regardless of small or large changes in the load, especially at the time of starting of the PEMFC operation. Therefore, the fuzzy-AGA-PI control can reduce the pressure difference between the cathode and anode in runtime PEMFCs more efficiently.

Conclusions
A hybrid adaptive PI decoupling control-more specifically, a fuzzy adaptive PI decoupling control based on optimization by the AGA-is proposed to achieve the nonlinear and approximate decoupling control of a PEMFC gas supply system. Comparison of the simulation results obtained using the proposed and the classical nonlinear control methods shows that the proposed control strategy not only can deliver smooth static tracking for setting the pressure, but also can improve the dynamic performance under various load changes. According to the requirements of practical PEMFC applications, the proposed control strategy can improve the FC performance and protect the proton membrane from damage caused by pressure differences. Because of its excellent control effect and wide adaptability, the presented hybrid adaptive PI decoupling control strategy can also be applied to the other components of PEMFC systems, including the control of water and heat management, air compressor, and fuel processor.