Constant Power Control of a Proton Exchange Membrane Fuel Cell through Adaptive Fuzzy Sliding Mode

Fuel cell is a device that converts the chemical energy from a fuel into electricity through a chemical reaction with oxygen or another oxidizing agent. The paper describes a mathematical model of proton exchange membrane fuel cells by analyzing the working mechanism of the proton exchange membrane fuel cell. Furthermore, an adaptive fuzzy sliding mode controller is designed for the constant power output of PEMFC system. Simulation results prove that adaptive fuzzy sliding mode control has better control effect than conventional fuzzy sliding mode control.


INTRODUCTION
Due to the environmental problems and energy crisis, fuel cells as pollution-free energy sources have been receiving more and more attention in the recent years.The Proton Exchange Membrane Fuel Cell (PEMFC) as one of the most popular kind of fuel cells has a wide scope of applications such as emergency power supply and small mobile power supply for outdoors power supply and high reliable and high stable power supply (Logan et al., 2010;Hatziadoniu et al., 2002;Padulles et al., 2000).PEMFC has many advantages including low temperature, low electrolyte corrosion, high efficiency (Pukrushpan et al., 2004).
Controller design is the main part in PEMFC as well as the major objectives is stability and robustness.One of the significant challenges in control algorithms is that many parameters such as operating temperatures, pressure and flow rates of fuel and oxidant gases and so on influence the performance of PEMFC (Kaytakoglu and Akyalm, 2007).Many research studies have been carried out on proton exchange membrane fuel cell technology.To date, many linear controllers are designed for PEMFC.The controllers can be implemented easily but it is hard to maintaining a fuel cell system in correct operating conditions when subjected to fast load changes (Riascos and Pereira, 2010).
Adaptive fuzzy sliding mode control Presented in this paper is a method of design by combining adaptive control, fuzzy control and sliding mode control (Mammar and Chaker, 2009;Kunusch et al., 2009).
The method can utilize fuzzy control to overcome the effect of mode inaccuracy and utilize adaptive control to enervate buffeting and overshoot caused by sliding mode control so that it has rapider response characteristic and better steady-state behavior than conventional fuzzy sliding mode control.

Fuel cells are made up of three adjacent segments:
The anode, the electrolyte and the cathode.They transform chemical energy on the anode side into electric and thermal energy on the cathode side.Two chemical reactions occur at the interfaces of the three different segments (Liu et al., 2006;Zhang et al., 2008;Wei et al., 2010;Zhou et al., 2011).Figure 1 shows the basic structure of a single cell.In PEMFC the following chemical reaction exists: In this electrochemical process hydrogen molecules are carried by flow plate channels on the anode side.Anode catalyst divides hydrogen on protons H + and electrons e − .At the cathode hydrogen protons H + and electrons e − combine with oxygen to form water and heat.The semi reactions on both electrodes can be expressed by the following equations (Carnes and Djilal, 2005;Moreira and Da Silva, 2009;Rezazadeh et al., 2010): Modeling of fuel cells is needed as powerful fuel cell stacks are getting available and have to be integrated into power systems.An adequate model can estimate overall performance of a fuel cell according to operating conditions.
The output voltage of a single cell can be defined as the following expression (Mammar and Chaker, 2009): where, E Nermst = The thermodynamic potential of the cell and represents its reversible voltage: where, p H2 and p o2 are the partial pressures of hydrogen and oxygen, respectively and variable T denotes the operating temperature.V act is the voltage drop due to the activation of the anode and cathode: 3 5 O2 4 0.9514 3.12 10 7.4 10 ln( ) 1.87 10 ln( ) where, I stack (A) is the electrical current and c o2 (mol/cm) represents the oxygen concentration in the catalytic interface of the cathode, determined by: 2 2 6 498/ 5.08 10 V ohmic = The ohmic voltage drop results from the conduction of protons through the solid electrolyte and electrons through the internal electronic resistance: ( ) where, R c (Ω) = The resistance to electron flow R m (Ω) = The resistance to proton transfer through the membrane V con = The voltage drop due to the mass transport which can be described by the following expression: max ln(1 ) where, (V) = A parametric coefficient depending on the cell 2 (A/cm ) J = The actual current density of the cell The output power of the single fuel cell can be written as: Fuel cell dynamic model can be set up based on the above described mathematical model.This model can reflect the relationship between the output voltage and current and pressure of hydrogen, oxygen (Rezazadeh et al., 2011;Fan et al., 2012).
An accepted dynamic model of the PEMFC is shown in Fig. 2.

DESIGN OF AN ADAPTIVE FUZZY SLIDING MODE CONTROLLER
In order to overcome the parameter uncertainty and external disturbance, an adaptive fuzzy sliding mode control is presented for constant power output.
In the aspect of control methods, fuzzy control and sliding mode control are different from conventional control theory.Each of them has its advantages and disadvantages.
Fuzzy control can express the amount of ambiguity in human thinking and possess several advantages such as model-free, universal approximation theorem.However, once control rule and coefficient are fixed, fuzzy control cannot well adapt to the change of conditions.
Sliding mode control can yield a closed loop system with an invariance property to uncertainties when the system states are in the sliding mode.But sliding mode control can cause the high frequency when fastening the response of the system.If only simply combining fuzzy control with sliding mode control, chattering brought with sliding mode control can be reduced to some extent.However, this method is still based on experiences; controller parameters do not possess adaptive and self-leaning ability.In addition, overshoot from fast response of the system easily occurs.Motivated by this, an adaptive fuzzy sliding mode controller is proposed.

Construction of the fuzzy sliding mode controller:
The fuzzy sliding mode controller can make the PEM fuel cell keep constant power out put * A switching function ( ) s k is designed as following: Here we use the proportion switching control method to design controller which meets the conditions for the existence of sliding mode.Controller is designed as: The fuzzy domain for s , s  and u ∆ is [-1，1].The triangular type membership function is chosen for the above fuzzy variables.Fuzzy control rule base is shown in Table 1.
In Fig. 3-5, the membership functions for input s , s  and output control u ∆ in the main fuzzy controller are shown.
In this paper, the output control u of the main fuzzy controller is designed as q O2 , which is the input molar flow of oxygen of the PEMFC.It shows the 3dimensional representation of control variable u for fuzzy variable ( s , s  ) is shown in Fig. 6.Construction of the auxiliary adaptive fuzzy controller: Using conventional fuzzy sliding mode control can realize constant power output of PEMFC; however, this control method brings about overshoot when fastening the response of the system.At the same time, the parameters of the controller don't have adaptive and self-learning ability in the process of control.
Here ΔK u (k) is the inferred change of duty ratio by the auxiliary adaptive fuzzy controller.
The triangular type membership function is chosen for error, change of error and output control variable.The fuzzy domain for e, ec is [-1, 1] and for u K is [-10,  10].The fuzzy set for e, ec and u K is {NB, NM, NS, ZE, PS, PM, PB}.The membership functions for input error e, change of error ec and output control u K of the auxiliary adaptive fuzzy controller are shown in Fig. 7 to 9.   The output control K u of the auxiliary adaptive fuzzy controller is the value of proportionality factor in the main fuzzy controller.The fuzzy control rule base of the auxiliary adaptive fuzzy controller is shown in Table 2 and the 3-dimensional representation of control variable K u for fuzzy variables (e, ec) is shown in Fig. 10.It can be seen from these figures that the fuzzy sliding mode controller can modify the oxygen flow to realize constant power output under varying load.The adaptive fuzzy sliding mode controller is characterized by a faster time response and higher precision compared to the fuzzy sliding mode controller.

CONCLUSION
Fuel cells need constant power output when load changes.The adaptive fuzzy sliding mode control described in this paper can not only have fast response characteristic, but also have good steady-state behavior and strong robustness compared with fuzzy sliding mode control.Simulation results indicate that the adaptive fuzzy sliding mode controller is very effective in tracking a given power and guarantees that the fuel cells have constant power output.
Fig. 1: A typical PEM fuel cell

fcP.
The error e(k), the change in error de(k) are given as follows:

Fig. 3 :
Fig. 3: Membership function of s in the main fuzzy controller

Fig. 5 :
Fig. 5: Membership function of u in the main fuzzy controller

Table 2 :
Control rules of the auxiliary adaptive fuzzy controller Ec