This Polymer Electrolyte Membrane (PEM) fuel cell system.

This paper reviews some of the designs of an air
flow controller which in turn maximizes the net power output in a Polymer
Electrolyte Membrane (PEM) fuel cell system. Experimental results show that the
performance and the power output of fuel cell depends upon gas flow rate, operating
and fuel stack temperature, humidity and pressure. However net power production
of the fuel cell depends heavily on the oxygen excess ratio in the cathode. A
time-varying and a complex non-linear dynamic system present many challenges to
design a oxygen and hydrogen excess ratio to an optimum value that maximizes
net power output over a wide range of operating conditions. Performance
improvement can be done using two modelling approaches: black box modelling and
detailed dynamic modelling. A fuzzy-PID (Proportional Integrator
Differentiator) hybrid controller and a DC-DC controller have been designed and
tested earlier. The results show that these control strategies can be used to
improve the system’s performance significantly. The control system performance
was determined by comparing the simulated results and flow rate obtained using
fuzzy logic controller. External voltage was kept constant and fuzzy-PID shows
better response than a manual controller.



1.     Introduction

 Fuel cell
technologies have been identified as a potential solution in solving the
problems of meeting increasing renewable energy demands. Fuel cells transform
chemical energy into electricity. Hence, it is an environment friendly energy
resource. Mitigation of environmental pollution and providing energy shortage
has led to fuel cells being considered as elements of alternative energy
system; capitalizing on high efficiencies and low emissions. Fuel cells can
provide large amounts of current hence power, with the thermodynamic
requirement being the appropriate flow of reactants. There are several types of
fuel cells, each using a different chemistry. PEMFC is commonly used to power
vehicles. Its performance and efficiency still needed to be improved, and the
issues of cost, reliability, it is necessary to learn more about   the mechanism that causes the performance loss,
such as non-uniform concentration, current density distributions, high ionic
resistance due to dry membrane, or high diffusive resistance due to flooding on
the cathode. Flow field will require optimum design to achieve high reliability
and performance.

performance of fuel cell and vehicle applications they are embedded into depend
on a delicate balance of the incorrect temperature, humidity, reactant
pressure, purity and flow rate. Thus, its clear that the performance of the
system depends upon the controller in place. For practical applications an
accurate controller model is required. Study of control oriented design and
power management is required for the understanding of system behavior, and for
subsequent design and analysis of model based control system 3.

Fuzzy control is one of the useful control
techniques for uncertain and ill-defined non-linear systems. Fuzzy logic based
controller has high performance and other numerous advantage. The most
important aspect being, the cost of the controller design and implementation. The
proposed hydrogen flow controller modify control active current to the load
change and setpoint current for controlling to the load 1. A proper
air-supply system is important for a PEMFC 4. Excess oxygen content in
cathode may lead to power loss and decreases net power output/efficiency. Also,
if there is oxygen starvation in the cathode it would lead to deterioration.
The electrode half reactions are as follows:

   H2 (a)                   2H+ + 2e-            

            Cathode:       2H+
  + 2e-                  H2

            Overall:    H2 (a)               H2 (c)

5 previously designed a model-based controller that lacked experimental
support whereas Feroldi 6 proposed a coordinative control strategy that
regulates air flow replenishment and air exiting the system simultaneously.
This shows both oxygen excess ratio and cell voltage are under control. Pukrushpan
7, 8 presented a system with transient behavior of air supply system which
was a single input single output feedback controller. This feedback controller
provided a stoichiometric air ratio. A semi-empirical model was used.

       A complex, non-linear and time-varying air
flow system can be approximated using principles like mass conservation,
theories of thermodynamics, fluid dynamics and heat transfer. Golbert and Lewin
9 have already developed a time varying model with its state space matrix,
did its controllability analysis and then presented an adaptive nonlinear
controller. Stefanopoulou and Suh 10 modelled and analyzed a DC-DC converter
with a compressor. This design was done considering the dynamics of fuel cell
system. This converter is employed in a model-based control techniques to tune
two separate controller for the compressor and the converter. They also
demonstrate the lack of communication and coordination between the two
controllers. This leads to a tradeoff in achieving the power output objectives.

       A PEMFC includes a number of components that
are related to controlling the flow, temperature, pressure and humidity. A
DC-DC converter transforms unregulated DC power to a regulated one as it is
focused on soft voltage sources that a fuel cell involves. This can also be
used to filter current from the fuel cell which could lead to degradation or
fuel cell failure. Though limiting the current drawn from the fuel cell
enhances the performance of the fuel cell but it degrades the voltage
regulation performance of the DC-DC converter. A physics based model was
developed in which hydrogen dynamics, humidity and temperature dynamics are
neglected as they are slower than the air flow dynamics. The importance of air
supply arise due to its parasitic loss.







2.     Fuel Cell System Models

       This section describes the fuel cell
system model developed by various people in their experiment and analysis.


2.1 Extremum seeking controller

This model 5, 8 is used for the analyzing the impact of oxygen supply,
temperature, and water content on power output. The model described manifold
filling dynamics, compressor inertia and partial pressures. The components that
the system has are fuel cell stack, a compressor, manifolds (cathode and
anode), on air cooler and a humidifier. There are nine state variables whose
governing equations can be classed into both manifolds and the compressor.
Conservation of mass and energy laws make the governing equations in the manifolds
whereas inertial dynamics of motor and compressor make up for the governing
equations in compressor. The state equations formed in the cathode are as


Using conservation of mass of water at cathode

The state equations formed in
anode manifold are as follows:


The compressor supplies the air
to the cathode that consumes the energy from thr motor which is generated from
the fuel cell. Mass flow rate of the air is determined by the inertial




2.2 Fuzzy control of Fuel Cells

       The components of a typical fuel cell
include gas diffusion layer, fuel stack, catalyst layer, membrane etc. The
redox reaction involved in the process is as follows:

H2                2H+   +   2e-

  Reduction     O2   +   4e-   +   4H+                  2H2O

        Electrical energy is obtained from the system
when a significant amount of current is drawn, but the actual cell potential is
decreased. There are several irreversible losses present in the actual fuel
cell system. These losses are called overpotential or polarization. These
originate from three sources namely activation, ohmic and concentration.
Activation dominant at low current density, ohmic varies directly with current
and increases with it over the range of current density. Concentration
overpotential lies at the higher range of current density where the cell
voltage is at a minimum.

closed loop feedback control system is used for actuating error signal. The
difference between input and output signal is termed as error. The feedback is
fed to the controller basically containing a proportional or an integral or a
derivative or a combination of pair of controllers. Thomya and Khunatorn
proposed a fuzzy logic controller that controls the active current from the fuel
cell by controlling the flow rate of hydrogen. A typical fuzzy controller
consists of five different steps involving:

Defining the input and output variables

Designing the fuzzy control loop




the inputs are error e(k) and change in error ce(k). The controller output
is called as ‘Read Current’. The relation between these variables is as

e(k) = set point current – read current

where, read current is the hydrogen flow rate
from the feedback loop which is proportional to terminal load and ?Uk
is referred to as change of duty ratio by fuzzy controller.

Ce(k) = e(k) – e(k-1)

variables are expressed as PB (positive big), ZO (zero) and NB (negative big).
Rules for writing the fuzzy variables are in table 1. For example:

If e(k) = PM and ce(k) = ZO, then u(k) will be

If e(k) = NB and ce(k) = PM, then u(k) will be

defuzzification method gives the output from the center of gravity of the
output. A membership function is set up to test controller design.


2.3 Adaptive control strategy

fuel cell used in the experimentation by Zhang, Liu, Yu and Ouyang is a
membrane-humidifying PEMFC with an active area of 150 cm2, 24 Nafion
112 cells in series and 1kW power output operating at a temperature of 65ºC and
a pressure of 30kPa. There are majorly four control subsystem that are used
now-a-days, which are air/hydrogen supply, the humidity of reactants, stack
temperature and power output. The humidifying membrane allows the gas to have
sufficient contact with the saturated vapor. This makes the humidifier that
much more important. A cooler is added to remove excessive heat during the
reaction. A proportional controller tracks with the pressure in the cathode and
anode. Some assumptions are made before modelling the air-supply subsystem.
These are (1) gases obey the ideal gas laws that is due to operation of the
system at the low pressure (2) coolant carry away the generated heat due to
relatively small volume of the stack. (3) properties of the gas remain same at
the inlet and outlet of the cathode (4) gas in cathode is fully humidified (5)
extra water carried out by exhaust gas (6) flow channel and diffusion layer
lumped as a single volume (7) gas pressure in the air tank kept constant.

gas flow regulator was designed by them that replenishes air into the stack
cathode. The input and output variables for the air regulator varies with
temperature, electromagnetism, humidity and gas pressure. Non-linearity is
obvious with the system and has an influence on the dynamics of the airflow and
can be assumed as time varying. This has a very complex design method that
involves a lot of solving of partial differential equations. To optimize the
performance of the air supply sub system an adaptive controller is used. This
controller helps to alleviate the dynamic variation that arise from varying
time. This involves placement of closed loop poles keeping the desired results
in mind. The operation process involves some goals that needs to be achieved:
(1) quantification of air flow (2) definition of ideal kinetics of cathode air
(3) designing a controller in which the airflow responds to the commands
accurately and dynamically.

reduce the complexity of the design of the digital controller, the model of the
gas flow regulator was designed using a discrete time equation. The air flow is
directly related to power output. Dynamic air flow can be attained using two
methods as done by two groups, Gelfi and Suh-Stefanopoulou, one used the
capabilities of a compressor of a fuel cell system using a blower. The other
used a dynamic coupling between a compressor and fuel cell in which the motor
was driven by fuel stack. This group involved Zhang, Liu, Yu and Ouyang, and
they did three tests of the design of the air flow system designed by them.
They checked the step response in all the tests they did and found out the
stability of the system after drawing the results from the graph.


2.4 DC-DC Convertors  

       Suh and
Stefanopoulou used a fuel cell with an active area of 280 cm2 with
381 cells and a power output of 75kW. This is applicable for automotive and
household purposes. They proposed a fuel cell reactant supply system that
consists of a supply manifold, hydrogen pressure control, an air flow control
and a humidifier cum temperature controller. A PI controller was developed for
the system. They investigated how a DC-DC controller can be used to filter fast
loads (current). It can be used to filter out fast load changes. Model was
designed, and the dynamic states were formed according to the flow rate in
cathode. They considered nonlinear static functions as well to achieve a real-time
situation. The DC-DC converter transforms the fuel stack power to the output
requirements that connects the device. They used a boost converter as it can be
used in PEMFC applications.














3.     Results and Conclusions


3.1 Extremum seeking approach

        The results of a simple static
feedforward (sFF) controller and a static feedforward with a PI (sFF + PI)
controller were compared to evaluate the performance of the extremum seeking
controller proposed by the researcher. The sFF is used to measure the
disturbance input and compute the compressor voltage output. This takes a form
of a typical feedforward compensator which is equal to the inverse of the DC
gain. A PI + sFF is used to measure the stack current. It also adjusts the
motor voltage about the optimal value in the feedforward loop. This approach
has a drawback i.e. the optimal value identified in the lookup table
corresponds to steady state values only. Also, the temperature of the fuel
stack must be 353K with a water content of 14. Only if these conditions are met
the optimality will be guaranteed. Simulation results indicate that the optimal
operating point can account for the time varying and non-linear parameters such
as stack temperature and water content using the compressor voltage online. This
constraint approach allowed them to explicitly set constraints on reactant
oxygen and membrane hydration. That enabled them to select more aggressive
extremum seeking parameters that eventually increased convergence speed with a
satisfactory overshoot. The conditions were defined, and the outcome of the
experiment was that the optimal values were found by the steady state analysis
and the final values were 22.5 kW net power with an oxygen excess ratio of 2.64
and the motor voltage corresponding to these values is 151 V. The net power
output from the extremum seeking approach was more than either the sFF or sFF +
PI at steady state. This indicates that the ES algorithm produces more net
power despite the variations in flow rates, temperature in fuel cell stack and
the non-linearity, the ES produces superior output when compared to both sFF
and sFF + PI.


3.2 Fuzzy Logic Controller






3.3 Adaptive control strategy

could become a vital alternative to internal combustion engine if an enough
power output and the need of load is met. To achieve this all the subsystems of
the fuel cell must function effectively and be dynamically co-operative with
each other. Non-linearity and time varying characteristics are a hinderance
during thus operation. An adaptive control strategy has been proposed by the
researcher to run the air-supply subsystem for air replenishment in cathode.
Some of its findings show that the designed adaptive control strategy could
lead to good system performance and stability. The performance of the system
became better and net power output of the system was increased.


3.4 DC-DC converter

low order fuel cell system model was developed with a DC-DC converter using all
the physical principles mentioned by the researcher along with stack
polarization. They captured the inertial dynamics of compressor, partial
pressure, and manifold filling dynamics. Relation between air supply and in
fuel cell and voltage regulation was developed. A model based controller was
designed to regulate the oxygen excess ratio and the bus voltage using
different methods and architecture. They compared the design on the performance
of the system at different operating conditions (medium to high load range). It
was verified that the linear decentralized controller device can achieve better
results over a wide range of net power.