Fuzzy Double Model Control for Air Supply on a PEM Fuel Cell System - Intelligent Computing for Sustainable Energy and Environment - page 395

P a,cain = P cain − P v,cain . (7)

With φ ca,in describes the relative humidity of air at the cathode inlet, and p sat | T
represent the vapor saturation pressure for temperature T [12].
In a real-time system, the size of the compressor outlet/cathode inlet compli-
cates the installation of a pressure sensor and converts the cathode inlet pressure
measuring into a dicult task. Therefore, a mathematical model which is used to
express the pressure P a,cain as a function of air flow rate W cain and the current
I has been used[13]
P cain =1 . 0033 + 2 . 1 10 − 4 I. (8)

The air flow rate W cain depends on the voltage V com applied to the compressor
motor and the model can be described as the following transfer function:
P com =0 . 1 / (0 . 01 s 2 +0 . 14 s +1) . (9)
It is clearly that the oxygen excess ratio depends on the oxygen consumption
w O 2 ,react and the oxygen mass flow rate w O 2 ,cain . And the oxygen consumption
cannot be influenced as it depends only on the measurable disturbance current
I ,asthe M O 2 , n and F are constants. So the regulation of the oxygen excess
ratio λ O 2 has to be carried out by manipulating the oxygen mass flow rate which
is regulated to the air flow rate. Hence, the compressor motor voltage V com will
be used as input signal in order to regulate the oxygen excess ratio λ O 2 .

10 − 4 W cain − × 4 . 757 ×

2.3 Control Object
As already mentioned above, the regulation of the oxygen excess ratio λ O 2 is
important in the fuel cell control, both for performance and safety. Tests showed
that the oxygen starvation can reduce the performance of fuel cell, even causing
the damage of the electro-catalyst [14]. To avoid this negative factor, the oxygen
excess ratio has to satisfy λ O 2 > 1, it means the mass of oxygen supply should
greater than the consumption.
Several experiments have been carried out in order to choose a suitable oxygen
excess ratio value to prevent the stack oxygen starvation and keep the fuel cell
working at the high eciency level. The experiment results show that the output
power for a certain current will increase along with the oxygen excess ratio until
reaching a maximum point. And in our work, a control objective of oxygen excess
ratio is chosen to λ O 2 ref = 4 through consulting the work [15]. This value can
be considered as a tradeoff between eciency and safety.

3 Fuzzy Double Model Control Design for Oxygen Excess
Ratio

This section presents the design of a double model controller based on the fuzzy
rules switching to regulate the oxygen excess ratio. First, we design a fuzzy con-
troller and a PID controller, and then a switching method between two control
strategies based on fuzzy rules in the double controller is proposed.