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3.1 Fuzzy Control and PID Control Design for Oxygen Excess
Ratio
The gas supply in the PEM fuel cell is the nonlinear and time-varying parameters
system. And the system parameters and control effect would be impacted by the
slight perturbation of sensors which is used to measure the air flow rate and
load current. Hence, a controller with strong robust performance is needed, and
the fuzzy control strategy is suitable for controlling this process. However, the
process with fuzzy control has the steady state error. So it is necessary to join
the integral elements to eliminate the steady state error, and the PID control
strategy is considered naturally.
Fuzzy Control Design.
In this work, the deviation
e
and deviation ration
ec
between the actual output and setting value are used to be the inputs of the
fuzzy controller, and the controller output
u
fuzzy
is the voltage of compressor.
e
(
k
)=
λ
O
2
,ref
(
k
)
−
λ
O
2
(
k
)
.
(10)
ec
(
k
)=[
e
(
k
)
−
e
(
k
−
1)]
/T
s
.
(11)
where
T
s
is the sample time. The actual range of
e
and
ec
is [-4, 4] and [-40, 40],
which can be converted to [-1, 1] by multiplying the factors. The output range is
[-80, 80]. The fuzzy subsets of input is NB, NM, NS, ZO, PS, PM, PB, and the
output fuzzy subsets is NB, N, ZO, P, PB. The basic form of fuzzy control rules
is: ”If the deviation
e
and the deviation ration
ec
is A and B, Then the fuzzy
control output is
u
fuzzy
.” The fuzzy control rules are obtained by Figure 2.
e
u
Fuzzy
NB
NM
NS
ZO
PS
PM
PB
NB
NB
N
N
P
ZO
ZO
ZO
NM
N
N
N
ZO
ZO
ZO
P
NS
N
N
ZO
ZO
ZO
ZO
P
ec
ZO
N
ZO
ZO
ZO
ZO
P
P
PS
N
ZO
ZO
ZO
ZO
P
P
PM
ZO
ZO
ZO
ZO
P
P
P
PB
ZO
ZO
ZO
N
P
P
PB
Fig. 2.
Fuzzy rules table of the fuzzy controller. Each entry is in the format of fuzzy
control output
u
fuzzy
with respect to the devision
e
and devision ration
ec
.
PID Control Design.
The key of the PID control design is to select the
appropriate PID controller parameters. Firstly, the mathematical model of the
oxygen supply process can be identified by the least squares method, and then
we could get the suitable parameters of PID controller by suboptimal reduction
algorithm [16] and PID parameters setting algorithm described in work [17].
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