WSEAS TRANSACTIONS on SYSTEMS

reduced to zero and ISG offers total driving

torque. If ^{λ }were lower than about 0.2, torque of ICE should be increased to its high efficiency

λ area and draws ISG to charge for FESS. If

were between 0.2 and 0.4, torque distribution depends on the actual drive cycle and both operating areas of ICE and ISG should be optimized to reduce fuel consumption to the greatest extent.

The variety of energy flows can be described by ‘IF-Then’ sentences in the fuzzy logic controller, which is also called the fuzzy rules. All the fuzzy membership functions and the control surfaces of fuzzy rules are presented by Fig.9.

Define the total number of fuzzy rules as K. The three fuzzy inputs “Vehicle torque factor”, “rotary speed” and “energy storage state” for

each fuzzy rule are denoted as

A, B,C

while

the two fuzzy outputs “ICE torque factor” and “ISG torque factor” for each fuzzy rule are

d

e n o t e d

as

β α , ~ ~

.

T h u s

th

e process o

f f u z z y

calculation can be expressed as follows: 1) Fuzzification: The three fuzzy inputs are computed by the membership functions (Figs.9) and can also be expressed as:

( ) { } ( ) { } ( ) { } ⎪ ⎪ ⎪ ⎪ ⎨ ⎧ ∈ ∈ − − ∈ h i g h V e r y H i g h M i d d l e L o w l o w V e r y C H i g h M i d d l e L o w l o w V e r y B A k k k C B A _ , , , , _ , , , _ 6 , 5 , 4 , 3 , 2 , 1 , 0 , 1 , 2 μ μ μ

(10)

2) Rules matching: Degree of fulfillment for the antecedent of each rule is computed by fuzzy logic operators that determines to which degree the rule is valid. The valid degree is given as follow: negative torque to regenerate barking energy; Under situation when vehicle runs at certain velocity, the energy flow depends mainly

on the energy storage state higher than

λ

. If

λ

were

ρ_{k }= min(μ_{Ak }(A), μ_{Bk }(B ), μ_{Ck }(C ))

(11)

## ISSN: 1109-2777

Jianhui He, Guoqiang Ao, Jinsheng Guo, Ziqiang Chen, Lin Yang

3) Fuzzy Inference: The “If–then” sentences are represented and the step (2) is used to modify the consequent of rules accordingly. For each fuzzy output, results of the inference steps are combined into a single value by equations as follows:

( ) ( K ) ( ) ( ) ⎪ ⎪ ⎩ ⎪ ∑ ∑ ρ ⎪ ⎨ ⎧ = = k ~ k ~ ~ k =1 K ~ ~ ~ ~ ~ β μ β μ ρ α μ α μ β β α α (12) k k k =1

4) Defuzzification: The centroid method is chosen for defuzzification, through which the accurate fuzzy output values are got according to equations as follows:

( ) ( ) ( ) ( ) ( ) ( ) ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ = = = = ∑ ∫ ∫ ∫ ∑ ∫ ∫ k k d d d d k k ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ k=1 K k=1 K ~ ~ ~ ~ ~ β β μ β β β μ β β β β α α μ α α α μ α α α α β β β α α α

K

k=1

# K

k=1

( ) ∫ k d k ~ ~ ~ α α μ ρ α

( ) ∫ k k ~ ~ ~ β β μ ρ β

(13)

Fig.9 Structure of fuzzy logic controller with all fuzzy membership functions and control surfaces of fuzzy rules presented

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Issue 5, Volume 8, May 2009