Research and Simulation of Electric Power Steering Based on Fuzzy Control

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Research and Simulation of Electric Power Steering Based on Fuzzy Control

Hui Zhang, Jinhong Liu,Yuzhi Zhang,Jing Ren

Xi’an University of Technology 710048 Xi’an, Shaanxi, China

[email protected]

Yongjun Gao

Xi’an Yongdian Electric Co.,Ltd 710015 Xi’an, Shaanxi, China

[email protected] Abstract--This article is concerned about the analysis, design,

and simulation of an electric power steering (EPS).The article begins by introducing the EPS system concept and comparing the technical and commercial benefits with existing technologies.

Being more versatile than conventional hydraulic power steering, EPS systems excel in engine efficiency, space saving, and environmental friendly. The remainder of the article is focused on the fuzzy logical control scheme in details elaborating on the fuzzifying, editing FIS and membership function and defuzzifying. The simulation model of EPS is set up based on its characteristic equations and on the principle of fuzzy logic control. At last, a series of tests are performed and some characteristic pictures are demonstrated. The feasibility, high reliability of the system and the validity of the control method are proved by the fruitful results which serve an instrumental meaning for a further research.

Index Terms--Electric Power Steering (EPS); Electronic Control Unit (ECU);Fuzzy Control Logic; modeling

I. E ^LECTRIC P ^OWER S ^TEERING

The last decade has seen rapid growth in power-steering systems fitment to vehicles, especially in Europe, which has an increase from 30% fitment in 1990 to over 80% by the year 2003. The use of electric rather than hydraulic actuation offers a wide range of benefits; better fuel economy is achieved (as shown in Fig. 1) because the required power is taken from the engine on demand and not continuously from an engine-driven pump, as in conventional HYPS [1].

0 1 2 3 4 5 6

mixed drive cycle

motorwa y drivi

ng city dri

ving

average result

(ECE15 )

1.3L with HYPAS 1.6L with EPAS

Up to 3.5% savings (City)

Average 3% savings

Incremental fuel consumption(%)

Fig.1. Typical EPS fuel consumption

The key components of an EPS system are shown schematically in Fig.2 which includes a (combined torque and position) sensor, an actuator (electric motor), an Electronic Control Unit (ECU), and control and diagnostic algorithms

implemented in software. The EPS system adopts a so-called column-type EPS system in which the assistant motor connected to the steering shaft through spur gears delivers assistant torque to the shaft.

¹

Ts

ECU

Kr Rp Br

P G Velocity

Td

Tm

，

Bm Km

Bc Kc

Mr

Torque sensor

Retarding Mechanism

θ ^c

θ ^m Rev

Ignition

Clutch Motor

HW

C urr en t Co nt ro l

Ts

ECU

Kr Rp Br

P G Velocity

Td

Tm

，

Bm Km

Bc Kc

Mr

Torque sensor

Retarding Mechanism

θ ^c

θ ^m Rev

Ignition

Clutch Motor

HW

C urr en t Co nt ro l

Fig.2. The schematic diagram of an column-type EPS system

II. T ^HE D ^{ESIGN OF} F ÛZZY L ÔGIC C ÔNTROLLER A. Why use fuzzy control logic?

Based on natural language and the experience of experts, fuzzy logic is conceptually easy to understand, flexible, tolerant of imprecise data, can model nonlinear functions of arbitrary complexity, and be blended with conventional control techniques. Fuzzy logic model is a very powerful tool for dealing quickly and efficiently with imprecision and nonlinearity [2].The schematic of assistant current control is shown in Fig. 3.

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China(50977078) the Provincial Natural Science Foundation of Shaanxi(2009JM7001）

the Provincial Education Department Foundation of Shaanxi (09JK676) the Key Technology R&D Program of Xi’an (CXY08005)

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Fig.3. The schematic of assistant current control

B. Fuzzifier

The motor’s assistant current can be determined by a two- input one-output fuzzy logic controller (see Fig.4). The steering wheel torque Ts and the velocity V serves the two inputs of the controller and its output is the motor’s assistant current I

cmd

.

Fig.4. the input and output variables of fuzzy logic controller According to the basic requirements of EPS, only when the steering torque is greater than 1Nm, the EPS system starts to function, and the maximum torque applied to the steering wheel is 10Nm so Ts can be rated on a scale of 1 to 10 and V can be rated on a scale of 0 to 120km/h.The input of torque Ts can be resolved into a number of different fuzzy linguistic sets: VBIG, QBIG, BIG, MEDIUM, SMALL, VSMALL.

And the fuzzy linguistic sets of velocity can be set as:{VFAST,QFAST,FAST,MEDIUM,SLOW,VSLOW,ZER O}. The output assistant current can be rated on a scale of 0 to 28A with the fuzzy linguistic sets:{VBIG,QBIG,BIG,MEDIUM,SMALL,VSMALL}.It

also adopts the trapezoidal membership function, trapmf.

Before the rules can be evaluated, the inputs must be fuzzified according to each of these linguistic sets. Ts and V adopts the trapezoidal membership function, trapmf, which has a flat top and really is just a truncated triangle curve.

C. Fuzzy rule

Fuzzy rule is based on the expert’s knowledge and experience; it’s a kind of linguistic statement with intuition inference. Fuzzy rule is commonly expressed as the forms of if-then, and, or and so on [3]. According to practical control

experience, the linguistic variable of fuzzy control rules can be expressed as tableⅠ.

TABLE I. T

HE

F

UZZY

R

ULE

of

Icmd

ZERO VSMALL SMALL

MEDIUM BIG

QBIG VBIG ZERO

ZERO VSMALL SMALL

MEDIUM MEDIUM BIG

QBIG VSLOW

ZERO VSMALL SMALL

SMALL MEDIUM MEDIUM

BIG SLOW

ZERO VSMALL VSMALL SMALL

SMALL MEDIUM MEDIUM MEDIUM

ZERO ZERO

VSMALL VSMALL

VSMALL SMALL

SMALL FAST

ZERO ZERO

ZERO VSMALL VSMALL VSMALL

SMALL QFAST

ZERO ZERO

VSMALL VSMALL

VSMALL VFAST

ZERO VSMALL SMALL

MEDIUM BIG

QBIG VBIG

ZERO VSMALL SMALL

MEDIUM BIG

QBIG VBIG ZERO

ZERO VSMALL SMALL

MEDIUM MEDIUM BIG

QBIG VSLOW

ZERO VSMALL SMALL

SMALL MEDIUM MEDIUM

BIG SLOW

ZERO VSMALL VSMALL SMALL

SMALL MEDIUM MEDIUM MEDIUM

ZERO ZERO

VSMALL VSMALL

VSMALL SMALL

SMALL FAST

ZERO ZERO

ZERO VSMALL VSMALL VSMALL

SMALL QFAST

ZERO ZERO

VSMALL VSMALL

VSMALL VFAST

ZERO VSMALL SMALL

MEDIUM BIG

QBIG VBIG V I_cmd

T

D. Defuzzifier

The centroid calculation is adopted when transforming the fuzzy value into crisp value during defuzzification. The surface plot (see Fig.5) looks good, but the function is surprisingly complicated.

Fig.5. Surface viewer

III. M ODELLING AND S IMULATION A. Dynamic Model Of Eps System

The mechanical equation of EPS system can be described as (1) ~ (5).

2

d 2

T

_s _h

d

^h _h

d

^h

T J B

dt dt

θ θ

− = + (1)

2

s a 2

T +T

_r _c

d

^c _c

d

^c

T J B

dt dt

θ θ

− = + (2) PEDS2009

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T

d

= ⋅ (3) k

_c

θ

_c

2

2 2

s m t a c m 2 m

T +g k i -k

_c

(g

_m _c

) d

^c

(g

_m _c

) d

^c

J J B B

dt dt

θ θ

θ = + + + (4)

a c

m e

di d

u Ria L g k

dt dt

= + + θ (5)

B. Simulation

The whole simulation of EPS system as shown in Fig.6 can be divided into 3 parts: mechanical model, motor model and ECU model. The mechanical model can be easily set up as a MIMO system according to (1) ~ (4) and the motor model is constructed with (5).Last but not least, it’s the fuzzy logical model based on which the ECU model is set up.

degree

U I_out

motor model Ts

I Degree

Ta

Tr

mechanical model

V

Ts

I Icmd

U

ecu model 60

V Icmd

To Workspace7

degree To Workspace6

t

To Workspace5 Iout

To Workspace4 U To Workspace3

Tr To Workspace2

Ta To Workspace1 Ts To Workspace

Sine Wave

Scope2

Scope1 Clock

Fig.6. The whole simulation of EPS system

IV. R ESULTS AND C ONCLUSIONS

When the Sinusoidal input Torque Ts with the amplitude of 4Nm and the period of π/2 is exerted on the steering wheel, the current response varies as the velocity changes from 0 to 120Km/h; some characteristic pictures are shown in Fig. 7.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-20 -15 -10 -5 0 5 10 15 20

reference current input torque PID regulate current reference current input torque PID regulate current

Torque (Nm), Current (A)

a) V=40km/h

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-15 -10 -5 0 5 10 15

b) V=60km/h

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-15 -10 -5 0 5 10 15

c) V=80km/h

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-15 -10 -5 0 5 10 15

d) V=120km/h

Fig.7. The characteristic response curves of Sinusoidal input torque Ts It can be seen that the higher the velocity is, the smaller amount of assistant torque is required, and the torque is indirect proportion to the current. The PID regulated current respond to the torque quickly and traces the reference current perfectly.

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Research and Simulation of Electric Power Steering Based on Fuzzy Control