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JOURNAL OF COMPUTERS, VOL. 8, NO. 3, MARCH 2013
Fuzzy PID Position Control Approach in
Computer Numerical Control Machine Tool
Guoyong Zhao
Department of Mechanical Engineering, Shandong University of Technology, Zibo, China
Email: zgy709@126.com
Yong Shen and Youlin Wang
Department of Mechanical Engineering, Shandong University of Technology, Zibo, China
Email: ssy706@163.com, wangyoulin_1006@sdut.edu.cn
Abstract—The traditional PID control approach is often
adopted in CNC machine tool position controller. The
approach is simple and easy to implement, but can’t achieve
rapid adjustment and less overshoot at the same time.
Consequently, on the basis of analyzing fuzzy control theory
and design method, the CNC machine tool fuzzy PID
position control approach is developed in the paper. The
approach makes full use of the advantages of fuzzy control
and PID control. The experiment results show that in
contrast to traditional PID position controller, the developed
approach can achieve better rapidity, shorter adjust time
and satisfied overshoot. It is much significant to highprecision CNC machining.
Index Terms—fuzzy PID position control, membership
function, fuzzy control rule, adjust time, overshoot
I. INTRODUCTION
The traditional proportional integral differential (PID)
control approach is often adopted to compute controlled
quantity in the computer numerical control (CNC)
machine tool position controller. The strongpoint of the
approach is simple and easy to implement [1-2]. However,
with the increasing requirement of practical manufacture
speed, precision and stability, the traditional PID
approach shows its disadvantage gradually. For example,
the poor adaptability and anti-jamming ability, and the
weakness that can’t achieve rapid adjustment and less
overshoot at the same time [3-5].
Aimed to the weakness of traditional PID approach,
the researchers all over the world study how to enhance
PID controller performance from two aspects mainly [68]. For one thing, improve the classical PID control
arithmetic. Y.X.Su combines nonline-differential tracker
and traditional PID controller in series, and process
signals with two nonline-differential trackers in order to
improve anti-jamming ability [9]. Guo Yanqing analyzes
each PID portion change trend with step input, and
This project is supported by the National Natural Science
Foundation of China (No.51105236), and the Shandong Province
Promotive research fund for excellent young and middle-aged scientists
of China(No.BS2011ZZ014).
Corresponding author: Guoyong Zhao, zgy709@126.com
© 2013 ACADEMY PUBLISHER
doi:10.4304/jcp.8.3.622-629
develops a universal nonlinear PID control model [10].
K.Z.Tang combines the traditional PID and self-adaption
nonlinear control, and compensates the linear model warp
with nonlinear model [11]. Hu Ligang devises the
nonline-differential tracker to receive corresponding
integral and differential signals, and process the signals
properly to build up nonlinear PID controller [12]. For
another thing, study PID control with intelligence
approach [13-15]. Ning Wang introduces the nonlinear
PID control approach based on nerve cell network, which
achieves nonlinear control through nerve cell network
parameters online adjustment [16].
Fuzzy control is an intelligence approach, and its
process flow is as follows. Above all, sample information
with computer; Secondly, transform the information into
fuzzy controlled quantity after fuzzy process; Thirdly,
compare the fuzzification information with repository
data, and process approximately the fuzzy information
with rule library; Finally, compute clear controlled
quantity according to fuzzy conclusion. The inner
information data are fuzzy quantity, so it is easy to make
use of human experience with natural language [17]. The
fuzzy controller framework is shown in Fig.1.
fuzzy controller
input
fuzzifi
-cation
reasoning
machine
rule library
eliminate
fuzzifi
-cation
output
database
repository
Figure 1. The fuzzy controller framework
In order to improve the traditional PID controller
performance, the CNC machine tool fuzzy PID position
control approach is developed in the paper, on the basis
of analyzing fuzzy control theory and design method. The
approach makes full use of the advantages of fuzzy
control and PID control. In the end, the contrast
experiments are done to validate introduced fuzzy PID
position control approach.
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II. THE FUZZY CONTROLLER FRAMEWORK DESIGN
described with natural language and carried out with
computer [18]. The fuzzy control elementary principle is
shown in Fig.2.
Fuzzy control approach is an automatic control
technology, which is based upon experience summing-up,
Fuzzy controller
input
fuzzifi
-cation
fuzzy
reasoning
fuzzy control
rule
sensor
output
eliminate
fuzzfication
actuating
machanism
control object
Figure 2. The fuzzy control elementary principle
The fuzzy controller can be divided into singlevariable fuzzy controller and multi-variable fuzzy
controller according to input and output variables, and
can be divided into self-adapting fuzzy controller, selforganizing fuzzy controller, self study fuzzy controller
and expert fuzzy controller according to function [19].
Especially, the single-variable fuzzy controller can be
divided into one-dimension fuzzy controller, twodimension fuzzy controller and three-dimension fuzzy
controller according to input variable amount. The input
variable amount is corresponding to fuzzy controller
dimension. The single-variable fuzzy controller
framework is shown in Fig.3.
The two-dimension fuzzy controller is easy to
implement with computer, so the two-dimension fuzzy
PID controller is adopted in the CNC machine tool
position control, which connects fuzzy control and
traditional PID controller.
In the traditional controller, the proportional
coefficient, integral coefficient and differential
coefficient are invariable. So the controller can’t adjust
automatically when loads change or outer disturbances
appear. It is a feasible approach to regulate the PID
coefficients automatically in order to enhance position
controller precision. The developed fuzzy PID position
controller is shown in Fig.4.
e
u
fuzzy reasoning
(a)
e
fuzzy
reasoning
e&
d/dt
u
(b)
e&
fuzzy
reasoning
e&&
e
d/dt
u
d/dt
(c)
Figure 3. The single-variable fuzzy controller framework
(a) one-dimension fuzzy controller
(b) two-dimension fuzzy controller
(c) three-dimension fuzzy controller
The strongpoint of fuzzy PID position controller
shown in Fig.4 is that the PID coefficients are reasoned
with three fuzzy controllers. And each fuzzy controller
adjusts quantification factor according to practical
requirement.
fuzzy PID controller
Ki
fuzzy controller
r(t)
1/s
Kp
e
control object
fuzzy controller
u(t)
Kd
fuzzy controller
du/dt
position feedback
Figure 4. The developed fuzzy PID position controller framework
Ⅲ. CNC MACHINE TOOL FUZZY PID POSITION CONTROL
APPROACH
A. Quantification Factor and Proportional Factor
The input signals are quantified with quantification
factor, then sent to fuzzy controller to fuzzification
© 2013 ACADEMY PUBLISHER
process. After fuzzy controller reasoning and eliminate
fuzzification, the precise output signals are achieved, and
are magnified or reduced so as to match adjacent module
well [20].
(1) Quantification factor
Suppose the input signals of fuzzy controller be e and
ec = de / dt in the two-dimension fuzzy controller.
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JOURNAL OF COMPUTERS, VOL. 8, NO. 3, MARCH 2013
They are clear numerical values, obtained by compute
sampling. Define x component span as elementary field.
The input signal x component turns to fuzzy quantity
after mapping transformation, and sends to fuzzy
reasoning module.
Suppose input component x elementary field be
X i = [− x, x]( x > 0)
Suppose fuzzy field be
N i = [− n, n](n > 0)
Define the transformation coefficient ki from X to N be
quantification factor
ki = n / x .
(1)
When elementary field isn’t symmetrical, such as
X i = [a, b] ( a ≠ b ), the quantification factor be
ki ' = 2n / b − a .
(2)
(2) Proportional factor
The clear quantity fuzzy field isn’t consistent with
implement machine elementary field sometimes, so the
field transformation is required. Define the
transformation coefficient from fuzzy field to elementary
field be proportional factor.
Suppose the fuzzy field be
N ' = [−n, n](n > 0)
Suppose the elementary field be
U = [−u, u ](u > 0)
Then the proportional factor ku can be obtained
ku = u / n .
(3)
Except for field transformation, the quantification
factor and proportional factor are important for system
control performance.
If quantification factor of error e is on the high side,
the rise velocity will turn quick, the overshoot will
increase, which may lead to unsteadiness. On the contrary,
if quantification factor of error e is on the low side, the
rise velocity will turn slow, which may destroy system
steady-state precision.
If quantification factor of error change ec increases, the
restrain force to error change will augment, which will
improve system stability; On the contrary, if
quantification factor of error change ec decreases, the
overshoot will increase, which will lead to system
instability.
Proportional factor is corresponding to the total system
magnify multiple. If proportional factor increases, the
system respond speed will turn quick; On the contrary, if
proportional factor decreases, the system transition time
will turn longer.
B. The Fuzzification of Input and Output Variables in
Fuzzy Controller
Quantify the fuzzy controller input signal with
quantification factor, then do fuzzification process. In
essence, fuzzification process is to confirm the language
variable in the field for a certain x in field X.
© 2013 ACADEMY PUBLISHER
The language variable words amounts is important to
system performance. If the language variable words is
more, the input and output variables will be described
more detailedly, and the fuzzy reasoning process turns
complicated; On the contrary, if the language variable
words is few, the input and output variables will be
described more roughly and poorly. The language
variable words amounts are selected from five to seven
commonly. For example, the language variable including
seven words is:
A = {NB, NM , NS , ZO, PS , PM , PB}
Where each word is defined as follows
NB---negative big
NM--- negative medium
NS--- negative small
ZO---zero
PS--- positive small
PM--- positive medium
PB--- positive big
The fuzzy field and language variable are connected
through membership function. The triangle-shape
function, Gauss-shape function, Bell-shape function, Zshape function and S-shape membership function are in
common use. Except the field boundary, the membership
function is centrosymmetric. The sharp membership
function curve leads to high distinguishability and
sensitivity; While the mild membership function curve
leads to low sensitivity.
The triangle-shape membership function is adopted to
study fuzzification process in the paper. Suppose the
input variable fuzzy field after fuzzification process is
Ak ∈ [−6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6] .
Suppose the language variable muster is
A = {NB, NM , NS , ZO, PS , PM , PB} .
The language variable value is shown in Fig.5. As
shown in Fig.5, the field is divided into thirteen grades
corresponding to seven language variables.
PB: about +6
PM: about +4
PS: about +2
ZO: about 0
NS: about -2
NM: about -4
NB: about -6
Seven words are adopted to describe error e, error
change rate ec, three output coefficient k p , ki and k d .
And the field is
{NB, NM , NS , ZO, PS , PM , PB} .
Fuzzy subset NB and PB adopt Z-shape membership
function and S-shape membership function. Fuzzy subset
PM, PS, ZO, NS and NM adopt triangle-shape function.
The input variable membership function is shown in Fig.6,
output variable membership function is shown in Fig.7,
and coefficient k p fuzzy control system is shown inFig.8.
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625
μ
NB
-6
NS
NM
-5
-3
-4
-2
ZO
1.0
-1
0
PM
PS
1
2
3
PB
x
6
5
4
Figure 5. The language variable value
(1)
k p fuzzy control rule
To increase
k p may reduce steady state error and
enhance system response velocity. However, the oversize
k p will lead to big overshoot, even instability; To
decrease
small
Figure 6. The input variable e and ec membership function
k p may reduce overshoot. However, the very
k p will lead to long adjust time. On the basis of
analyzing the connection between error e, error change
rate ec and parameter k p , the k p fuzzy control rule is
built up shown in Table 1.
TABLE 1
THE
kp
FUZZY CONTROL RULE
ec
Kp
NB
NM
NS
ZO
PS
PM
PB
PB
PB
PM
PM
PS
ZO
ZO
PB
PB
PM
PS
PS
ZO
NS
PM
PM
PM
PS
ZO
NS
NS
PM
PM
PS
ZO
NS
NM
NM
PS
PS
ZO
NS
NS
NM
NM
PS
ZO
NS
NM
NM
NM
NB
ZO
ZO
NM
NM
NM
NB
NB
e
Figure 7. The output variable
k p , ki
and
kd
NB
NM
NS
ZO
PS
PM
PB
membership function
(2)
ki fuzzy control rule
The integral control mainly play role on steady state
error elimination. If parameter ki is on the high side, the
system may be instable; If parameter
Figure 8. The coefficient
kp
fuzzy control system
C. The Fuzzy Control Rule Design
The fuzzy control rule is based on expert experience
knowledge and practical data analyzed result. The
essential principle of fuzzy control rule is to achieve
optimal dynamic and static state system performance.
The fuzzy PID control approach reasons the three PID
coefficients with fuzzy controller. Firstly, measure error e
and error change rate ec from time to time; Secondly,
adjust control parameters online according to the fuzzy
connection between e, ec and control parameter.
© 2013 ACADEMY PUBLISHER
ki is on the low
side, the system can’t be effective to reduce steady state
error. On the basis of analyzing the connection between
error e, error change rate ec and parameter ki , the ki
fuzzy control rule is built up shown in Table 2.
(3) k d fuzzy control rule
The differential control can forecast the change trend
of error in advance, and output corresponding restrain
signal. The oversize k d will lead to long adjust time;
While the very small
k d will lead to unsatisfied
overshoot when error changes sharply. On the basis of
analyzing the connection between error e, error change
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JOURNAL OF COMPUTERS, VOL. 8, NO. 3, MARCH 2013
rate ec and parameter
k d , the k d fuzzy control rule is
built up shown in Table 3.
PS)(
TABLE 2
THE
ki
(32) If (e is PS) and (ec is ZO) then ( k p is NS)(
ec
PS)(
Ki
NS
ZO
PS
PM
PB
NB
NB
NM
NM
NS
ZO
ZO
NB
NB
NM
NS
NS
ZO
NS
NM
NM
NS
NS
ZO
PS
PS
NM
NM
NS
ZO
PS
PM
PM
NM
NS
ZO
PS
PS
PM
PM
The relevant fuzzy contain connection are as follows:
ZO
ZO
PS
PS
PM
PB
PB
R32 (k p ) = PS (e) ∧ ZO(ec) ∧ NS (k p )
ZO
ZO
PS
PM
PM
PB
PB
PS
PM
PB
kd
FUZZY CONTROL RULE
ec
Kd
NB
NM
NS
ZO
PS
NS
NB
NB
NB
NM
PS
PS
NS
NB
NM
NM
NS
ZO
ZO
NS
NM
NM
NS
NS
ZO
ZO
NS
NS
NS
NS
NS
ZO
ZO
ZO
ZO
ZO
ZO
ZO
ZO
PB
NS
PS
PS
PS
PS
PB
PB
PM
PM
PM
PS
PS
PB
e
NB
NM
NS
ZO
PS
PM
PB
D. The Fuzzy Reasoning Process
The fuzzy approximate reasoning and synthesis
principle is
U * = ( A* )T o R .
(4)
Where fuzzy contain connection
fuzzy condition propositions:
R consists of 49
49
.
= U Rj
(5)
j =1
It can be obtained with Mamdani reasoning arithmetic:
U * = ( A* )T o R
= ( A* )T o U R j
.
(6)
j =1
=U
j =1
49
k d is PS) (1)
(40) If (e is PM) and (ec is PS) then ( k p is NM)(
PM)(
ki is
k d is PS) (1)
R32 (ki ) = PS (e) ∧ ZO (ec) ∧ PS (ki )
R32 (k d ) = PS (e) ∧ ZO (ec) ∧ ZO (k d )
R33 (k p ) = PS (e) ∧ PS (ec) ∧ NS (k p )
R33 (ki ) = PS (e) ∧ PS (ec) ∧ PS (ki )
R33 (k d ) = PS (e) ∧ PS (ec) ∧ ZO(k d )
R39 (k p ) = PM (e) ∧ ZO (ec) ∧ NM (k p )
R39 (ki ) = PM (e) ∧ ZO (ec) ∧ PS (ki )
R39 (k d ) = PM (e) ∧ ZO (ec) ∧ PS (k d )
R40 (k p ) = PM (e) ∧ PS (ec) ∧ NM (k p )
R40 (ki ) = PM (e) ∧ PS (ec) ∧ PM (ki )
R40 (k d ) = PM (e) ∧ PS (ec) ∧ PS (k d )
According to the above-mentioned fuzzy rules, the
kp ,
ki and k d fuzzy reasoning output results can be
obtained as follows, which are shown in Fig.9, Fig.10 and
Fig.11 respectively.
(1) From Fig.6, it can be obtained:
Consequently, the fuzzy output is
U 32 (k p ) = ( A* )T o R32
= ( PS (e = 1.5) ∧ ZO(ec = 0.75)) o R32 (k p )
= UU j
= 0.5 ∧ 0.25 ∧ NS (k p )
= (0.25 NS )k p
*
j =1
Suppose the clear input quantity e=1.5, ec=0.75 on
some period. According to Fig.6, e is corresponding to
fuzzy subset PS and PM; The ec is corresponding to ZO
and PS. According to Table 1, Table 2 and Table 3, the
following principles are activated by the two input
quantities.
© 2013 ACADEMY PUBLISHER
PS)(
ki is
= PS (e = 1.5) ∧ ZO(ec = 0.75) ∧ NS (k p ) . (7)
49
(( A* )T o R j )
(39) If (e is PM) and (ec is ZO) then ( k p is NM)(
PS (e = 1.5) = 0.5
ZO (ec = 0.75) = 0.25
R = R1 U R2 U R3 ... U R49
49
k d is ZO) (1)
NM
TABLE 3
THE
ki is
NB
e
NB
NM
NS
ZO
PS
PM
PB
k d is ZO) (1)
(33) If (e is PS) and (ec is PS) then ( k p is NS)(
FUZZY CONTROL RULE
ki is
U 32 (ki ) = ( A* )T o R32
= ( PS (e = 1.5) ∧ ZO (ec = 0.75)) o R32 (ki ) . (8)
= (0.25PS )ki
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627
U 32 (k d ) = ( A* )T o R32
U 40 (ki ) = ( A* )T o R40
= ( PS (e = 1.5) ∧ ZO (ec = 0.75)) o R32 (k d ) . (9)
= ( PM (e = 1.5) ∧ PS (ec = 0.75)) o R40 (ki ) . (17)
= (0.25ZO)k d
= (0.5PM )ki
(2) From Fig.6, it can be obtained:
PS (e = 1.5) = 0.5
PS (ec = 0.75) = 0.75
Consequently, the fuzzy output is as follows:
U 40 (k d ) = ( A* )T o R40
= ( PM (e = 1.5) ∧ ZO (ec = 0.75)) o R40 (k d ) . (18)
= (0.5PS )k d
U 33 (k p ) = ( A* )T o R33
= ( PS (e = 1.5) ∧ PS (ec = 0.75)) o R33 (k p ) . (10)
= (0.75 NS )k p
U 33 (ki ) = ( A* )T o R33
= ( PS (e = 1.5) ∧ PS (ec = 0.75)) o R33 (ki ) . (11)
= (0.75PS )ki
U 33 (k d ) = ( A* )T o R33
Figure 9. The fuzzy subset after
kp
fuzzy reasoning
Figure 10. The fuzzy subset after
ki
fuzzy reasoning
Figure 11. The fuzzy subset after
kd
fuzzy reasoning
= ( PS (e = 1.5) ∧ PS (ec = 0.75)) o R33 (k d ) . (12)
= (0.75ZO )k d
(3) From Fig.6, it can be obtained:
PM (e = 1.5) = 0.5
ZO(ec = 0.75) = 0.25
Consequently, the fuzzy output is as follows:
U 39 (k p ) = ( A* )T o R39
= ( PM (e = 1.5) ∧ ZO (ec = 0.75)) o R39 (k p ) .(13)
= (0.25 NM )k p
U 39 (ki ) = ( A* )T o R39
= ( PM (e = 1.5) ∧ ZO (ec = 0.75)) o R39 (ki ) .(14)
= (0.25PS )ki
U 39 (k d ) = ( A* )T o R39
= ( PM (e = 1.5) ∧ ZO(ec = 0.75)) o R39 (k d ) .(15)
= (0.25PS )k d
(4) From Fig.6, it can be obtained:
PM (e = 1.5) = 0.5
PS (ec = 0.75) = 0.75
Consequently, the fuzzy output is as follows:
U 40 (k p ) = ( A* )T o R40
= ( PM (e = 1.5) ∧ PS (ec = 0.75)) o R40 (k p ) . (16)
= (0.5 NM )k p
E. The Output Elimination Fuzzification
The elimination fuzzification process is to substitute
reasoning fuzzy subset with an appropriate numerical
value. The elimination fuzzification approach in common
use includes area gravity model approach, weighted
average method and so on. The area gravity model
approach is adopted to eliminate fuzzification in the
paper.
IV. POSITION CONTROL SIMULATION EXPERIMENT
© 2013 ACADEMY PUBLISHER
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JOURNAL OF COMPUTERS, VOL. 8, NO. 3, MARCH 2013
A. The Feeding Servosystem Structure
The position servo control modes of CNC machine can
be divided into open control, half-closed loop control and
closed loop control according to framework. The modes
in high precision CNC machine include half-closed loop
control and closed loop control mainly.
Three-loop cascade control scheme is adopted on
modern CNC machine mostly, which consist of position
loop, velocity loop and current loop from outside to
inside. Every control loop has its own feedback signal
and connects each other.
The screw pair drives are adopted in CNC feeding
system usually. Neglecting the influence of mechanicallydriven nonlinear factors such as screw pairs, the
approximate structure model of closed loop feeding
servosystem is shown in Fig.12.
instruction
signal
position
controller
D/A
speed
control
unit
output
displacement
position controller can achieve shorter adjust time and
satisfied overshoot.
(2) If change the input unit step signal to 1.2(t) at t=5s,
the traditional PID controller step response curve and the
developed fuzzy PID position controller step response
curve are shown in Fig.14.
From Fig.14 it can be seen, in contrast to the
traditional PID controller, the developed fuzzy PID
position controller has quicker transition process, better
rapidity and satisfied overshoot.
(3) If add a step disturbance signal at t=5s whose
amplitude is 0.2, the traditional PID controller step
response curve and the developed fuzzy PID position
controller step response curve are shown in Fig.15.
From Fig.15 it can be seen, in contrast to the
traditional PID controller, the developed fuzzy PID
position controller can spend lesser adjust time to come
back to steady-state.
1/S
position
measurement
Figure 12. The feeding servosystem structure
B. The Contrast Experimentation on Position Control
The common medium CNC machine tool feeding
system mathematic model is introduced [21], the transfer
function is
G ( s) =
10
s + 9s + 23s + 15
3
2
The servo system simulation modules are set up with
Matlab/Simulink to compare the traditional PID
controller with the developed fuzzy PID position
controller.
The traditional PID controller coefficients can be
obtained with Z-N approach:
K p = 11.52 , Ti = 0.6575 , Td = 0.1644 .
Figure 13. The traditional PID controller step response curve and the
developed fuzzy PID position controller step response curve
The fuzzy PID position controller coefficients can be
obtained after NCD toolbox optimization:
K e1 = 4.5301 , K ec1 = 1.6418 ,
K up = 0.2321 , K e 2 = 2.5207 ,
K ec 2 = 1.2610 , K ui = 10.1362 ,
K e 3 = 8.4617 , K ec 3 = 2.8396 ,
K ud = 0.7395 .
(1) Aimed to the unit step input signal, the traditional
PID controller step response curve and the developed
fuzzy PID position controller step response curve are
shown in Fig.13.
From Fig.13 it can be seen, in contrast to the
traditional PID controller, the rise time with the
developed fuzzy PID position controller increases from
0.33s to 0.40s; The adjust time decreases from 3.69s to
1.59s markedly; And the overshoot decreases from
59.35% to 5.1%. In conclusion, the developed fuzzy PID
© 2013 ACADEMY PUBLISHER
Figure 14. The traditional PID controller step response curve and the
developed fuzzy PID position controller step response curve with
mutation signal
JOURNAL OF COMPUTERS, VOL. 8, NO. 3, MARCH 2013
Figure 15. The traditional PID controller step response curve and the
developed fuzzy PID position controller step response curve with a step
disturbance signal
V. CONCLUSIONS
The traditional PID control approach is often adopted
to compute controlled quantity in the CNC machine tool
position controller. The approach is simple and easy to
implement, but can’t achieve rapid adjustment and less
overshoot at the same time.
In order to improve the traditional PID controller
performance, the CNC machine tool fuzzy PID position
control approach is developed in the paper, which makes
full use of the advantages of fuzzy control and PID
control. The experiment results show that in contrast to
traditional PID position controller, the developed
approach can achieve better rapidity, shorter adjust time
and satisfied overshoot.
ACKNOWLEDGMENT
The authors are grateful to the Project of the National
Natural Science Foundation of China (No.51105236), and
the Shandong Province Promotive research fund for
excellent young and middle-aged scientists of
China(No.BS2011ZZ014).
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Guoyong Zhao was born in Shandong, China in 1976. He has a
Ph.D. in Mechanical and Electronic Engineering (2007) from
Dalian University of Technology, Dalian, China. His main
interest is mechanical manufacturing and automation
technology.
Yong Shen was born in Shandong, China in 1987. He is a
master postgraduate majored in mechanical manufacturing and
automation in Shandong University of Technology, Zibo, China.
His main interest is mechanical manufacturing and automation
technology.
Youlin Wang was born in Heilongjiang, China in 1955. He is a
professor worked in Shandong University of Technology. His
main interest is mechanical manufacturing and automation
technology.