Kinematic Analysis of Lifting Booms System for Aerial Work Platform Based on Differential
Forward Incremental PID controller
Tianhong Luo*
Haiyan He**
Xinxian Yin***
Sunke Zhu****
Jiayuan Luo*****
*Professor, Department of Mechanical-electrical and Automotive Engineering, Chongqing Jiaotong University,
Chongqing, 400074, China;
**Graduate Student, Department of Mechanical-electrical and Automotive Engineering, Chongqing Jiaotong
University, Chongqing, 400074, China;
***Graduate Student, Department of Mechanical-electrical and Automotive Engineering, Chongqing Jiaotong
University, Chongqing, 400074, China;
****Associate Professor, Department of Mechanical-electrical and Automotive Engineering, Chongqing Jiaotong
University, Chongqing, 400074, China;
*****Doctor, Department of Mechanical-electrical and Automotive Engineering, Chongqing Jiaotong University,
Chongqing, 400074, China;
Abstract: By analyzing the kinematic characteristics of lifting booms system (LBS) of aerial work platform (AWP)
about its working process, this paper provided a differential forward incremental PID (DFI-PID) controller to
improve its control accuracy. Based on operating principles and structural parameters of LBS, three mathematical
models were established: the mechanical motion system of each lifting booms, the mechanical-hydraulic coupling
system and the electro-hydraulic proportional system. Meanwhile, a model of LBS was built up based on the
electro-hydraulic proportion of AMES. A joint simulation was conducted by integrating the differential forward
incremental PID (DFI-PID) controller into AMES (working as a major simulation environment) through certain
software interface. Then, a DFI-PID closed-loop controller was designed to analyze the effect of the PID controller
on LBS. The result showed that compared with the conventional PID controller, the DFI-PID closed-loop
controller had better steady and higher robustness towards command changes and load disturbance. Besides, the
validity of joint simulations was also proved.
Keywords: Aerial work platform (AWP); Lifting booms system (LBS); Kinematic analysis; Closed-loop control
system; Differential forward incremental PID (DFI-PID) controller
obstacles and reach the predetermined position, this
0 Introduction
As an emerging technological industry, AWP is
an important branch in the engineering machinery
field and is widely applied in shipbuilding,
construction, municipal construction, fire control
and port cargo etc [1,2]. Stability of LBS is an
important factor to evaluate the success of AWP
products and to ensure the safe operation of AWP as
well. What’s more, the flexible structure of the
folding-arm AWP makes it possible to surmount
can be applied to lower operating height AWP [3,4].
With the development of digital control
technology, problems that could not be solved by
analog PID controller before [5,6] are now easily
done on a digital computer. Thus, based on current
digital control technology, a series of control
algorithm has been promoted to improve system
quality and meet the needs of different control
systems [7]. Therefore, in this paper, an algorithm
of the DFI-PID controller was established, in which
two advantages of incremental PID and differential
forward PID was highlighted, respectively. Firstly,
this algorithm is only related to the change of the
most recent K power instead of accumulating, so
that the faulty operations influence is minored and a
better control effect can also be obtained by
weighted processing [8]. Secondly, this method only
has differential influence on the output rather than a
1-lower arm；2- the middle arm；3-upper arm；4- job hopper；
given instruction [9]. Overall, the improved PID
5-arm mechanical；6-arm mechanical；
algorithm can be applied to situations where the
7-lower arm cylinder；8-in arm cylinder；9-leveling cylinder；
instructions of lifting arms are frequently given in
10-rotary table
the process of adjusting the lifting positions. At this
Fig 1: The structure of folding-arm AWP
point, it is useful to avoid the excessive overshoot
from instruction changes. Additionally, it also can
avoid some tiny faulty operations that affect the
control accuracy. Thus, the improved algorithm
contents the needs of being continuous, stable, and
fast dynamic responded in lifting and lowering
process.
Based on current lifting booms control system
(LBCS) technology, this paper employed the
MATLAB/Simulink
software
to
establish
an
integrated system model with the closed-loop
controller. Meanwhile an integrated environment of
the
LBCS
was
built,
with
this
integrated
environment conducting combination to analyze of
this system.
1 The structure of the Lifting Booms
System
2 Mathematical models of the LBS
This
section
mathematical
researched
model
three
parts
of
for the LBS,
such
as
mechanical motion for each lifting arm, the
hydraulic coupling mechanical of the LBS and the
electro-hydraulic system for the mechanical of the
LBS.
2.1 Mathematical model of mechanical
motion for each lifting arm
There provided three motion mathematical
models, the lower arm, the middle arm and the
upper arm as objects.
2.1.1 Motion mathematical model of the
lower arm and the upper arm.
The structure of the opening chain of series
arm forms applied in the LBS was commonly used
in industry, including the lower arm, the middle arm,
upper arm, and a work platform. Each lifting arm
and the link of the lower arm with the rotary table
were hinged with the horizontal hinge pin. The
Fig 2: Vector diagram of arms barycenter
hinge joint was provided with a special sliding
bearing to reduce the resistance while the working
arm rotating.
The concrete structure is shown in Fig. 1:
From the simplified mechanical model of the
arms, the mechanical movement was coincided with
the cosine theorem formula and the equation was
defined:
y 2  a 2  b 2  2ab cos 
(1)
Where
y is total length of the lower arm (the
upper arm)cylinder; For the lower arm,
a is
the
distance of the two hinge joints, one hinge joint is
intersection for the oil cylinder of the lower arm and
for the lower arm and the middle arm, another hinge
point is intersection for the middle arm lower
connecting rod and the lower arm; l 2 ,
l3
the rotary table, another hinge joint is intersection
for the rotary table and the lower arm; b is the
middle arm connecting rods of isometric;
distance of the two hinge joints, one hinge joint is
total length of middle oil cylinder.
are the
l5 is the
intersection for the rotary table and the lower arm,
With the method of the reverse theory, namely
another hinge joint is intersection for the oil
that the middle arm and the lower arm were
cylinder of the lower arm and the lower arm;  is
assumed to be frame and the driving link ，
the angle of the lower arm and rotary table.
While, for the upper arm,
a
respectively. Then the change of
is the distance
l5 ( y ) was
of the two hinge points, one hinge point is
confirmed through the variation of angle of the
intersection for the upper arm cylinder and the
driver and the frame.
middle arm, another hinge point is intersection for
the middle arm and the upper arm;
b
is the
distance of the two hinge points, one hinge point is
This equation can be defined via the complex
vector method:
A sin   B cos   C  0
(3)
intersection for the upper arm and the middle arm,
another hinge point is intersection for the upper arm
and the upper arm cylinder;

is the angle of the
middle arm and the upper arm.
y and  with respect
Took the derivative of
to time t, then the equation is given as
y '  f t ' , where
t
represents the lower
ab sin 
Furthermore, the following relations can be
tan( / 2)  ( A  A2  B 2  C 2 ) /( B  C )
(4)
(2)
a  b  2ab cos 
2
And C  l 22  l12  l32  l 42  2l 1 l 4 cos 1
achieved based on above equation formulas.
arm or the upper arm.
ft 
With A  2l1l3 sin 1 , B  2l3 l1 cos 1  l 4  ，
2
2.1.2 Motion mathematical model of the
middle arm
2.2 Mathematical model of the hydraulic
coupling and mechanical of the LBS
Suppose that a scheme that considered the
lifting arm was rotating at a speed of equiangular
and the electro-hydraulic proportion servo valve
was matching and symmetry. This application
x1  
required
，
x2  y , x3  dy , x4  p1 , x5  p 2 , hence,
dt
Fig 3: Vector diagram of middle arm barycenter
state space formula of nonlinear model was defined
via flow continuity equation and force balance
l4 , l 6 are the simplified connecting rods of the
middle arm（In order to facilitate the analysis, the
arm is divided into two sections）, namely the
rack;
l1 is
the driver parts which is the distance of
the two hinge points, one hinge point is intersection
equation.
x1  x 3 / f t
proportion of link, resulting from the dynamic
x 2  x3
x 3  K / m x 2  B / m x 3   A1 / m x 4   A2 / m x 5
（5）
performance of the amplifier was very high.
x 4   A1 / V1 x 3  C i / V1 ( x 4  x 5 )  C e / V1 x 4
Transfer function is defined as:
 (C d wxv / V1 ) 2 /   p s  x 4 
Wi s   I s  / U s   K a
 (C d wxv / V2 ) 2 /  x 5
2) Transfer function of the electro-hydraulic
x 5   A2 / V2 x 3  C i / V2 ( x 3  x 4 )  C e / V2 x 5
（6）
proportional valve.
Where,
t represents the lower arm, the middle
arm or the upper arm;
Ws s  
xv s 

I s  s 2
 is the rotation angle of the lifting arm;
m is the equivalent quality of piston and
（7）
s s  1
Here: Ksc is the proportional gain;
load;
s is
B is the viscous damping coefficient of
piston and load;
 s2
K SC
 2
the inherent frequency of proportional
valve;
 is the damping ratio.
K is the spring stiffness of load;
A1 and A2 are effective area of non-rod
cavity and rod cavity for the hydraulic cylinder,
3) Transfer function of the power element.
respectively;
The hydraulic power units of each lifting arm
ps is the pressure of oil supply;
were valve controlled asymmetrical cylinder. The
p0 is the return oil pressure,
follow
approximately pressure of 0;
type
took
consideration
of
piston
displacement variation, which cased by asymmetric
Xv is the displacement of spool;
cylinder area. Specifically, inertia load and external
W is the area gradient of throttle window
load were mainly taken into account, the transfer
for slide valve;
function is as shown:
Kq
Cd is the flow coefficient;
X P
Ci and Ce are the inside and outside
Ap
Xv 
leakage coefficient of the hydraulic cylinder,

K ce 
Vt

 1
s   FL 
A2 p s 
1 
A p2 C  T e K ce  
1  2

 s 2 2

s 2 
s  1
h h

respectively;
p1 and p2 are the two cavity pressures of
Here: Kq is the flow gain;
（8）
 h is the inherent
frequency of hydraulic; ξ is the hydraulic damping
the hydraulic cylinder, respectively;
V1 =V10 /β，V2 =V20 /β，V10 and V20 are
the initial volume of the non-rod cavity and rod
ratio; C is the variation coefficient of equivalent
area for the load flow; T is the variation coefficient
cavity for the hydraulic cylinder, respectively;
β is the modulus elasticity of oil bulk.
of elastic modulus for the effective bulk;

is the
oil tanks area; Kce is the flow-pressure coefficient;
Ap is the equivalent area of the load flow; Ps is the
2.3 Mathematical model of
electro-hydraulic
system
for
mechanical of the LBS
the
the
1) Transfer function of amplifier.
oil pressure;
 e is the modulus of elasticity for oil.
4) The principle of the DFI-PID controller
algorithm.
In order to discuss the formula accurately, the
Compared with conventional PID controller,
electrical links were regarded as general electric
the DFI-PID algorithm combined advantages of the
amplifier, namely the input and the output were
differential forward PID and the incremental PID.
voltage and current. Also, it could be seen as a
The essence of the differential forward PID was
early operation; this method was only to conduct the
output in differential while not for a given
k
u k   K p e(k )  K 1  e(i )  K D e(k ) - e(k  1)  u 0
（11）
i 0
instruction [10]. However, the incremental PID
Here, u 0 is the based value of control
control relevant to the change of the nearest K
quantity，is the same as output value of controller
when K=0; uk  is the output value of controller
power rather than accumulating, so that the missing
movements have minor influence and it was easy to
get a good control effect through weighted
for k th sampling time;
K1
coefficient;
processing [11,12]. The input signals of r are
present as lifting adjusting position of LBS.
coefficient,
a. Principle of the differential forward PID
coefficient,
K1 
KD 
K PTS
T1
Kp
is
KD
;
K PTD
T1 ; TS
is proportion amplifying
integral
amplifying
is differential amplifying
is sampling period.
control
When
The characteristic of this method only had
the
actuator
was
employed
the
incremental accumulation of control quantity
differential influence on the output instead of a
instead of actual value of control quantity, the PID
given instruction [13]. The structure of differential
control required incremental algorithm, according to
forward PID controller is shown in Fig.4.
the type (11) the output value of (k-1)th sampling
r
e
time can be obtained:
u
Kp(1+1/Tis)
k -1
u k - 1  K p e(k - 1)  K1  e(i )  K D e(k - 1) - e(k  2)  u 0
-
（12）
i 0
c

 （13）
T  e0  ek  k
 T
uk   K p ek   
  ei   d ek   ek  1
Ti 
2
i 0
 T


(1+Tds)/(1+0.1Tds)
Fig.4: The structure of differential forward PID controller
The control formula of differential incremental
is obtained:
u(k )  u(k  1)  K P [e(k )  e(k  1)]  K P
Ts
e(k )  u d (k )
Ti
u d (k )  T1u d (k  1)  T2 y(k )  T3 y(k  1)
T1 
(9)
(10)
Where, Ts is the sampling time ； Td is
Kp is scale
coefficient； Ki is integral coefficient；  =0.1; T1，
T2 ，T3 are present as coefficients of differential
parts；All of
algorithm of the control quantity can be obtained:
u(k )  uk   uk  1
u(k )  q0 ek   q1ek  1  q2 ek  2
Td
T  TS
Td
T  d
T 
Td  TS ; 2 Td  TS ; 3 Td  TS
differential time of constant ；
With type (11) and type (12), incremental
Kp、Ki、T1、T2、T3 are justified online.
（14）
uk   uk  1  q 0 ek   q1ek  1  q 2 ek  2 （15）
Here，

3T Td 

q 0  K p 1 

2
Ti
T 


T
T
q1   K p 1  2 d 
T 2Ti

q2  K p 



Td
T
Therefore, if analog parameters(Kp，Ti and Td)
of the PID controller were available, then in a
shortly sampling time, the parameters of q 0，q1 and
q2 could be calculated out with Kp，Ti and Td.
b.Basic principle of the incremental PID controller
algorithm
The AWP is only performing the differential
for output y (t) of hydraulic cylinder piston rod for
The discretization of the PID algorithm as
each lifting arm; the differential output signal
shown below, the differential equation of the
contains controlled parameters and the change of
continuous time PID algorithm turn into describes
the rate. The output is worked as a measured value
the difference equation of discrete time, and then
putting into the proportional integral controller, as a
PID algorithm for the discrete is obtained:
result to strengthen the system to overcome the
overshoot effect, thus, compensating the process lag
3.1 Models and setting parameters
to improve the control quality. This method is only
Under the environment of AMEsim with the
related to the change of the nearest K power rather
principle of the lifting arm electro-hydraulic system
than accumulating, so the missing movements have
and MATLAB / Simulink modeling, various kinds
minor influence, moreover, it is easy to have a good
of modules of AMEsim model could be got from
control effect through weighted processing [14].
the Planar mechanical module library and the
Although, piston rod displacement for a desired
Mechanical module library. Finally, either with
value changes, there has little error actions and the
MATLAB /Simulink interface technology, AMESim
output won't change substantially. In addition,
played a major role in simulation environment and
because of the controlled quantity has few
built up the whole simulation model of the lifting
mutations, even if the given value is to alter, the
arm system [15, 16]. For the limits of the software
charged quantity is slowly to change, thereby it is
model library, some sections couldn’t be completely
no longer result in mutant differential.
copied from the prototype element, so that some of
them were replaced, but all of them observed the
3. Dynamic characteristics analysis of the
LBS
principle of the system characteristic unchanged.
The model is as shown in Fig.5.
Fig 5: Simulation model of lifting system
In Fig. 5, Body1 is the lower arm, Body2 is lower
on lower connecting rod, Body8 is working bucket.
connecting rod of the middle arm, Body3 is upper
Denote the formula parameters by actual
connecting rod of the middle arm, Body4 is the
length and the function of (2) can be simplified, as
middle arm, Body5 is the upper arm, Body6 is
given below:
leveling on upper connecting rod, Body7 is leveling
350250 sin 
ft  
Where
(16)
1401000 cos   2212801
t
(1) was negative. With the aid of the triangle cosine
formula and actual structure parameters, a formula
represents the lower arm.
According to the initial installation of the
for
y
and 1 can be defined:
middle arm, determined the sign in the formula of
y
16 sin 1  362  50 cos 21  312 cos 1
1
18761  10480 cos(2 arctan(
))  1.326
125
6 cos 1  6
That is the relation formula of the piston rod
y
(17)
displacement(y) with angle  ：
1
16 sin   362  50 cos 2  312 cos 
18761  10480 cos( 2 arctan(
))  1.326
125
6 cos   6
Took the derivative of
y
and 
with
(18)
y '  f t ' , where t represents the middle
arm.
respect to time t, then the equation is given as






128 sin    16a sin  2arctg 13 8 sin    a  
 393

 cos   1  

ft  


 50





8
sin


a
1
 5 cos a  12.5 sin 2   11a  103 sin   18761  10480 cos 2arctg ( 3

 


cos


1



a  78  25 sin 2    78 cos 
(19)
Pressure of relief valve e
21
MPa
The diameter of piston
100
mm
The diameter of piston rod
50
mm
The length of the piston rod
0.52
m
Kp
1.2
—
Ki
0.01
—
Kd
0.01
—
The diameter of piston
113
mm
The diameter of piston rod
56
mm
The length of the piston rod
0.906
m
Kp
1.25
—
according to the actual type of each element,
Ki
0.01
—
submodel of corresponding element could be
Kd
0.05
—
selected in the drop-down list. Besides, simulation
The diameter of piston
63
mm
The diameter of piston rod
35
mm
The length of the piston rod
0.33
m
Kp
1.4
—
Ki
0.01
—
Kd
0.03
—
Here,
Denoted the formula parameters by actual
length of the upper arm and the function of (2) can
The
lower
arm
be simplified, as given below:
ft  
102542 sin 
(20)
410168 cos   810857
Selecting submodel system is very important
for obtaining the correct simulation results. In the
actual situation and udder the mode of submodel,
The
middle
arm
parameters were set up, as shown in Table. 1.
The
upper
Table 1: Simulation parameters of the system
arm
Numerical
Parameter
Company
value
-2
Viscosity of hydraulic oil
5.1×10
Pa.s
Medium density of hydraulic oil
850
kg/m3
Model
Bulk modulus of hydraulic oil
1700
MPa
parameter
Temperature reference of hydraulic oil
40
℃
Maximum displace of main hydraulic pump
70
ml/r
Rated engine speed
1500
r/min
3.2 Testing and analyzing the LBS
3.2.1 Steady state analysis of the lifting
arm system
When simulation model of the system was
established and the corresponding initial parameters
In this section, the results of the steady state
were set, steady-state simulation of the lifting arm
analysis of the electro-hydraulic system for each
electro-hydraulic system could be in progress. Bode
arm were achieved from the graph of Fig.6, 7 and 8,
diagram of the LBS is as shown in Fig. 6, 7 and 8.
as shown in Table 2. The tests reported above
According to the control theory, quite stable
showed that each LBS has better stability.
conditions of the system are as shown:
Table 2: The results of steady-state analysis
Amplitude margin Kg ≥6dB
Amplitude
Phase margin γ =30 °~ 60 °.
margin(db)
Phase margin（°）
The lower arm system
7.9
42.9
The middle arm system
7.13
55.6
The upper arm system
12.1
35.6
3.2.2 Dynamics analysis of the LBS
When the LBS is working, lifting sequence
and displacement of each lifting arms are different.
In order to research it conveniently, this research
took an example of the highest position and the
operator used the most commonly operation
Fig 6: Bode diagram of lower arm barycenter system
sequence to analysis the result. What’s more, setting
up simulation running time of 120s, step 0.01s. The
analysis results of the simulation are shown as
follows.
1) The lower arm
In order to improve stability and reliability of the
system, the DFI-PID controller algorithm was
employed. The AMESim system with the aid of the
batch processing, optimal parameters of the PID
system was obtained. Furthermore, compared with
the traditional hydraulic model (conventional PID
controller) and draw the comparison chart of the
entrance flow for the hydraulic cylinder, as shown
Fig 7: Bode diagram of middle arm barycenter system
in Fig. 9.
0.020
DFI—PID controller
Y:Velocity[m/s]
0.015
Conventional
PID
0.010
0.005
0.000
-0.005
0
20
40
60
80
100
120
X:Times [s]
Fig 9: The velocity of lower arm barycenter
Fig 8: Bode diagram of upper arm barycenter system
In Fig. 9, barycentric velocity of the lower arm in
the vertical direction can be quickly reached at a
0.020
the
0.015
using
of
the
DFI-PID.
The
dynamic
characteristic of the system was improved greatly.
2) The middle arm
As the same with the lower arm, in order to
Y:Velocity[m/s]
steady value without overshoot, this occurs due to
0.010
DFI—PID controller
0.005
0.000
improve the dynamic characteristics, the DFI-PID
-0.005
controller was applied. The same method was used
-0.010
Conventional PID
0
20
40
compared with the traditional hydraulic model
(conventional PID controller) and
60
80
100
120
X:Times [s]
to get the optimal parameters of the PID system,
Fig 11: The velocity of upper arm barycenter
draw the
comparison diagram of the entrance flow for
hydraulic cylinder, as shown in Fig. 10.
Fig. 11 shows that barycentric velocity of the
upper arm in the vertical direction can be quickly
reached at a steady value without an overstrike. This
0.020
DFI—PID controller
was achieved by DFI-PID controller, the dynamic
Y:Velocity[m/s]
0.015
characteristic of the system was improved greatly.
0.010
4) Working platform
0.005
In harmony with the method of the lifting booms
0.000
analysis, with the algorithm of DFI-PID controller,
Conventional PID
-0.005
0
20
60
40
80
100
120
X:Times [s]
Fig 10: The velocity of middle arm barycenter
then compared with the traditional hydraulic model
(the conventional PID controller) and finished the
contrast diagram of barycentric velocity in the
vertical direction for the operating platform, as
From the graph of Fig.10, velocity in the
shown in Fig. 12.
vertical direction of the middle arm can reach at a
Conventional PID
steady condition rapidly with no overshoot. This
of the stability and reliability for the system were
improved.
3) The upper arm
Y:Velocity[m/s]
great phenomenon was obtained by DFI-PID, much
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
DFI—PID
controller
-0.05
Simulation analysis of the upper arm was
identical with the middle arm. The AMESim system
-0.10
-0.15
0
20
40
60
80
100
120
X:Times [s]
with the aid of the batch processing, optimal
parameters of the PID system was obtained. The
comparison chart of the entrance flow for the
Fig 12: The velocity of working platform
hydraulic cylinder (see Fig. 11) was achieved by
comparing with DFI-PID controller and the
conventional PID controller.
From the graph of Fig.12, the speed of operation
platform in the vertical direction is running
smoothly without jitter. Stability and reliability of
the proposed system had been improved obviously.
4.
Conclusion
This paper analyzed the operational mechanical
of the AWP-LBS, based on which mathematical
model of lifting system, electromechanical coupling
model and transfer function of electro-hydraulic
multi-body dynamics[J]. International Conference
system were established. By taking advantages of
on Intelligent Control and Information Processing,
simulation analysis software in MATLAB and AMES
2010:798 - 802
and the interface technology, an integrated simulation
[3] Xue
Jinlong.
Research
on
platform of the LBS was built to make united
Electro-hydraulic Control System for Self-propelled
simulation realized. The results show that the system
and Folding-arm Type Aerial Working Platform’s
simulation model is effective and the DFI-PID
Working Device[D]. Xi'an: Chang'an University,
controller can achieve better dynamic characteristics.
2013.07
The major aim of this paper is to research on the DFIPID controller, the results are as follows:
[4] Li Huai, Shi Hui-chao, Dai Yu. Dynamics
simulation and finite element analysis of aerial
1) Efficiency of the design can be improved by
building a simulation model with AMES and
platform
folding
arm[J].Construction
Mechanization, 2010,(02):41-43.
modifying the design parameters instead of the
physical parameters debugging.
truck
[5] Masao
NOZAWA.
Development
and
Improvement of Mobile Work Platform for Use in
2) Steady-state analysis of lifting booms for the
upper arm, the middle arm and the lower arm (with
Apple Orchards[J]. Japanese Journal of Farm Work
Research, 2010, (02): 41-42
Bode diagrams) shows that electro-hydraulic system
of each arm is stable.
[6] Shu-wang Du, Zhi-lin Feng, Zhi-ming Fang.
Design of improved PID algorithm for position
3) DFI-PID controller can perform better in
control of servo unit[J]. International conference on
vertically changing the speed of each arm smoothly
Computer and Communication Technologies in
and stably than conventional PID controller. Thus,
Agriculture Engineering, 2010,(3): 333 - 335
[7]M.Zhou,N.Pagaldipti,H.L.Thomas,Y.K.Shyy.
good dynamic and static characteristics are obtained,
without overshoot and oscillation.
An integrated approach to topology,sizing,and shape
4) Practical function of the promoted DFI-PID
in this paper has been proved through this research
optimization[J]. Structure and Multi disciplinary
Optimization，2004(26):208-317.
and the MATLAB /Simulink and AMESim are tested
[8] Liang Chunying, Wang Xi, Ji Jianwei, etc.
to be valid and reliable, which puts lights on the future
Research of PID Algorithm for Valve Controlled
research and design on the AWP.
Hydraulic Motor Variable Rate Fertilizer Control
System[J].Computer and Computing Technologies in
Acknowledgment
Agriculture VII, 2014.
The authors are thankful for the support of the
[9] Zhang Jing. Differential forward PID
Scientific and Technological Project of Chongqing City
controller based on RBF network[J]. Ordnance
(CSTC 2009AC6077) and also give their sincere thanks
Industry Automation,2007,(09):60-62.
to
Chongqing
Jiaotong
University
for
[10] Yang Xiao-sheng, PENG Zhi-jian, XIAO
offering
experiment support.
Yi-bo.
Temperature
control
system
based
on
differential ahead PID algorithm of poly-silicon ingot
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