This document discusses the application of fuzzy-PID and multi-neuron adaptive PID control algorithms to control warp tension in a rapier loom. It presents simulations comparing the two algorithms. The results show that the multi-neuron adaptive PID control algorithm provides faster response and smaller overshoot than the fuzzy-PID control algorithm or traditional PID control algorithm.

1. The application of Fuzzy-PID and Multi-neuron adaptive PID control algorithm
in the control of warp tension
Lei Li1,2
, Jiancheng Yang1,2
1. School of Mechanical and Electronic Engineering
Tianjin Polytechnic University
2. Advanced Mechatronics Equipment Technology
Tianjin Area Major Laboratory
Tianjin 300160, China
li_lei5656@163.com
Yongli Zhao1,2
, Yan Liu1,2
, Liangchao Cong1,2
1. School of Mechanical and Electronic Engineering
Tianjin Polytechnic University
2. Advanced Mechatronics Equipment Technology
Tianjin Area Major Laboratory
Tianjin 300160, China
Abstract—For the purpose of control warp tension of rapier
loom and prevent negative impacts on the quality of the fabric
by reasons of the excessive fluctuation. This paper took let-off
system of SAURER400 rapier loom as investigated subject and
laid out the application of fuzzy-PID and multi-neuron
adaptive PID control method. This paper gone through with a
simulation by use of Simulink of the Matlab and took the
simulation results compared with the simulation curve of
multi-neuron adaptive PID and fuzzy-PID. The results show
that the simulation curve of multi-neuron adaptive PID
control algorithm was fast response and small overshoot.
Keywords-warp tension; multi-neuron PID control; fuzzy
PID; algorithm; network
I. INTRODUCTION
Loom warp tension had a significant impact on the
quality of fabric. In the weaving, whether or not to maintain
the stable warp tension had been a great concern to people
[1-3]. At present, whether in domestic or abroad, the PID
control algorithm and fuzzy-PID control algorithm were
mainly applied to control loom warp tension in the area of
industry control, but the multi-neuron adaptive PID control
algorithm was very little to involve. The shortcomings of the
PID control algorithm were that the PID parameters would
be setting generally by the manual work and it was very
difficult to guarantee the efficiency of PID control always at
the optimum condition by one-time-tuning PID parameters;
The fuzzy-PID control needed the very rich experience,
moreover the parameter setting also had a certain limitation.
Because of these deficiencies of the two kinds of algorithms,
but also the loom exist the characteristics of non-linear,
time-varying and multiple interference. Therefore, the multi-
neuron adaptive PID control algorithm was put forward to
control the warp tension in this paper.
II. THE PID CONTROL METHOD OF WARP TENSION
PID control algorithm is a very common control method
in industry. Its merits are principle simply, easy tuning and
using and so on. A large number of actual operate
experiences and theoretical analysis proves that this control
method can be widely used in most of the industrial
production sector, and has strong applicability and
effectiveness of regulation [4].
PID controller is a linear controller, differential
equations’ mathematical model of PID controller can be
written as:
( )
( ) ( ) ( ) ( )
t
p D
I 0
1 de t
u t K e t e t d t T
T d(t)
⎡ ⎤
= × + × ⋅ + ×⎢ ⎥
⎣ ⎦
∫ (1)
In the equation, PK is proportionality coefficient, IT is
integral time constant , DT is differential time constant.
In the actual system, in order to make the control
algorithm easy to realize, using the rectangle method to
replace the part of integral in (1), then differential equation
would be obtained as follow:
0
( ) { ( ) ( ) [ ( ) ( 1)]}
k
D
p
iI
T T
U k K e k e i e k e k
T T=
= × + × + × − −∑ (2)
III. FUZZY-PID CONTROL METHOD
A. Fuzzy-PID control principle
In fuzzy control theory, fuzzy controller’s effect is
through the computer, according to fuzzy input information
that transferred from exact quantity, carried out fuzzy
reasoning according to linguistic control rules which
obtained from the summary of manual control strategy,
given fuzzy output decision and then converted them into
exact quantity, achieved the purpose of control the
controlled objects [5]. This reflects that while people control
the controlled objects, the observed input exact quantity
converted into fuzzy quantity constantly, after a series of
human logical reasoning which will make a fuzzy decision,
and then converted the decided fuzzy quantity into exact
quantity, to realize the whole process of manual control. It
can be seen that the fuzzy controller reflects the
mathematical model which fuzzy set theory, linguistic
variables and fuzzy reasoning do not have, however the
control strategy is the effective application of complex
system which is only a qualitative description by the form of
language.
There are three steps when designing the fuzzy
controller. First of all, blur the exact quantity, the main
purpose of this step is convert linguistic values of linguistic
variables into fuzzy subset in a proper universe, so this step
can be called fuzzification of variables; Secondly, sum up
the practical hand-on background, then express these hand-
V7-678978-1-4244-6349-7/10/$26.00 c 2010 IEEE

2. on background as control rules by use of a group fuzzy
conditional statement, and calculate the fuzzy relation which
determined by fuzzy control rules, this step also can be
called fuzzy decision; Lastly, for the actual control,
precision the output results of fuzzy decision, this step is
called defuzzification.
Fuzzy PID controller based on the error E and error
variation EC as input, they can meet the requirements of at
different times of E and EC which can be self-tuning to the
PID parameters. Modifying the PID parameters online by
use of fuzzy control rule, then it constitutes a fuzzy PID
controller, its structure was shown in Fig.1 [6-8].
Figure 1. The simplified schematic of fuzzy PID control system
B. Fuzzy-PID simulation
“Fuzzy Logic Toolbox” of Matlab offered various ways
in designing of fuzzy logic controller and system. The
toolbox offered commonly used utility functions which can
generate and edit fuzzy inference system, this paper use
“GUI” function edits function and generate fuzzy control
system. Operate “Fuzzy” function in Matlab and enter into
the fuzzy logic editor, choose Mamdani as controller type.
Based on the above analysis, input the membership function
and quantization interval of E, EC, PK , IK , DK , input
fuzzy control rules in the form of “if-then”. Take the method
of “and” as “min”, the method of “or” as “max”, he method
of “implication” as “min”, the method of “aggregation” as
“max”, the method of “defuzzification” as “centroid”, and
establish a new “FIS” file, named as “fuzzypid.fis” folder.
Since the universe of each variables are {-3 -2 -1 0 1
2 3}, and they all obey triangular distribution, therefore,
the membership function of each variable distribution were
similar, and was shown in Fig.2. The interface of fuzzy
inference system was shown in Fig.3.
Establish a fuzzy inference system which has two inputs,
three outputs as needed. According to the requirements of
the above, setup input and output’s membership function,
establish control rules of fuzzy inference system according
to control rule table, the establishment form of control rules
was shown in Fig.4.
The fuzzy inference system can be established like this,
suppose quantized value of system error E and change rate
of error EC were 0.5. By the control rule base, it is easy to
see the quantized value of PKΔ , IKΔ , DKΔ that exported
are -1.5, 0.84, 0.25 respectively. Then the output display of
fuzzy PID control system was shown in Fig.5.
Figure 2. The membership function of variable
Figure 3. The interface of fuzzy inference system
Figure 4. The control rules interface of inference system
The Fig.5 reflects the influence of the shedding and beat-
up to the warp. By the comparison and analysis the above
figure, it can be seen that the surface smoothness of the B is
prior than the A, this is because the different of two fuzzy
design rules, result in simulation results are also different.
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3. A
B
Figure 5. The output display of fuzzy PID control system
The simulation results of the fuzzy PID show that the
preparation of fuzzy rules have a closely relationship with
the production process, only have a good understanding to
technologies that can make out perfect fuzzy rules, and then
design a good fuzzy controller. Although the simulation
results of the A is better than the B, some parts are not very
smooth, if we have not a deep understanding on textile
technology, this fuzzy PID control method can not be used
to control the loom’s electronic let-off and take-up.
IV. MULTI-NEURON ADAPTIVE PID CONTROL METHOD
A. Multi-neuron adaptive PID control principle
Artificial neural network is a network that was
constituted by the interconnection of artificial neurons.
Using artificial neural network to simulate the human brain
that can process intelligent neural network information and
artificial neuron is one important factor. There are more than
fifty kinds of structure of artificial neural network models,
the most common are thirteen kinds, which have typical
Hopfield associative memory network, Boltzmann learning
machine and error back-propagation training algorithm of
multi-layer network. A typical artificial neuron model is
shown in Fig.6.
In the figure, [ ], ,1 2 nl l lL was input quantity, ( )f ⋅ was
excitation function, it reflected the information processing
characteristic of nerve cells. Different form of excitation
Figure 6. A typical artificial neural model
functions would cause the neuron have different non-linear
characteristics, and the network function is also different.
Using semi-linear function as excitation function, make the
output of neuron as all the signals’ weighting and driving.
The commonly used excitation functions are threshold type,
piecewise-linear type and S-shaped curve, they are used for
the Boolean system and Continuous system respectively. iθ
was the threshold quantity, jiw was the connection weights
from the j neuron to the i neuron of last layer. iS represented
external input signals, it can control the internal state of
neuron iu and the output of the i neuron iy . This model can
be described as follows in mathematical language:
i ji i i i
j
a w l S θ= + −∑ (3)
( )i iu g a= (4)
( ) [ ( )]i i iy f u f g a= = (5)
Industrial control needs to maintain its continuity,
usually use S-shaped curve as the excitation function,
including logarithm, tangent and sigmoid function, etc.. The
two sigmoid functions describe as follows:
1
( )
1 exp( )
f x
x
=
+ −
(6)
1 exp( )
( )
1 exp( )
x
f x
x
− −
=
+ −
(7)
They reflected the saturated characteristic of excitation
function. In the feed-forward neural network training, the
former is used to study the functions that have not passing
the original point, while the latter is just opposite. Such as
learning the slope of a straight line, with the latter can
quickly learn, but with the former will not be able to learn.
Artificial neural network has a great ability of
information synthesis, learning and memory, self-learning,
adaptive and approximate any non-linear function, either can
handle the process that hard to describe by models and rules,
and it has been successfully applied in some uncertain
systems’ control. Artificial Neural Network faced the main
problems in practice control are algorithm complexity, long
learning process, the parameters’ convergence speed slowly,
existence of local minimum points, etc. Combined neural
network with PID control can achieve a better control result.
There two kinds of main combination pattern: one is
addition of a neural network based on the conventional PID
controller, and use neural network to adjust PID parameters
online; another is adopt single neuron or multi-neuron
structure, the input values of neurons are deviation that
V7-680 2010 2nd International Conference on Computer Engineering and Technology [Volume 7]

4. treated by proportional, integral, differential. The major
disadvantages of first method are complicated in structure
and have not achieved to the aim that combined neural
networks with PID control rules. This paper focuses on
study the multi-neuron adaptive PID controller.
B. The simulation of multi-neuron adaptive PID
controller
The simulation has written a multi-neuron adaptive PID
control model which based on supervised Hebb rule by use
of MATLAB language, invoked it in the simulation
environment of Simulink, and embedded into the simulation
model of system then it can be simulated [9]. In the
simulation environment of Simulink, build up simulation
model for multi-neuron self-adaptive PID control algorithm
by use of Simulink was shown in Fig.7.
Figure 7. The multi-neuron adaptive PID overall control system
In the Simulation, take learning rate Pη , Iη , Dη as 50,
300, 1 respectively. Initial weight are 0.3, 0.3, 0.3, take
neuron proportional coefficient k as 0.5, sampling period as
0.001s.
The step response curve of multi-neuron adaptive PID
control algorithm was shown in Fig.8.
Figure 8. The step response curve of multi-neuron adaptive PID
In order to compare the two kinds of control algorithm
conveniently, the simulation curve of traditional PID control
algorithm and multi-neuron adaptive PID control algorithm
were shown in the same oscilloscope through
MATLAB/Simulink simulation toolbox. The step response
curve of the two simulation results were shown in Fig.9.
Compared with the two simulation curves of Fig.8 and
Fig.9, it can be seen that the system response time is slower,
Figure 9. The step response curve of PID and multi-neuron adaptive
PID
and have a large range of overshooting under the action of
traditional PID controller. The transition time of system
which based on multi-neuron adaptive PID control algorithm
is about 400s, and there is no overshooting exist, system
stability. So it obviously that multi-neuron adaptive PID
controller has a better control effect.
V. CONCLUSIONS
The simulation results manifested that multi-neuron
adaptive PID control algorithm had a lot of advantages
whose system response time is quicker and there is no
overshooting exist, system stability and no fluctuation. The
transition time of system which based on multi-neuron
adaptive PID control algorithm is about 400s.
ACKNOWLEDGMENT
I wish to thank the IEEE for providing this template and
all colleagues who previously provided technical support.
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