A Design for Ink-Supply Circulation System based on Advanced PID

A Design for Ink-Supply Circulation System based on Advanced PID
2015 International Conference on Computational Science and Engineering Applications(CSEA 2015)
ISBN:978-1-60595-296-3
A Design for Ink-Supply Circulation System
based on Advanced PID Control
Xinbo Wang1,a, Jianhua Hu1,b, Yunkuan Wang1,c,
Haibo Jin2,c, Sheng Wang2,c, Qi Cao2,c
1
Institute of Automation, Chinese Academy of Science, Beijing, China
2
Bohai Shipyard Group Corporation, LTD, Liaoning, China
a
[email protected], [email protected], [email protected],
Keywords: ink-supply circulation system; advanced control; system identification; genetic algorithm
Abstract: This paper presents a well-designed ink-supply circulation system to guarantee adequate
ink supply and maintain a stable negative pressure environment for large digital ink jet printing
system. In order to make this system fit for a variety of situations, we put forward an adaptive
control algorithm. At first, the least square method is used for the identification of the system. Then
a fitness function is defined with the consideration of system error, control energy, rising time and
overshoot, and genetic algorithm is used to search for the best PID parameters. The system we
design has been applied to some industrial companies and has a good performance on digital
printing.
Introduction
Nowadays, along with the development of printing technology and computer technology,the
printing field has changed so much from traditional printing to digital printing. Low cost and the
ability of continuous and stable running are the two demands of a large digital ink jet printing
system[1]. Though an industrial printhead is very expensive, it has the advantages of excellent
performance and long service life. To reduce the cost, ink-supply system should be separated from
the printhead[2].
Ink-supply system provides ink and negative pressure environment for the printhead[3]. It is an
important part of the digital ink jet printing system and has a significant influence on print effect.
For one thing, we should guarantee adequate supply of ink. If the printhead is lack of ink, ink
breaking phenomenon will appear when the printing system is running which will do harm to
continuous production. For another thing, we should ensure accurate control of ink supply pressure.
Variations in the vacuum can result in image defects. If the negative pressure is too low, ink will
drop from the nozzles. If the negative pressure is too high, it is possible to cause the printhead to
ingest air and stop firing. Therefore, adequate ink supply and stable negative pressure environment
are the purposes in designing an ink-supply system[4,5].
With the printing speed of a large digital ink jet printing system getting faster and faster,
traditional negative pressure ink-supply system cannot meet the new requirements. It is necessary to
design a new ink-supply system-“ink-supply circulation system”. According to the major
technological transfer project-“A design for large scale digital ink jet printing system”, this paper
presents a well-designed ink-supply circulation system. It can not only guarantee adequate ink
supply, but also maintain a stable negative pressure environment.
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In practical application, the number of printheads and the type of ink are variable. Using the same
PID parameters cannot get the ideal control effect. In order to make this ink-supply circulation
system fit for a wide variety of situations, we put forward an adaptive control algorithm. At first, the
least square method[6,7] is used for the identification of ink-supply circulation system. After getting
the mathematical model, we set up a fitness function, and use genetic algorithm[8-9] to search for the
best PID parameters.
A design for ink-supply circulation system
Compared with traditional negative pressure ink-supply system, ink-supply circulation system
provides three main benefits to the print system. It allows for quicker priming times, helps maintain
inks that are prone to sedimentation, and it keeps the printhead wetted when handling quick drying
inks.
When designing a circulation system, it is important to maintain an outlet pressure from 10
inches H2O to 50 inches H2O depending on the jetting fluid, application and system. The key word
is maintain. Whatever pressure is right for the application, it is important to make the circulation
system to maintain that amount.
Fig.1 shows the ink-supply circulation system we design. It consists of three parts: ink supply,
circulation and vacuum generator.
Fig.1 ink-supply circulation system
Ink supply is made of an ink-supply reservoir, an ink-supply pump and a filter. It is used to
provide ink for the circulation reservoir. As the circulation reservoir empties, it signals the
controller which causes it to refill from the ink-supply reservoir. Vacuum generator is used to
maintain an inlet pressure at a certain level (30mbar). Circulation is the most important part of the
system. It works in the following manner:
1) Slave circulation pump draws ink from circulation reservoir.
2) The ink passes through the degasser to get the air out.
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3) It then passes through the filter to remove any impurities.
4) On one hand, the degassed and filtered ink returns to circulation reservoir. On the other hand,
the ink fills the printhead.
5) The printhead prints then circulates additional ink to circulation reservoir through circulation
pump.
By controlling the speed of the circulation pump, the circulation system can maintain an outlet
pressure at the point we set. Fig.2 is the control block diagram.
Fig.2 circulation control block diagram
System identification and parameter tuning
The ink-supply circulation system we design can not only provide adequate ink supply, but also
maintain a stable negative pressure environment for printhead. However, in practical application,
each time we change the number of printheads, the type of inks or the operating temperature, we
have to adjust the PID parameters manually. In order to make this system be adaptive to a variety of
situations, an advanced PID control algorithm shown as Fig.3 based on system identification and
genetic algorithm is applied.
Fig.3 advanced PID control algorithm
Least Square Method. As it is very difficult to get the mathematical model of this system from the
theory, system identification becomes the best choice. Consider a grey-box model shown as Fig.4:
Fig.4 grey-box model
u(k) is the input of the system, y(k) is the output of the system, z(k) is the Observed value of y(k),
G(k) is the model of the system, v(k) is the measurement noise.
The differential equation of system is defined as
n
n
i 1
i 1
y (k )   ai y(k  i)   bi u (k  i)
(1)
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Then
n
n
i 1
i 1
z (k )   ai y(k  i)   bi u (k  i)  v(k )  h(k )  v(k )
(2)
Where h(k )   y(k  1), y(k  2),, y(k  n), u(k  1), u(k  2),u(k  n) ,
  [a1 , a2 ,an , b1 , b2 ,bn ]T .
Let Z  [ z (1), z (2),, z (m)]T , H  [h(1), h(2),, h(m)]T , then we can get the system parameters
as follows:
ˆ  ( H T H ) 1 H T Z
(3)
Genetic Algorithm. When getting the model of the system, the PID parameters can be tuned
through genetic algorithm. With the consideration of system error e(t), control energy u2(t), rising
time tu and overshoot, the fitness function[10] is defined as



w1  e(t ) dt w2  u 2 (t )dt w3t u
e(t )  0

0
0
J  


2
w1 0 e(t ) dt w2 0 u (t )dt w3t u  w4 0 e(t ) dt e(t )  0
(4)
where w1  0.95 , w2  0.05 , w3  2 , w4  100 .
Steps for GA:
Step1: Determine the search space of Kp, Kd, Ki and the length of encoding;
Step2: Generate initial population randomly consist of 50 individuals, set iteration number
K=100;
Step3: k=1;
Step4: Evaluate the fitness of every individual in the current generation;
Step5: Generate the next generation by selection, crossover, mutation;
Step6: k=k+1; if k>K, go to step7; Otherwise, go to step4.
Step7: Termination. A solution is found that satisfies minimum criteria or fixed number of
generations reached.
Result
Fig.5 shows the result of system identification. There are two observed signals, u(k) and z(k),
where u(k) is the control signal and z(k) is the outlet pressure. The sample period is 0.01s. Assuming
that the system is a three-order model,  is estimated as

  [-2.0478,1.3869,-0.3263,0.1731,-0.1918,0.0428]
The curve plotted with “*” shows the predictive value of the outlet pressure. It is very close to
z(k), which indicates a good identification.
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Fig.5 result of system identification
After getting the model of the ink-supply circulation system, PID parameters are tuned by genetic
algorithm. Fig.6 shows the control effect with tuned PID parameters. It has the advantages of small
overshoot and little response time.
Fig.6 control effect with tuned PID parameters
So far, the ink-supply circulation system we design has been applied to some industrial
companies and played an important role in digital printing. Fig.7 shows the ink-supply circulation
systems in practice.
Fig.7 applications
Conclusion
This paper presents a well-designed ink-supply circulation system. It can not only guarantee
adequate ink supply, but also maintain a stable negative pressure environment. What’s more, this
system is applicable to a variety of situations. It can drive from one to thirty printheads. In different
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cases, in order to get the ideal PID parameters, an advanced PID control algorithm based on system
identification and genetic algorithm is put forward. After getting the measured value of the system,
the model can be identified by least square method. With the consideration of system error, control
energy, rising time and overshoot, a fitness function is defined. Finally, we can get the best PID
parameters based on genetic algorithm. When applying this circulation system into practice, it has a
better performance on print effect and plays an important role in digital printing.
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