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Researches on Temperature Control Strategy of SMHS-Type 3D Printing Based on Variable Universe Fuzzy Control

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Selective micro heat sintering (SMHS)-type 3D printing technology is a widely applied method in rapid prototyping, which uses an electric heating component to sinter non-metallic powder. It requires precise control of the heating component's energy and its sintering time. Temperature is one of the key factors that affect the forming quality of fused-type 3D printing technology. Aiming at the nonlinear and time-delay characteristics of temperature control in fused-type 3D printing, a fuzzy control method based on variable universe fuzzy control was studied. This fuzzy control method adopts a set of nonlinear expansion-contraction factors to make the variable universes change with the adaptive error, which can help acquire adaptive temperature adjustment in the rapid prototyping process control. The results of the simulation and experiment showed that the controlled temperature response was faster, the overshoot was smaller, and the stability was better compared to the conventional fuzzy proportion integration differentiation (PID) algorithm after the temperature reached the target temperature. The printed results indicated that the universe fuzzy PID control can effectively improve the accuracy of the workpiece shapes and that the density distribution of the workpiece is increased, which can help improve the forming quality.
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Wu, T. et al.
Paper:
Researches on Temperature Control Strategy of SMHS-Type
3D Printing Based on Variable Universe Fuzzy Control
Tao Wu, Yiru Tang, Dongdong Fei, Yongbo Li, and Wangyong He
School of Automation, China University of Geosciences
Wuhan 430074, China
E-mail: wutao@cug.edu.cn
[Received July 8, 2016; accepted October 26, 2016]
Selective micro heat sintering (SMHS)-type 3D print-
ing technology is a widely applied method in rapid
prototyping, which uses an electric heating component
to sinter non-metallic powder. It requires precise con-
trol of the heating component’s energy and its sinter-
ing time. Temperature is one of the key factors that
affect the forming quality of fused-type 3D printing
technology. Aiming at the nonlinear and time-delay
characteristics of temperature control in fused-type
3D printing, a fuzzy control method based on vari-
able universe fuzzy control was studied. This fuzzy
control method adopts a set of nonlinear expansion-
contraction factors to make the variable universes
change with the adaptive error, which can help ac-
quire adaptive temperature adjustment in the rapid
prototyping process control. The results of the sim-
ulation and experiment showed that the controlled
temperature response was faster, the overshoot was
smaller, and the stability was better compared to the
conventional fuzzy proportion integration differenti-
ation (PID) algorithm after the temperature reached
the target temperature. The printed results indicated
that the universe fuzzy PID control can effectively im-
prove the accuracy of the workpiece shapes and that
the density distribution of the workpiece is increased,
which can help improve the forming quality.
Keywords: temperature control on 3D printing, fuzzy
control, variable universe, constant energy printing
1. Introduction
Selective micro heat sintering (SMHS)-type 3D print-
ing is a new type of rapid prototyping technology. It
adopts a thin film thermal print head for sintering non-
metallic powder. It needs precise control of the hot-spot
energy and sintering time. The thermal head of the print
system has the advantages of rapid increase in tempera-
ture and sensitive resistance change due to the presence of
a sensitive temperature sensor with a negative temperature
coefficient thermistor inside the print head. The SMHS-
type 3D printing control system is a nonlinear, strong cou-
pling, time-delay system. The temperature of the thermal
print head used in this type of 3D printer rises quickly.
Actually, it is very difficult to develop an accurate mathe-
matical model with the characteristics of nonlinearity and
time lag; as a result, the conventional fuzzy control has
difficulty achieving a good control effect [1, 2]. Refer-
ence [3] put forward the idea of a variable universe fuzzy
control: in the case of fuzzy rules being kept constant,
the control adjusts the universe of variables according to
the error and error change rate to improve the applicabil-
ity of fuzzy rules to the control system. In other words,
it actually increases the rules by universe shrinking with
interpolation node encryption, which ultimately improves
the accuracy of the fuzzy system. In view of the prob-
lem of lower control precision of conventional fuzzy con-
trollers, a variable universe fuzzy controller in which the
universe was contracted along with its error reduced, was
presented for this control system [4, 5]. In this study, a
mathematical model for temperature control of an SMHS-
type 3D printer was developed. The printing process was
completed by using a variable universe fuzzy control to
improve the precision of the temperature control and real-
ize constant energy printing.
2. Modeling of the Temperature Control
System of SMHS-Type 3D Printing
2.1. Control Characteristic of SMHS
The heat generated by a thermal print head is due to the
thermo-electric effect. It is approximately proportional
to the square of the current. The formula of the temper-
ature and heating time, excluding the thermal exchange
between the thermal print head and the air, is as follows:
ΔT=I2Rt
cm =(VHVcom)2Rts
(R+Ric)2cm ...... (1)
where ΔTis the temperature variation, Ric =11.7Ωis the
driver IC resistance, tsis the strobe printing pulse width,
VH is the heat voltage, Ris the heater’s average resis-
tance, and Vcom =0.5 V is the common electrode voltage
drop.
In the case of the same materials, fixed heat capacity,
and weight, the ideal working state is that there should be
a first-order linear relationship between the temperature
166 Journal of Advanced Computational Intelligence Vol.21 No.1, 2017
and Intelligent Informatics
Temperature Control Strategy of SMHS-Type 3D Printing
of the thermal printing head and its heating time.
The formula for obtaining the linear relationship be-
tween heat energy and temperature variation is
Q=cm(T2T1)=cmΔT........ (2)
where Qis the heat energy, ΔTis the temperature varia-
tion, mis the mass of the powder, and cis the heat capacity
ratio.
With the use of the polyamide powder PA66, a com-
mon printing material, as an example, when it is heated
from room temperature (25C) to 170C, its heat energy
is calculated as follows: based on the experiment data, the
specific heat capacity of polyamide c=1.675 J/(g·C) and
the polyamide powder mass contacted by the first line of
the print header are very small, approx. 0.2 g. The energy
required for heating is 48.575 J.
Base on the data sheets of print head, a frame of data
printed has 448 heat points, which supply a current of
30.4 mA per point and a heating resistance of R=750 Ω.
Because every point of the print head can provide an av-
erage power of 0.69 W, 448 points can thus provide an
energy of 309.12 W. Therefore, the temperature lag time
is about
t=Q
448P=48.575
448 ×0.69 =0.157[s] .... (3)
2.2. Modeling of the Temperature Control System
The controlled variable of the system is the tempera-
ture of the thermal printing head through its electric heat-
ing device. An electric heating device is a self-balancing
system. It can be described as a two-order system with a
pure lag. The response characteristics of a two-order sys-
tem and those of a first-order system are similar because
their open-loop response curves are all S-shaped curves
without vibration. Therefore, the use of the two-order sys-
tem can be equivalent to the use of the first-order system
with the same static gain, time constant, and time delay.
Therefore, the approximate transmission function of the
temperature control model is defined as follows [6]:
G(s)= K
Ts+1e
τ
s........... (4)
where K,T,and
τ
represent the open-loop gain, inertial
time constant, and pure lag time, respectively.
Based on the print head thermal characteristics and ac-
tual test data, the values for these variables were K=1,
T=0.1s,and
τ
=0.05. The formula for the transmission
function is defined as follows:
G(s)= 1
0.1s+1e0.05s......... (5)
3. Variable Universe Fuzzy Controller
3.1. System Requirements
The main control objective of the thermal print head
temperature control system is to increase the temperature
rapidly and safely, enabling it to reach the set tempera-
Fig. 1. Structure of fuzzy system.
ture. The system allows only a little overshoot because
too much of it may have a bad effect on the forming qual-
ity, and, typically, the overshoot should be less than 2%.
Moreover, the printing supplies such as the polyamide
powder need a constant heat energy after they reach the
melting point and absorb the heat to melt. The temper-
ature change may seriously affect the quality of the 3D
printing.
3.2. The Fuzzy PID Controller
The working principle of the fuzzy proportion integra-
tion differentiation (PID) strategy is based on the error
and the error change rate as input, using a PID control,
and on the calculation of three aspects of different com-
binations as an output control. The current PID optimiza-
tion design methods are often difficult to consider because
of the system requirements for reliability, speed, and ro-
bustness [7]. The fuzzy controller determines the param-
eters of the PID controllers according to the current sys-
tem state. The structure of the fuzzy PID control system
is shown in Fig. 1. There are three basic processes for
designing a fuzzy controller: fuzzy, fuzzy inference, and
non-fuzzy treatment.
3.3. Factor Selection for Expansion and Contrac-
tion
Designing a reasonable expansion-contraction factor is
the key to the successful use of the variable universe
fuzzy controller. The purpose is to determine a reason-
able mechanism of the change in the universe and, also,
to achieve a good control effect. The field remains un-
changed when the input error and the error change rate
are large. The universe contracts when the input error
and the error change rate are reduced. The fuzzy field
of the subset contracts accordingly. It is equivalent to in-
creasing the fuzzy rules and improving the control preci-
sion. Moreover, the design of the variable universe fuzzy
control does not need too much expert knowledge [8]. A
grasp of the rules’ trend on the whole is enough. The di-
vision of the universe is shown in Fig. 2. The initial fuzzy
universe of the error and the error change rate can be set
as
X=[E,E].............. (6)
where Eis a real number. Dividing [E,E]into seven
parts, we obtain the following:
{NB,NM,NS,ZO,PS,PM,PB}...... (7)
Vol.21 No.1, 2017 Journal of Advanced Computational Intelligence 167
and Intelligent Informatics
Wu, T. et al.
Fig. 2. Initial universe and fuzzy partition.
Fig. 3. Universe contraction and expansion.
where the variables represent “Negative Big, “Nega-
tive Middle,” “Negative Small,” “Zero,” “Positive Small,
“Positive Middle,” and “Positive Big,” respectively.
Using
α
(x)as an expansion-contraction factor, we can
transform the initial fuzzy universe as
X=[
α
(x)E,
α
(x)E].......... (8)
where
α
(x)determines the situation of the universe.
Fig. 3 shows that the core of the theory of variable uni-
verse is the selection of the expansion-contraction factor
and that the changes in the factor determine the shape of
the theory after the universe changes.
Based on the relationship between the error and the uni-
verse, it is clear that, when x[E,E], the expansion-
contraction factor x→
α
(x)must satisfy the following
conditions:
(1) When the error value of xis B, the expansion-
contraction factor should also be big. In the case of a
large error, only the rough control rules are adopted,
the rules do not need to be increased, and the domain
is not changed. Hence, d
α
(x)/dx should be small.
(2) When the error value of xis M, the expansion-
contraction factor should also be medium. In this
condition, the control rules should be appropriately
increased, and the field should be reduced. Hence,
d
α
(x)/dx should be medium too.
(3) When the error value of xis S, the expansion-
contraction factor should also be small. In this
case, precise control rules are needed, the fuzzy
rules should be increased rapidly to speed up the
convergence speed, and the change in speed of the
expansion-contraction factor should be fast so that the
Fig. 4. Different expansion-contraction factors and error
change rates.
error rapidly tends to zero. Hence, d
α
(x)/dx should
be big.
The commonly used proportional expansion-
contraction factor and exponential expansion-contraction
factor both have the aforementioned characteristics. Here,
we discuss an improved expansion-contraction method
compared to the exponential expansion-contraction
factor. Expansion-contraction factors must meet the
following conditions:
Duality:
α
(x)=
α
(x);
Zero avoidance:
α
(0)=0,
α
(0)0;
Monotonicity:
α
(x)strictly monotonically increas-
ing on [0,X];
Coordination: x[0,1],|x|≤
α
(x)X.
Expansion-contraction factors have two common
forms: proportional and exponential. They are described
in Eqs. (9) and (10), respectively:
α
(x)=|x|
E
τ
;
τ
=1 ......... (9)
α
(x)=1
λ
1ek1x2;
λ
1>0,k1>0 ....(10)
Whichever form is used, its ultimate goal is to ensure that
every change in the universe is the best to achieve a bet-
ter control performance [9]. There is also an improved
expansion-contraction factor, which is described as
α
(x)=1
λ
2ek2|x|+k3x2;
λ
2>0,k2>0,k3>0 (11)
where the initial fuzzy universe is set to X=[2,2],
λ
1=1,
λ
2=1, k1=0.8, k2=0.9, and k3=0.01. A
sketch map of the different expansion-contraction factors
and error change rate is shown in Fig. 4. It shows that the
error change rate of the improved expansion-contraction
factor was even greater than those of the other two factors
when the error was small. It made the universe change
168 Journal of Advanced Computational Intelligence Vol.21 No.1, 2017
and Intelligent Informatics
Temperature Control Strategy of SMHS-Type 3D Printing
Tabl e 1 . Fuzzy PID control rules.
rapidly and shortened the stabilizing time of the systems.
When the error was medium, the error change rate was
large, the rate of change gradually became smaller, and
the expansion-contraction factor began to contract.
3.4. Fuzzy Control Principle
Fuzzy control is the application of fuzzy logic theory
in control engineering. Its basic principle is to use lan-
guage to summarize the operators’ control strategy and to
use linguistic variables and the fuzzy set theory format to
control the algorithm [10].
Based on experience and perceptual reasoning, the PID
parameter tuning experience is summed up and described,
and the control rules are obtained. The fuzzy rules are
shown in Table 1 .
4. Simulation and Printing Results
A variable universe fuzzy PID controller was designed
in Section 3 and applied to the SMHS-type 3D printing
temperature control system. Finally, we developed the
model and simulated the process in MATLAB; moreover,
we compared the control effect between the conventional
fuzzy PID control and the variable universe fuzzy PID
control. The variation in temperature einside the print
head was within the range of 0C to 240C, the basic uni-
verse for the error change rate of the temperature variation
was 100C/ms to 100C/ms, and the fuzzy language in-
ferences eand ec were turned into the integral universe
{−6,5,4,3,2,1,0,1,2,3,4,5,6}.
Based on the characteristics of the temperature control
system of the thermal printing head, the control parame-
ters were as follows: Kp=2.4, Ki=0.1, and Kd=0.025.
The selected expansion-contraction factor is defined in
Eq. (12):
α
(x)=10.98e0.9|x|+0.01x2.......(12)
The simulation result under different working condi-
tions is shown in Fig. 5. It shows that the simulated
response curves of the two different approaches were at
170C, 187C, and 238C. It also clearly shows that, un-
Fig. 5. Response curves of the variable universe and com-
mon fuzzy controls under different inputs.
Fig. 6. Response curves of the variable universe and com-
mon fuzzy controls at different intervals of the printing pro-
cess.
der the large step jump, the universe fuzzy PID control
had a better performance in terms of overshoot and time
adjustment than the common fuzzy PID control; however,
the former’s response time was longer than that of the lat-
ter. The value of the overshoot for the two approaches was
less than 2% and about 4%–10%, respectively.
For a more realistic example, Fig. 6 shows the output
curves of the two control modes in the actual printing pro-
Vol.21 No.1, 2017 Journal of Advanced Computational Intelligence 169
and Intelligent Informatics
Wu, T. et al.
(a) (b)
Fig. 7. Printed results: (a) universe fuzzy PID control and
(b) common fuzzy PID control.
cess. It shows that the input was 170C at the beginning,
which simulated the process of commencing work. After
the step signal was given, the overshoot of the response
curve under the common fuzzy PID control was about
16.7%, which was about 2.3% lower than that of the uni-
verse fuzzy PID control. In addition, the adjustment time
of the former was longer than that of the latter. During
the printing process, “shifting of lines” is an unavoidable
operation. When this operation is performed, the temper-
ature of the print head will reduce to a certain degree at
first, and then it will recover to its previous temperature
after about 0.1 s, as shown in Fig. 6.However,there-
sponse curves of the two control methods were much the
same during this change. The results showed that the uni-
verse fuzzy PID control had a better control effect than
the common fuzzy PID control under the large step input
condition, whereas the control effect was almost the same
when the step input was small.
After the completion of the theoretical analysis and
software simulation, these two control methods were ap-
plied to the actual printing process. The printed results
are shown in Fig. 7. It is obvious that the printed result
of the universe fuzzy PID control is clearer than that of
the common fuzzy PID control; moreover, the shape of
the former is closer to the design requirements, which can
help improve the forming quality.
5. Conclusion
A variable universe fuzzy PID algorithm with adaptive
variation of error for a set of nonlinear expansion fac-
tors was designed in this paper, aimed at addressing the
difficulty of accurately controlling the temperature of an
SMHS-type 3D printing control system.
First, based on the control characteristics of SMHS, a
temperature control system model was developed and the
corresponding transfer function was given. Then, the con-
trol object of the print head temperature was discussed
and the fuzzy PID controller with variable universe was
designed. Next, the MATLAB simulation results showed
that the variable universe fuzzy PID control was better
than the traditional fuzzy PID control in the case of the
large step jump. At a temperature of 170C of the step sig-
nal input, the overshoot of the response curve of the com-
mon fuzzy PID control reached 16.7%, which was 2.3%
lower than that of the variable universe fuzzy PID con-
trol; moreover, the control effect of the latter was faster
and more stable. However, when the input was a small
step signal, the control effect of these two control meth-
ods was similar. Finally, images of the actual printing
effect were given. It can be seen clearly that the image
printed by the universe fuzzy PID control was clearer and
closer to the design requirements.
In our future work, on the precondition of ensuring the
control effect under the condition of a large step input,
we will further optimize the universe fuzzy PID control
algorithm to improve the control effect compared with
the common fuzzy PID control when the input is small.
We firmly believe that the universe fuzzy PID control will
have good application prospects in the printing equipment
industry.
Acknowledgements
This work was supported by the Open Research Fund of the Re-
search Center for Advanced Control of Complex Systems and In-
telligent Geoscience Instrument, China University of Geosciences
(Wuhan) (No. AU2015CJ018); the Fundamental Research Funds
for the Central Universities, China University of Geosciences
(Wuhan) (No. CUGL120238); and the Natural Science Founda-
tion Project of Hubei Province and Geological Survey Project by
China’s Ministry of Land and Resources (No. 1212011120255).
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170 Journal of Advanced Computational Intelligence Vol.21 No.1, 2017
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Temperature Control Strategy of SMHS-Type 3D Printing
Name:
Tao Wu
Affiliation:
School of Automation, China University of Geo-
sciences
Address:
No. 388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China
Brief Biographical History:
2004-2007 Teaching Assistant, College of Mechanical and Electronic
Engineering, China University of Geosciences
2008-2012 Lecturer, College of Mechanical and Electronic Engineering,
China University of Geosciences
2013- Associate Professor, Courses on Motor and Electric Drive, Sensors
and Measurement Technology, School of Automation, China University of
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Name:
Yiru Tang
Affiliation:
School of Automation, China University of Geo-
sciences
Address:
No. 388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China
Brief Biographical History:
2011-2015 B.E., School of Automation, China University of Geosciences
Main Works:
Computer programming, motor control
Name:
Dongdong Fei
Affiliation:
School of Automation, China University of Geo-
sciences
Address:
No. 388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China
Brief Biographical History:
2010-2014 B.E., School of Automation, China University of Geosciences
Main Works:
Computer programming, intelligent instrument
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Yongbo Li
Affiliation:
School of Automation, China University of Geo-
sciences
Address:
No. 388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China
Brief Biographical History:
2005- Associate Professor, School of Automation, China University of
Geosciences
2010-2014 Ph.D. degree, Geodetection and Information Technology,
China University of Geosciences
Main Works:
Tube cold centering automatic control, development of intelligent
instrument
Name:
Wangyong He
Affiliation:
School of Automation, China University of Geo-
sciences
Address:
No. 388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China
Brief Biographical History:
2003-2006 Teaching Assistant, Department of Mechanical Engineering,
China University of Geosciences
2006-2014 Lecturer, Faculty of Mechanical & Electronic Information,
China University of Geosciences
2014- Lecturer, School of Automation, China University of Geosciences
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“Position Synchronization on the Biaxial System with PID Neural
Networks control,” Applied Mechanics and Materials, Vol.462-463,
pp. 766-770, 2013.
“Design of Single axis Control system based on FM354,” Advanced
Materials Research, Vol.926-930, pp. 1289-1292, 2014.
“A Technology for Lebus Grooving Based on Synchronous Follow
Motion,” Machine Tool & Hydraulics, 2013.
Vol.21 No.1, 2017 Journal of Advanced Computational Intelligence 171
and Intelligent Informatics
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A novel observer-base output feedback variable universe adaptive fuzzy controller is investigated in this paper. The contraction and expansion factor of variable universe fuzzy controller is on-line tuned and the accuracy of the system is improved. With the state-observer, a novel type of adaptive output feedback control is realized. A supervisory control-ler is used to force the states to be within the constraint sets. In order to attenuate the effect of both external disturbance and variable parameters on the tracking error and guarantee the states to be within the constraint sets, a robust con-troller is appended to the variable universe fuzzy controller. Thus, the robustness of system is improved. By Lyapunov method, the observer-controller system is shown to be stable. The overall adaptive control algorithm can guarantee the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. In the paper, we apply the proposed control algorithms to control the Duffing chaotic system and ChuaÕs chaotic circuit. Simulation results confirm that the control algorithm is feasible for practical application.