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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 =(VH−Vcom)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(T2−T1)=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 (25◦C) to 170◦C, 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+1e−0.05s......... (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

1e−k1x2;

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

2e−k2|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 0◦C to 240◦C, the basic uni-

verse for the error change rate of the temperature variation

was −100◦C/ms to 100◦C/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)=1−0.98e−0.9|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

170◦C, 187◦C, and 238◦C. 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 170◦C 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 170◦C 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

and Intelligent Informatics

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

Geosciences

Main Works:

•“Design and Simulation of a tube linear electric-magnetic hammer,”

Shock and Vibration, Vol.34, pp. 220-224, 2015.

•“Research on Impact Stress & Fatigue Simulation of a New

Down-to-the-hole impactor Based on ANSYS,” J. of the Institution of

Engineers, pp. 1-8, 2016.

•“The Scalar Control Research based on Fuzzy PID of BDFM

Stand-alone Power Generation System,” The 2011 Int. Conf. on Electric

Information and Control Engineering (ICEICE2011), pp. 2806-2810,

2012.

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

Name:

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

Main Works:

•“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