Applied Mechanics and Materials Vols. 16-19 (2009) pp 140-144
© (2009) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.16-19.140
Online: 2009-10-12
Design of Self-regulating Fuzzy Control
System for Vacuum Sintering Furnace
Qigao Feng1,2,a, Hanping Mao1,b and Xueming Zhang2,c
1
Institute of Agricultural Engineering, Jiangsu University, Zhenjiang, China, 212013
2
School of Machinery and Electricity, Henan Institute of Science & Technology, Xinxiang, China,
453003
fqg@hist.edu.cn, bmaohp@ujs.edu.cn, cxmzh@hist.edu.cn
a
Keywords: Vacuum sintering furnace, Temperature control, Fuzzy PID control, Fuzzy rules
Abstract. Although the traditional PID controller is widely used in many practical application
fields, it’s unsuitable for the control of the complex plant. The powder metallurgy sintering process
had such characteristics as nonlinearity and large delay, etc., and it’s difficult for the conventional
PID controller to meet the control requirements. According to these traits, we used a parameter
self-adjusting fuzzy controller to control the heating temperature of the vacuum sintering furnace. In
practice it shows that every quality index and control effect of this scheme is better than that of
traditional PID controller.
Introduction
The vacuum sintering furnace is the key equipment in the course of the powder metallurgy
production, and the control precision of the sintering temperature will affect the quality of the
production directly. Of all the parameters, the sintering temperature is the most important. It
possesses such features as nonlinearity, time varying, and large delay, etc., and it’s impossible to
attain the accurate mathematical model of the control system by means of mathematical methods.
Thus the traditional PID controller can’t adapt to the varying operating conditions of the vacuum
sintering furnace, and it’s difficult to achieve the required control precision and satisfy the realtime
control of the temperature parameter, and it’s often result in overshoot and slow increase or
decrease of the temperature.
As an intelligent control method, fuzzy control has been developed into a successful branch of
automation and control theory since it was proposed by Zadeh. With the development of fuzzy
control systems, lots of fuzzy design methods have appeared in the practical applications. Among
various kinds of fuzzy control methods, Tankagi and Sugeno proposed a design and analysis
method for overall fuzzy systems, in which the qualitative knowledge of a system was first
represented by a set of local Takagi-Sugeno fuzzy model (T-S) [1]. The outstanding advantage of
the fuzzy control system is that it does not need the accurate mathematical model of the object, and it
is able to adjust the parameters to adapt to the change of the system in-line. In addition, it is
insensitive to parameters varying, and has strong robustness. It is perfectly applied to overcome the
effects of nonlinearity, time varying of many practical systems [2-4]. For the problem that the
steady-state error is hard to be eliminated with a fuzzy controller, a fuzzy PID controller for the
temperature control system of the vacuum sintering furnace is presented in this paper. The proposed
controller combine the merits of the two control strategies, which has flexibility, perfect anti-interfere
capability of the fuzzy control, and the high steady-state precision of PID control. The practical
control effects showed that the proposed fuzzy self-adjusting PID control system has such better
dynamic and static features as less rise time, less transition time, and miner overshoot.
The Control Requirement of the System
The temperature control accuracy is of great importance in the operating of the vacuum sintering
furnace. If the temperature increases or decreases too fast, the production quality will be affected
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Applied Mechanics and Materials Vols. 16-19
141
seriously and produce degraded products. Fig. 1 gives the temperature control requirement in the
operating process. In the practical heating process, the numbers of the temperature phases will be
different according to the materials to be sintered. As can be seen in Fig. 1, the whole sintering
procedure consists of the following steps:
(1) The free increase phase of the temperature (o-b);
(2) The temperature increase phase at constant speed (c-d). In this phase, the increase speed of
the temperature should be controlled to rise at a constant value;
(3) The constant temperature phase (b-c, d-e, f-g) which the temperature is required to keep
steady;
(4) The temperature decrease phase at constant speed (e-f). In this phase, the decrease speed of
the temperature should be controlled to decline at a constant value;
(5) The free decrease phase of the temperature (g-h).
Fig.1 The schematic diagram of the sintering temperature requirement
From Fig.1 we can see that, apart from the free increase phase (o-b) and the free decrease phase of
the temperature (g-h), other temperature phases must be able to reach the corresponding control
precision. Since there exist high inertia, large lag, and obvious overshoot in the temperature of the
sintering furnace, neither the conventional PID control nor the ordinary fuzzy control can achieve
the control demands [5-6]. Here we adopt the parameters self-tuning fuzzy control strategy to fulfill
the task.
Design of the Control System
According to the actual heating process of the vacuum sintering furnace, we presented the
parameters self-tuning fuzzy PID controller to control heating process in order to achieve such
control effects as small overshoot, fast response, good adaptability, high stability, etc. The
schematic diagram of fuzzy PID control is shown in Fig.2.
Fuzzy inference
de/dt
Kp
rin +
-
e
Ki
Kd
PID controller
Sintering furnace
Yout
Fig.2 Schematic diagram of fuzzy PID controller
The fuzzy PID controller of the heating system adds a fuzzy regulator to the common PID
controller and forms a mixed fuzzy PID controller. In the mean time, a system rule base is added so as
to be used to realize the fuzzy regulating for the parameters of conventional PID controllers. The
parameters of the conventional PID controller, i.e., Kp, Ki, Kd, are regulated in-line in accordance with
the system error, and the system control rules are adjusted indirectly, and also the lost information of
the conventional fuzzy controller is compensated during the fuzzy quantification, so the robustness,
adaptive ability, and control precision of the control system can be enhanced [7].
In order to guarantee real time control in the fuzzy PID controller, the fuzzy control table is
usually calculated off-line, and then the control scheme of lookup in-line is adopted.
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(1) It is in accordance with the controlled plant to determine error E, variable rate of error C, the
controlled variable U, and the actual varying range of the coefficient of the variable integration
element KI [-Xe, Xe], [-Xc, Xc], [-Yu, Yu] and [-Yk, Yk]. The universe of discourse of the above four
fuzzy subset is chosen to be {-n, -n+1, …, -0, 0, +0, …, n-1, n}{-m, -m+1, …, -0, 0, +0, …, m-1, m
}, {-l, -l+1, …, -0, 0, +0, …, l-1, l}, {0, …k-1, k}, in which n, l, m, k may be chosen a little minor
than those of the conventional fuzzy controller.
(2) The linguistic labels for Error E, variable rate of error C, the controlled variable U, and the
actual varying range of Kp, Ki, Kd are determined to be {NL, NM, NS, NZ, Z, PZ, PS, PM, PL},
{NL, NM, NS, NZ, Z, PZ, PS, PM, PL}, {NL, NM, NS, NZ, PZ, PS, PM, PL}, {Z, PS, PM, PL},
and membership functions are selected properly.
(3) In order to reduce the numbers of the control rules, the control of the system is divided into
two parts, the control of output error and the control of the system parameters. Since the control of
the output error is more important than that of the system parameters, more of the fuzzy subset of
the output error is defined, and more of the rules in rule base are set up correspondingly [8-10].
The control system error becomes as small as possible under the rule base. The control rule list is
obtained by means of the design experience of the conventional fuzzy controller. The desired value
of the varying parameters control system makes system error become zero and the overshoot is the
smallest. In the course of the system design, the following should be obeyed according the
conventional design experience [11-12].
(1) When the sign of E and EC is identical, the control variable u deviates to the desired value
and approaches to the desired value when they are different.
(2) When E is big: To accelerate the speed of response, avoid derivative saturation caused by
immediately rising to a large value of E in the early period and avoid large overshoot, a big Kp, a
small Kd and a small Ki are needed.
(3) When E is small: To keep reducing the error and prevent oscillation caused by large
overshoot, decrease the value of Kp, choose a small Ki and a moderate Kd.
(4) When E is quite small: To eliminate steady-state error, avoid overshoot and keep a good
static performance and strong capability of disturbance rejection, increase the value of Ki, choose a
small Kp and Kd.
According to the above laws and the control experience of engineers, the control rules of Kp, Ki
and Kd are shown in Table 1, 2, 3, respectively.
Table 1
Rule table of fuzzy control of Kp
EC
E
NB NM NS
Z
PS PM PB
NB PB PB PM PM PS
Z
Z
NM PB PB PM PS PS
Z
NS
NS PM PM PM PS
Z
NS NS
Z PM PM PS
Z
NS NM NM
PS PS PS
Z
NS NS NM NM
PM PS
Z
NS NM NM NM NB
PB
Z
Z NM NM NM NB NB
Practical Control Effects and Discussion
According to the above design, we applied the fuzzy PID controller to the heating process control of
the vacuum sintering furnace. Compared with the conventional PID control scheme, the control
system employing the parameters self-tuning fuzzy control strategy has achieved outstanding
control effects, as shown in fig. 3. On the basis of the influence of the parameters on the control
system, we can attain the basic principle of parameters self-tuning as follows:
(1) Kp, Ki and Kd can be regulated after completing the fuzzy rule table of Kp, Ki and Kd;
Applied Mechanics and Materials Vols. 16-19
143
(2) When E and EC is bigger, larger scaling factor is essential to strengthen the control effort to
reduced settling time;
(3) When E and EC is smaller, namely, the system is close to steady state, in order to guarantee
the control precision, the scaling factor should be reduced, and the output control effort should be
adjusted subtly [9-10]. Here, we proposed a gain updating factor of output scaling factor, which is the
function of error and change of error.
Table 2
Rule table of fuzzy control of Ki
EC
E
NB NM NS Z
PS PM PB
NB PB PB PM PM PS PS
Z
NM PB PB PM PM PS
Z
Z
NS PM PM PM PS
Z
NS NM
Z PM PS PS
Z
NS NM NM
PS PS PS
Z NS NS NM NM
PM Z
Z NS NM NM NM NB
PB
Z NS NS NM NM NB NB
Table 3
E
NB
NB NB
NM NB
NS NM
Z NM
PS NS
PM Z
PB
Z
Rule table of fuzzy control of Kd
EC
NM NS
Z
PS PM PB
NB NB NM NM Z
Z
NB NM NS NS
Z
Z
NM NS NS
Z
PS PS
NS NS
Z
PS PS PM
NS
Z
PS PS PM PM
Z
PS PM PM PB PB
Z
PS PM PB PB PB
(a) The common PID control effect
(b) The fuzzy PID control effect
Fig.3 Comparison between the common PID and the fuzzy PID control
Conclusions
It is difficult for the traditional PID controller to realize the speedy and accurate response without
overshoot, so the fuzzy PID controller is proposed to the heating control system of the vacuum
sintering furnace. By making use of PID control and fuzzy control synthetically, the control effect of
the heating system has been increased to a great extent. The hybrid control is designed to eliminate
the static error which exists in the fuzzy controller and achieve the requirements for real-time and
high precision by means of adaptive tuning the system parameters. The practical results showed that
the proposed method had strong adaptive ability, fast dynamic response and the strong robustness and
exhibited obvious advantages compared with the traditional PID controller.
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10.4028/www.scientific.net/AMM.16-19
Design of Self-Regulating Fuzzy Control System for Vacuum Sintering Furnace
10.4028/www.scientific.net/AMM.16-19.140
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