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本科畢業(yè)設(shè)計(jì)
（英文文獻(xiàn)翻譯）
英文題目：Gain-scheduling fuzzy temperature controller or one-way input system
譯文題目：增益規(guī)劃的模糊溫度控制器的單向輸入系統(tǒng)
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Gain-scheduling fuzzy temperature
controller for one-way input system
Shiuh-Jer Huang1,2 and Chen-Chuan Wang2
1Department of Vehicle Engineering, National Taipei University of Technology, No. 1, Sec. 3, Chung-Hsiao East Road, Taipei, Taiwan 106
2Department of Mechanical Engineering, National Taiwan University of Science and
Technology, No. 43, Keelung Road, Sec. 4, Taipei, Taiwan 106
In many chemical and semiconductor manufacturing processes, temperature is an important control parameter for obtaining the desired product quality. Generally, the temperature control system has non-linear time-varying, slow response, time-delay and one-way control input characteristics. It is difficult to estimate accurately the dynamic model and design a general-purpose temperature controller to achieve good control performance. Here a model-free intelligent gain-scheduling fuzzy control strategy is proposed to design a temperature controller for an iron closed chamber with heater input only. The concept of gain scheduling is employed to adjust the mapping ranges of fuzzy membership functions during the control process for improving the control performance. The experimental results show that the steady-state errors of the step input responses are always less than 0.28C without overshoot by using this control scheme. It is suitable for industrial temperature control systems.
Key words: fuzzy control; gain scheduling; temperature control and one-way input.
1. Introduction
Temperature is an important control parameter in chemical, material and semiconductor manufacturing processes. For example, material annealing, thin film deposition and TV glass melting furnace all need appropriate temperature control systems. Some of the temperature control systems have heating and cooling control phases and others only have a heating input control phase. Their dynamic behaviours have significant differences. The temperature control system witch input only is
Address for correspondence: Shiuh-Jer Huang, Department of Vehicle Engineering, National Taipei University of Technology, No. 1, Sec. 3, Chung-Hsiao East Road, Taipei, Taiwan 106. E-mail: hd3601@ntut.edu.tw
Figures 1and 6–11appears in colour online: http://tim.sage.pub.com
more difficult to monitor than two phase control systems to obtain good control performance. How to design a general-purpose temperature controller with good response speed, smaller steady-state error and without overshoot for industrial implementation is still a challenge in the control research field. Currently, on–off control and PID control schemes are employed in commercial products. A PID controller was proposed in 1936. It has been widely used in industrial automatic control systems. However, how to adjust the control gains is the key factor of implementing a PID controller. If the accurate dynamic model of a control system is available, the Ziegler and Nichols rule (Ziegler and Nichols, 1942) and IMC control strategy (Chien and Fruehauf, 1990; Rivera et al., 1986) can be used to calculate the appropriate gains. However, the heating plant has time-delay and temperature dependence non-linear behaviours. It is hard to establish an accurate dynamic model for a PID controller design. Generally, it needs a trial-and-error process to obtain a good control response. When the system has external disturbance or set-point change, its transient response may deteriorate. It needs an online operator to readjust it or switch it to manual control. This is not a convenient application and the production parameters may not maintain in a good level in manufacturing processes. Hence model-free intelligent control schemes have gained the attention of researchers.
A self-tuning PID control strategy was proposed to control water bath temperature
(Yusof et al., 1994). A frequency loop-shaping technique is employed to tune the PID gains of the temperature controller of a chemical vapour deposition (CVD) diffusion furnace (Grassi and Tsakalis, 2000). The appropriate gains of this approach are searched based on the system output response of an on–off open-loop relay control. In addition, fuzzy control has been successful employed in many industrial processes, as it has model-free intelligent characteristics. Recently, fuzzy control theory has been used to improve the adaptivity and robustness of a PID controller. A hybrid fuzzy and PI control for TV glass melting furnace temperature control has been proposed (Moon and Lee, 2000, 2003). The fuzzy logic scheme also is applied to adjust PID controller gains (Chen and Li, 2003; He et al., 1993; Visioli, 2001). The PID gains of these approaches are non-linear functions of tracking control performance. They can be adjusted automatically based on the output error. It can achieve better robustness, quick response and smaller overshoot than that of a traditional PID controller. However, it is difficult to design a general-purpose fuzzy control rules table and the corresponding fuzzy parameters. Hence, a self-organizing fuzzy controller (Lu and Chen, 1994) and adaptive fuzzy control scheme (Haissig, 1999) were employed to design the temperature controller to obtain the stable adaptive behaviour, but these control strategies still cannot achieve both a quick transient response and an accurate steady-state response.
Usually, temperature control systems have non-linear time-varying and time-delay
characteristics. It is difficult to estimate an appropriate dynamic model for model-based controller design. Especially, the temperature control problem with one-way heater input only has time-delay and asymmetric control behaviour. It is
difficult to achieve precise temperature control accuracy with a good transient response based on traditional control algorithms. Here the model-free gain-scheduling fuzzy control scheme is employed to design the heater input single-phase temperature controller with fuzzy gain parameters, auto-switching to achieve a good transient response and small steady-state error. A general-purpose intelligent temperature controller is the designed goal of this paper. The temperature dynamic response performance of the fuzzy gain-scheduling controller will be compared with that of an auto-tuning PID controller. The experimental test rig is a hollow metal chamber with heater control input only.
2. System structure
The PC-based control system structure of a temperature monitoring system is shown in Figure 1. The PC sends the control voltage into an SCR driver through the D/A card. A 12-bit low cost ASIO-113 AD/DA/8255 interface card is selected for this control system. The MAXTHERMO SCR driver has a 250 Q inner resistance to transform the 1–5 V control voltage into 4–20 mA control input current for the heating rod. This SCR can monitor the power output of a single-phase 110-V and 20-A alternative current power source. It regulates the current input of the heating rod for raising the temperature of the hollow metal chamber. The medium inside the hollow cylinder chamber is air. The temperature of the hollow metal cylinder is measured using a resistance temperature sensor (RTD) and fed back into the PC through the A/D card. The temperature control algorithm is implemented with Ctt program. A hollow metal chamber experimental test rig is built for evaluating the control performance. The dimension of the hollow iron cylinder is 250 mm in height and
51 mm in diameter with a 10-mm diameter hollow hole for installing the heating rod and the RTD PT100 temperature sensor. The accuracy of the selected PT100 RTS sensor is about 0.28C within the 3008C temperature measuring range. The sensitivity of this RTD sensor is 0.0015 per 8C. The sampling frequency of the following experiments is set as 40 Hz.
3. Auto-tuning PID control
The key factors which influence the control system performance of a PID controller is how to find the optimal proportional gain, integral time constant and derivative time constant. For practical implementation, these gains adjustments are achieved by expertise or an experienced engineer, and a trial-and-error modification. It is time-consuming work and the dynamic response behaviour cannot be guaranteed. Hence, a relay feedback evaluation method was proposed to find the gain parameters of a PID controller (Astrom and Hagglund, 1984). Firstly, an on–off switching control is employed for the first two cycles. When the system temperature is less than the setting command, the control power is fully opened to drive the temperature up.
Control unit
PC
A/D Interface card
D/A Interface card
DC 15V
RTD temperature transmitter
SCR driver AC 110V
RTD SENSOR
Plant
Figure 1 PC-based temperature control system structure
When the temperature reaches the setting value, the control input is switched off immediately. Then the critical gain, Ku, and critical period, Pu, can be found from these input–output response curves as Figure 2, where
4d
Ku ?
a e1T
Hence, the gain parameters can be calculated by using the experienced formula of
Ziegler–Nichols.
Kp ? 0:6Ku , Ti ?
Pu
2 , and Td ?
Pu
8 e2T
Temperature (°C)
y
Setting point
Time delay power
ON
u
Pu a
Time (s)
d
Time (s)
OFF
Figure 2 The estimating of critical period and critical gain from on–off control
That means
p ? u i ?
K 0:6K , K Kp
Ti
and Kd ? Kp Td e3T
These PID control gains can be employed to monitor the system temperature step change.
4. Gain-scheduling fuzzy logic controller
Since this temperature control system has obvious time-delay and one-way input non-linear behaviour , it is difficult to establish an appropriate dynamic model for the precise model-based controller design. In addition, the overshoot transient response of the temperature control system, with time-delay and single-phase heating input dynamic features, is difficult to avoid and eliminate quickly. Hence, how to design a general-purpose temperature controller with small overshoot and quick response will be a challenge research topic. Here the model-free gain-scheduling fuzzy control strategy is proposed to solve this problem. The control block diagram is shown in Figure 3.
Usually the motivation of a fuzzy approach is that the knowledge is insufficient and
the dynamic model has uncertainty. Fuzzy set theory was employed to simulate the logic reasoning of human beings. The major components of a fuzzy controller are a set of linguistic fuzzy control rules and an inference engine to interpret these rules.
Fuzzification
ge
Knowledge base
Uk
gu
e Defuzzification
yr
d
+
? ce
D D
gce
Decision logic
Xr
Plant
Figure 3 Fuzzy control block diagram of the temperature control system
These fuzzy rules offer a transformation between the linguistic control knowledge of an expert and the automatic control strategies of an activator. Every fuzzy control rule is composed of an antecedent and a consequent; a general form of the rules can be expressed as
RiIF X is A1 and Y is A2 , THEN U is C1 e4T
where Ri is the ith rule, X and Y are the states of the system output to be controlled and U is the control input. A1, A2 and C1 are the corresponding fuzzy subsets of the input and output universe of discourse, respectively.
The output importance of each fuzzy rule depends on the membership functions of the linguistic input and output variables. In this control system, two input indices of the fuzzy controller are temperature error e and error change ce, and the output index is the control voltage u. In order to simplify the computation of the fuzzy controller, seven equal span triangular membership functions are employed for fuzzy controller input variables e and ce. They are NB, NM, NS, ZO, PS, PM and PB. The membership functions of these fuzzy variables are shown in Figure 4. The divisions of this membership functions can be expanded or shrunk by changing the scaling parameters of membership functions. The gain scaling parameter is used to map the corresponding variable into this nominal range. In human beings’ intuition, when the temperature error is large, the control voltage should be increased to provide more energy to heat the control chamber and reduce the temperature error. On the other hand, when the error is approaching to the zero subset of membership functions, the
E
NB NM NS ZO
PS PM PB
?1.2ge
?0.8ge
?0.4ge 0
0.4ge
0.8ge
1.2ge
CE
NB NM NS ZO
PS PM PB
?1.2gce
?0.8gce
?0.4gce 0
0.4gce
0.8gce
1.2gce
U
NB NM NS ZO
PS PM PB
?1.2gu
?0.8gu
?0.4gu 0
0.4gu
0.8gu
1.2gu
Figure 4 Fuzzy input and output variables membership functions
controller should provide fine-tuning to correct the little change of temperature error and reduce the overshoot tendency. These two conditions can be traded off by scaling the divided spans of membership functions with a gain parameter. These mapping parameters are specified as ge, gce and gu for the error, error change and control voltage, respectively, whose values are listed in Table 1.
The parameters ge and gce are scaling factors selected to specify the uzzy input
variables operating ranges of temperature error and error change, respectively. The parameter gu is a gain designed to adjust the fuzzy logic control voltage and simplify the trail-and-error effort for designing the fuzzy rules table. This approach is a new gain-scheduling fuzzy control structure. These parameter values are not critical for this gain-scheduling fuzzy logic controller. They can be roughly determined by
Table 1 Fuzzy gains scaling factors
Fuzzy gain parameters
Parameters
ge
gce
gu (608C)
gu (1008C)
gu (2008C)
Coarse-tuning
5
2
2.6
2.9
3.6
Fine-tuning
2
1
2.0
2.4
3.2
simple experimental tests. Then the same values can be applied to different temperature setting points step response control with appropriate steady-state accuracy. For this temperature control system, ge ? 5 and gce ? 2 for the coarse- tuning operation, and ge ? 2 and gce ? 1 for the fine-tuning operation can be used in any different temperature setting points. The corresponding fuzzy membership functions covering ranges of temperature control errors are 68C for the coarse-tuning and 2.48C for the fine-tuning operations, respectively, as shown in Figure 5. The controller software program can automatically switch between the coarse-tuning and fine-tuning control ranges based on the temperature error feedback signal. The control gain value gu depends on the temperature setting points because of the environmental heat equilibrium problem. It needs a little trial-and-error work to find an appropriate gain value for a certain range of temperature settings, for example 50–808C, 80–1208C,
120–1508C, and so on. These parameter values are not critical. Each gain parameter within a certain range can achieve reasonable dynamic responses. Otherwise, we need to design a different fuzzy control rules table for each temperature setting range. That would be a more time-consuming and tedious work than the proposed approach.
In this study, the whole universe of discourse of the membership functions were
divided into two divisions, the fine-tuning and coarse-tuning areas. Figure 5 shows the individual spans of two sets of different membership functions. In the beginning of a temperature step response, the controller would automatically choose a large division of membership (coarse-tuning area) in response to the large error. When the temperature converges and approaches the steady state, the controller would switch the membership function covering range into the fine-tuning area to correct the steady-state error. This control strategy can switch automatically between different control ranges and divisions of membership functions based on the feedback signals of control variables errors, e and ce by changing the gain scaling factors of membership functions only. In addition, the system heat equilibrium control voltage is included in the fuzzy rules table for substituting the extra designed offset control value of other control algorithms to simplify the controller design problem and control law calculation.
In this paper, 49 fuzzy rules are employed to control the chamber temperature by
regulating the SCR input voltage. Those fuzzy rules are listed in Table 2. These rules are established based on the testing responses of a PID control and certain trial- and-error processes. The offset control voltage for dealing with the system heat
Coarse tuning
NB NM NS
ZO PS PM PB
?6
Fine tuning
NB
?2.4
?4
NM
?1.6
?2
NS
?0.8
Scaling
ZO
2
PS
0.8
4
PM
1.6
6
PB
2.4
?6 6
Fine tuning
Coarse tuning
Figure 5 Membership functions division
equilibrium is added into these fuzzy rules directly. The fuzzy controller will derive the control voltage automatically, which includes the heat equilibrium offset control voltage and the error correction control voltage. However, a PID controller needs carefully to design the Ki gain by tedious trial-and-error for each temperature step response to achieve the appropriate transient response. Otherwise, the temperature response speed will have be slowed down before it reaches the specified value or have long period of oscillation. The membership function used in this paper for the fuzzification is of a triangular type. The function can be expressed as
1
μexT ? w e-jx - aj t wT e5T
where w is the distribution span of the membership function, x is the fuzzy input variable and a is the parameter corresponding to the value 1 of the membership function. The height method is employed to defuzzify the fuzzy output variable to
Table 2 Fuzzy rules table for the heater
E
U
NB
NM
NS
ZO
PS
PM
PB
CE
NB
-1.2
-1.15
-1.1
-1.0
-0.9
-0.5
0.85
NM
-1.15
-1.1
-1.0
-0.9
-0.5
0.85
0.9
NS
-1.1
-1.0
-0.9
-0.5
0.85
0.9
0.95
ZO
-1.0
-0.9
-0.5
0.85
0.9
0.95
1.0
PS
-0.9
-0.5
0.85
0.9
0.95
1.0
1.1
PM
-0.5
0.85
0.9
0.95
1.0
1.1
1.15
PB
0.85
0.9
0.95
1.0
1.1
1.15
1.2
obtain the control voltage of the SCR heater driver of this temperature control system. The relevant equation is