英文原文
FUZZYDECOUPLING CONTROL OF MELT
TEMPERATURE AND MELT PRESSURE FOR PLASTIC
ELECTROMAGNETISM DYNAMIC EXTRUDER
WEN Shengping，QU Jinping
National Engineering Research Center of Novel Equipment for Polymer Processing，Dept of Industrial Equipment and Controlling ,
South China University of Technology，Guangzhou 510640,China
Keywords: Melt temperature， melt pressure, fuzzy decoupling control, electromagnetism dynamic extruder.
Abstract
The plastic electromagnetism dynamic extruder has gained wide applications because of its novel structure and fine engineering performance。In the polymer processing，melt temperature and melt pressure control is crucial to the quality of the extruded product。A new fuzzy decoupling control algorithm of melt temperature and melt pressure for the novel extruder is introduced in the transfer function matrix system,
which is obtained through the experimental data with system identification。The control system is implemented on programmable computer controller。Experimental results show melt temperature and melt pressure can be successful individually controlled by the heater power and the screw speed。The good system performance verifies the control strategy’s validity。
1 Introduction
Polymer extrusion is a complex nonlinear multivariable coupling process。There are many factors affecting the stability of extrusion process and the quality of extruded products。The equipment is the crucial factor。There are already many kinds of extruder。Unlike the traditional extruder。a new kind of electromagnetism dynamic extruder was invented by professor Qu Jinping[5].He introduced the vibration force field into the whole process of polymer extrusion。The vibration force field brings new changes to the energy balance，quality balance and momentum balance of the whole extrusion process。Control of vibration frequency and vibration magnitude can effectively control the dynamic extrusion process。The electromagnetism dynamic extruder is shown in Fig.l，Researches on the dynamic extruder show the good performance of the machine。Besides the extruder，melt pressure and melt temperature are key variables to the extrusion process。Melt pressure directly influences the output of the product。While melt temperature's fluctuation can change melt viscosity and consequently influences melt pressure and flow rate. Therefore，the dominant variables are melt temperature and melt pressure in the dynamic extrusion process.
Fig.l: the structure of electromagnetism dynamic Plasticating extruder.
1 screw,2 barrel,3 rotor,4 stator,5 support base,6 hopper
In order to get high product quality，control of melt pressure and melt temperature for the traditional extruder has been done with different control method。In 1970s，Dormeier，S.[4] firstly introduced the digital PID control to melt Temperature cascade control。The diameter of the screw is 45mm.Because of the limit of hardware development，the sample period is 15s.The cascade PID control is shown in Fig.2.
Fig.2: melt temperature cascade PID control.
ntroduced into the barrel-wall temperature control。Richey Dubay，Adam C.Bell and Yash P.Gupta used model prediction method to establish the multiple-input multiple-output model for the temperature control of the different sections of the barrel[6].Ching-Chih Tsai and Chi-Huang Lu investigated the multivariable temperature control of the barrel based on the generalized predictive algorithm[2].The mathematic model of the heating process shown in Fig.3 was built according to the energy balance。Chi-Huang Lu also adopted the self-adaptive prediction control to the barrel temperature control[3]。Achievements gained were mainly about the traditional extruder。Melt temperature and melt pressure control of the electromagnetism dynamic extruder has seldom reported by now。Melt temperature and melt pressure control based on a new fuzzy control algorithm for the electromagnetism dynamic extruder is investigated in this paper.
Fig.3: physical model of the extruder barrel
Achievements gained were mainly about the traditional extruder。Melt temperature and melt pressure control of the electromagnetism dynamic extruder has seldom reported by now。Melt temperature and melt pressure control based on a new fuzzy control algorithm for the electromagnetism dynamic extruder is investigated in this paper.
2 Modelling of the system
The electromagnetism dynamic extruder has five heating zones。Temperatures of the first four heaters are set by manual。The temperature of the heater on the die is to be controlled by the new control strategy。There are five thermocouples positioned in the barrel-wall to measure the barrel wall temperature。One infrared temperature transducer is positioned nearest the exit of the melt to measure melt temperature。Melt pressure is measured by a strain-gauge-type pressure transducer positioned in the die-wall。Melt pressure is controlled by screw speed。Step response of melt pressure and melt temperature to heater power on the die and screw speed were acquired through experiments.Fig.4 and Fig.5 are experimental step responses of melt temperature.
Fig.4: step response of melt temperature to
Heater 5 temperature
Fig.5: step response of melt pressure to Heater 5 temperature
Response of melt pressure and melt temperature to the heater power and screw speed is a self-balanced system。The response is over damping。So the system is considered as a second order system and system parameters can be identified from experimental data [8].The transfer function of the second order self-balance system with a pure delay is expressed as following.
Where K is system gain is delay time，T is time constant, is damping ratio. Then we get the transfer function identified from experimental data.
Where Tm，Pm are melt temperature and melt pressure W is the heater5 power，and n is the screw speed.
3 Fuzzy decoupling control algorithm。
According to the coupling relationship of melt temperature and melt pressure，we bring about a fuzzy decoupling controller for melt temperature and melt pressure control shown in Fig.6[1,7].
Fig.6: system structure of the fuzzy decoupling control
Where Tm and Pm are actual outputs of melt temperature and melt pressure。Tm set and Pm set are set points of melt temperature and melt pressure。The whole system consists of fuzzy controller，decoupling compensator unit and fuzzy adjusting components unit。Decoupling coefficients d21 and dl2 vary according to the fuzzy adjusting components，so that the coupling of the two loops can be eliminated.
3.1 Decoupling coefficients under steady state
Under steady state，according to the Equ.2,The steady state gain matrix is given by
Decoupling coefficients [8] defined by the principle of decoupling compensator are given by From(3)and(4),we get the decoupling coefficients under steady state.
3.2 Adjusting of decoupling coefficients under dynamic process
Decoupling coefficients mentioned above are derived from the steady state。It can entirely eliminate the coupling of melt temperature and melt pressure under steady state。In order to reduce the coupling under dynamic process，decoupling coefficients should be regulated。The modification unit is shown in Fig.7.
Fig.7 Diagram of multivariable fuzzy control with modifying
Compensator
The system output response can be written as below:
Here，ui(i=1,2)is the output of the fuzzy controller,△Yi (i=1,2)is the increment of the system output，and aij (i=1,2;j=1,2)is modifying coefficient. According to equ.7, output increment L\YI at time step n-1 and n can be expressed as:
After eliminating all from equ.8,a12 can be written as:
In the same way, a21 can be written as:
In order to eliminate the coupling between loops under dynamic process，it must let aij=O(i=1,2;j=1,2;i:I;j).If aij≠O (i=1,2;j=1,2;i*-j),it means that decoupleing coefficients is unreasonable。Decoupling coefficients are adjusted according to modifying coefficient by fuzzy logic. Fuzzy sets of decoupling coefficients and modifying coefficients are defined as {NB，NS，ZO,PS,PB}.The fuzzy control rule table of adjusting decoupling coefficients is shown in Table 1.
Table 1: fuzzy control rule table of adjusting decoupling coefficient。
3.3 Design of fuzzy controller FLCI and FLC2
Design of FLCI is the same as that of FLC2,so we only introduce the design of FLC 1.Two dimension fuzzy controller is adopted。Inputs of the fuzzy controller are error (E)and ratio of error change(EC).Output(U)is the control signal sent to the plant。Fuzzy sets of E,EC and U are defined as{NB,NM,NS,ZO,PS,PM,PB}and universe is chosen as {-6,-5,-4,-3,-2,-1,0,1,2,3,4, 5,6}.The membership function is the triangular function shown in Fig.8.
Fig.8：membership function.
In the dynamic extrusion process，we have gained such experiences “as if temperature is low，rising of temperature is slow，then heater power should be increased”，and “if temperature is high，rising of temperature is quick，then the heater should be stopped”。Based on manual experience，we get the fuzzy rules as following.
(1)If E=NB or NM and EC=NB or NM then U=PB
(2)If E=NB or NM and EC=NS or ZO then U=PB
(3)If E=NB or NM and EC=PS then U=PM
…………
According to the rules，we can get the fuzzy control table。After fuzzy decoupling，melt temperature is controlled by the averaged heater power and melt pressure is controlled by the screw speed。For melt temperature control，the output of the controller is directly transferred to the PWM signal，which is amplified to regulate the average power of heater。For melt pressure control，incremental method is adopted。Sample time for melt pressure is 20ms.Sample time for melt temperature is 500ms and period of the PWM signal is 10ms.
4 Implementation of the control system and experimental results
4.1 Implementation of the control system
Hardware design of the control system includes the choice of the master controller，design of the interface circuit，design of the drive and amplifier circuit，and design of hand machine interface(HMI).According to the control requirements and the characteristics of the plant，B&R PCC2003 is chosen as the master controller，Programmable computer controller (PCC)has the standard functions of the Programmable logic controller(PLC) and has the time division multiplexing operating system of the industry computer。PCC can conveniently process the analogous and digital signals and is easy to configuration because of its modular structure. Program based on PCC can be developed with the advanced language and mixture of different languages。The configuration is shown in Fig.9.
Fig.9: configuration of the control system.
4.2 Experimental results
LLDPE is chosen as experimental material。The temperatures of heater 1-4 are set to be 165°C,180°C,180°C,and 175°C individually。Melt pressure is set to be 10Mpa and melt temperature is set to be 170°C.When the operation becomes stable，melt pressure is changed to 12Mpa.Fig.IO shows that actual pressure can quickly come to the set point while temperature remains to be 170°C.Fig.II shows that when melt temperature set point is changed to be 180°C,the response of melt temperature is quick。Melt temperature comes to the set point while melt pressure is almost remain unchanged.Fig.5 shows that the effect of the open loop control and melt pressure decreases rapidly with the rise of melt temperature。After adopting the fuzzy logic decoupling control，F(xiàn)ig.II verifies the validity of the new control method and melt pressure remains constant despite the variability of melt temperature.。The case is the same to melt temperature versus variability of melt pressure and details are omitted here.
Fig.I0: change of melt pressure with unchanged melt temperature.
Fig.1I: change of melt temperature with unchanged melt pressure.
5 Conclusions
This paper investigated the decoupling control of melt pressure and melt temperature for the electromagnetism dynamic extruder。A new control algorithm based on fuzzy logic is introduced，which consists of fuzzy controller, decoupling compensator unit and fuzzy adjusting components
Unit。The implementation of the control system is based on B&R PCC2003.Experimental results show that melt temperature and melt pressure can be successful individually controlled and verifies the validation of the fuzzy control strategy.
Acknowledgements
The authors gratefully acknowledge the Instrument Foundation of National Natural Science Foundation of China (No.20027002).
References
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[3]Chi-Huang Lu；Ching-Chih Tsai." Adaptive decoupling predictive temperature control for an extrusion barrel in a plastic injection molding process"，IEEE Transactions on Industrial Electronics,48,5,968-975, 2001.
[4]Dormeier，S. "Extruder control"，IFAC PRP 4 Automation，Ghent，Belgium,551-560,1980.
[5]Qu Jinping，"The novel method and equipment for polymer extrude processing"，China Plastics,11,3,69-73,1997.
[6]Rickey Dubay，Adam C.Bell，Yash P.Gupta."Control of plastic melt temperature:：A multiple input multiple output model predictive approach"，Polymer Engineering and Science,37,9,1150-1563,1997.
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中文譯文
模糊解耦控制熔體 溫度和熔體壓力塑料
電磁動態(tài)擠出機(jī)
文生平平 瞿金平
摘要
塑料電磁動態(tài)擠出機(jī)由于其新穎的結(jié)構(gòu)和良好的工程業(yè)績已獲得廣泛的應(yīng)用。在聚合物加工，熔融溫度和熔體壓力的控制對擠壓產(chǎn)品的質(zhì)量至關(guān)重要。一種新的模糊解耦控制算法控制熔融溫度和熔體壓力的新型擠出機(jī)引進(jìn)了系統(tǒng)傳遞函數(shù)矩陣， 這是通過對實(shí)驗(yàn)數(shù)據(jù)與系統(tǒng)辨識來實(shí)現(xiàn)的。可編程計(jì)算控制器通過控制系統(tǒng)來執(zhí)行。實(shí)驗(yàn)結(jié)果表明通過加熱器功率和螺桿轉(zhuǎn)速調(diào)節(jié)能成功地對熔融溫度和熔體壓力進(jìn)行單獨(dú)控制。良好的系統(tǒng)性能驗(yàn)證了控制方法的有效性。
關(guān)鍵詞：熔體溫度，熔體壓力，模糊解耦控制，電磁動態(tài)擠出機(jī)
1導(dǎo)言
聚合物擠出是一個復(fù)雜的非線性多變量耦合過程。有許多因素影響擠壓工藝的穩(wěn)定和擠出產(chǎn)品的質(zhì)量，設(shè)備是關(guān)鍵因素?，F(xiàn)在已經(jīng)有許多種類的擠出機(jī)，與傳統(tǒng)的擠出機(jī)不同的是，瞿金平教授發(fā)明了一種新型的電磁動態(tài)擠出機(jī)。他介紹了振動力場到全過程的聚合物擠出，振動力場作用帶來了整個擠壓工藝新的變化的能量平衡，質(zhì)量平衡，動量平衡?？刂普駝宇l率和振動幅度可有效控制動態(tài)擠壓過程。電磁動態(tài)擠出如圖1所示，對動態(tài)擠出機(jī)的研究表明這機(jī)器性能良好。
圖1：電磁動態(tài)塑化擠出機(jī)的結(jié)構(gòu)。
1螺桿， 2機(jī)筒， 3轉(zhuǎn)子， 4定子， 5支撐座， 6漏斗
此外，擠出機(jī)熔體壓力和熔體溫度是變量擠出過程的關(guān)鍵。熔體壓力直接影響輸出制品的質(zhì)量。雖然熔體溫度的波動會改變?nèi)垠w粘度和進(jìn)而影響熔體壓力和流量。但是，在動態(tài)擠壓工藝中占主導(dǎo)地位的變量是熔體溫度和熔體壓力。為了獲得高質(zhì)量的產(chǎn)品，傳統(tǒng)擠出機(jī)對熔體壓力和熔體溫度的控制已經(jīng)應(yīng)用了不同的控制方法。在20世紀(jì)70年代， 由Dormered首先介紹了數(shù)字PID控制熔化溫度串級控制。螺桿直徑是45毫米。由于硬件開發(fā)的限制，樣本時(shí)間為15s。梯級PID控制如圖2所示 。
圖2 ：熔體溫度串級PID控制。
20世紀(jì)90年代以來，現(xiàn)代控制理論已逐漸引入到對每段機(jī)筒壁溫度控制。里奇達(dá)貝、亞當(dāng)角貝爾和佳日體育古普塔使用模型預(yù)測方法，建立了多輸入多輸出模式，溫度控制每段機(jī)筒的不同部分。蔡清池和盧紀(jì)宏研究了基于廣義預(yù)測算法多變量的機(jī)筒溫度控制。該數(shù)學(xué)模型的加熱過程依據(jù)能量平衡，中如圖3所示。盧紀(jì)宏還通過自適應(yīng)預(yù)測控制用在每段機(jī)筒的溫度控制。其取得的成就主要是對傳統(tǒng)擠出機(jī)、熔融溫度和熔體壓力控制電磁動態(tài)擠出機(jī)、熔體溫度和熔體壓力控制的基礎(chǔ)上新的模糊控制算法的電磁動態(tài)擠出機(jī)進(jìn)行了研究。
圖3 ：擠出機(jī)筒的物理模型
2 系統(tǒng)建模
電磁動態(tài)擠出機(jī)有五個加熱區(qū)。溫度的前四個加熱器由手動控制。新的控制策略所控制是加熱溫度。有5個熱電偶安裝在每段機(jī)筒內(nèi)來衡量每段機(jī)筒溫度。一個紅外線溫度傳感器安裝在最近的熔體出口處以測量熔體溫度。測量熔體壓力的應(yīng)變式壓力傳感器定位在模具壁。熔體壓力通過螺桿轉(zhuǎn)速控制。加熱器功率的芯片和螺桿轉(zhuǎn)速的熔體壓力和熔體溫度的階躍響應(yīng)通過實(shí)驗(yàn)獲得。圖4和圖5是實(shí)驗(yàn)步驟反應(yīng)熔體溫度。
圖4 ：熔體溫度階躍響應(yīng)隨加熱器溫度的變化
圖5 ：熔體壓力階躍響應(yīng)隨加熱器溫度的變化
加熱器功率和螺桿轉(zhuǎn)速的熔體壓力和熔體溫度響應(yīng)是一個自我平衡系統(tǒng)。這響應(yīng)是過阻尼。因此，該系統(tǒng)被視為二階系統(tǒng)，系統(tǒng)參數(shù)由實(shí)驗(yàn)數(shù)據(jù)確定。
傳遞函數(shù)的二階自平衡系統(tǒng)與滯后表示為以下幾點(diǎn)：
K是系統(tǒng)增益， T是延遲時(shí)間， T是時(shí)間常數(shù)，是阻尼比。
然后我們得到的傳遞函數(shù)查明實(shí)驗(yàn)數(shù)據(jù)。
是熔體溫度和熔體壓力。 W為加熱器功率， n為螺桿轉(zhuǎn)速。
3模糊解耦控制算法
根據(jù)熔體溫度和熔體壓力耦合關(guān)系，我們得到一個模糊解耦控制器的熔融溫度和熔體壓力控制如圖6所示。
圖6 ：系統(tǒng)結(jié)構(gòu)的模糊解耦控制
這里的和是的熔體溫度和熔體壓力實(shí)際產(chǎn)生值。和是對熔體溫度和熔體壓力設(shè)定值。整個系統(tǒng)由模糊控制器，解耦補(bǔ)償器和模糊調(diào)整部分。解耦系數(shù)d21和d12主要根據(jù)模糊調(diào)整部分確定，因此，耦合的兩個循環(huán)是可以消除的。
3.1解耦系數(shù)狀態(tài)下的穩(wěn)定
在穩(wěn)定狀態(tài)，根據(jù)方程2穩(wěn)態(tài)增益矩陣，解耦補(bǔ)償給出了解耦系數(shù)所確定的原則
解耦系數(shù)[ 8 ]所確定的原則，解耦補(bǔ)償給出了
由（ 3 ）和（ 4 ） ，我們得到的解耦系數(shù)下的穩(wěn)態(tài)
3.2調(diào)整動態(tài)解耦系數(shù)的進(jìn)程
解耦系數(shù)來自上述穩(wěn)態(tài)。它可以完全消除耦合熔體溫度和熔體壓力下的穩(wěn)態(tài)。為了降低耦合下的動態(tài)過程，解耦系數(shù)應(yīng)加以k控制。修改單位如圖7所示：
圖7 圖的多變量模糊控制與修改補(bǔ)償
該系統(tǒng)的輸出響應(yīng)如下：
在這里， （ 1 = 1,2 ）是模糊控制器輸出，（ 1 = 1,2 ）是系統(tǒng)輸出增量，（i= 1,2 ; j = 1,2 ）是修改系數(shù)。
根據(jù)方程7 ，產(chǎn)量增量在時(shí)間步長n-1和N上可以表示為：
在消除一切從方程8 ， 可寫為：
同理可得：
為了消除與動態(tài)過程下循環(huán)之間的耦合，它必須讓。如果，那么這意味著解耦系數(shù)是不合理的。解耦系數(shù)根據(jù)模糊邏輯的修改系數(shù)調(diào)整的。模糊集的解耦系數(shù)和修改系數(shù)是指。模糊控制規(guī)則表的調(diào)整解耦系數(shù)如表1所示：
表1 ：模糊控制規(guī)則表的調(diào)整解耦系數(shù)。
3.3模糊控制器FLC1和FLC2的設(shè)計(jì)
FLC1的設(shè)計(jì)和FLC2一樣 ，所以我們只介紹FLC1的設(shè)計(jì)。二維模糊控制器獲得通過。對模糊控制器輸入錯誤的( E）和錯誤的比例變化（EC） 。輸出( U )是發(fā)送到工廠的控制信號。(E)、(EC)和(U)的模糊集被定義為{NB NM NS ZO PS PM PB}和天地寫為為 （-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6 ）。隸屬函數(shù)為三角形函數(shù)，如圖8所示
圖8 ：隸屬函數(shù)。
在動態(tài)擠出過程中，經(jīng)驗(yàn)告訴我們：“如果溫度低或者溫度上升緩慢，那么加熱器功率應(yīng)增加”，“如果氣溫高，溫度上升很快，那么加熱器應(yīng)停止加熱” 。基于以往經(jīng)驗(yàn)，我們得到的模糊規(guī)則如下。
（ 1 ）如果E=NB或者NM和EC=NB或者NM然后U=PB
（ 2 ）如果E=NB或者NM和EC=NS或者ZO接著U=PB
（ 3 ）如果E=NB或者NM和EC=PS接著U=PM
. . . . .
根據(jù)以上規(guī)則，我們可以得到的模糊控制表。 模糊解耦后，熔體溫度由加熱器平均功率控制，熔體壓力由螺桿轉(zhuǎn)速控制。對于熔體溫度控制，控制器的輸出直接移交給PWM信號，PWM被放大用于校正加熱器的平均功率。熔體壓力控制通過增量法獲得。熔體壓力的采樣時(shí)間為20ms，熔體溫度采樣時(shí)間為500ms，PWM的周期信號為10ms ，
4控制系統(tǒng)執(zhí)行情況和實(shí)驗(yàn)結(jié)果
4.1執(zhí)行控制系統(tǒng)
控制系統(tǒng)的硬件設(shè)計(jì)包括選擇主控制器、接口電路設(shè)計(jì)、驅(qū)動器和放大器電路設(shè)計(jì)、和機(jī)器手的界面（ HMI ）設(shè)計(jì) 。根據(jù)控制要求和廠的特點(diǎn)，B&R PCC2003被評為主控制器?？删幊逃?jì)算機(jī)控制器（PCC）作為了可編程邏輯控制器（ PLC ）的標(biāo)準(zhǔn)功能配置，有時(shí)用于波分復(fù)用系統(tǒng)的工業(yè)計(jì)算機(jī)產(chǎn)業(yè)。PCC因其模塊化結(jié)構(gòu)可以方便地處理類似的信號和數(shù)字信號，很容易配置。一個先進(jìn)的語言和混合不同的語言計(jì)劃在PCC的基礎(chǔ)上發(fā)展起來，如圖9所示：
圖9 ：配置的控制系統(tǒng)。
4.2實(shí)驗(yàn)結(jié)果
實(shí)驗(yàn)材料是LLDPE。溫度加熱器1-4列分別設(shè)為165℃， 180℃，180℃ ，175 ℃。熔體壓力為10Mpa和熔體溫度為170 ℃，當(dāng)操作變得穩(wěn)定時(shí)熔體壓力改12Mpa 。圖10表明， 實(shí)際壓力迅速增加到設(shè)置點(diǎn)時(shí)的溫度仍然是170℃ 。圖11表明，當(dāng)熔體溫度設(shè)定值更改為180℃時(shí)， 反應(yīng)熔體溫度迅速增加到設(shè)置點(diǎn)，熔體的壓力幾乎保持不變。圖5表明，開環(huán)控制的效果和熔體壓力跌幅的快慢隨熔體溫度的變化。通過模糊邏輯解耦控制，驗(yàn)證圖11改變?nèi)垠w壓力，熔體溫度保持不變的情況下新的控制方法的有效性。以改變?nèi)垠w溫度，不改變?nèi)垠w壓力與該例子方法是相同，具體細(xì)節(jié)這里省略。
圖10 ：改變?nèi)垠w壓力，熔體溫度不變。
圖11 ：改變?nèi)垠w溫度與不該變?nèi)垠w壓力。
5結(jié)論
本文討論了解耦控制熔體壓力和熔體溫度的電磁動態(tài)擠出機(jī)。介紹了一種基于模糊邏輯新的控制算法，其中包括模糊控制器，解耦補(bǔ)償器單元和模糊調(diào)整組成部分單元。執(zhí)行控制系統(tǒng)是基于B&R PCC2003 。實(shí)驗(yàn)結(jié)果表明，熔體溫度和熔體壓力能成功取得單獨(dú)控制和驗(yàn)證了模糊控制方法的有效性。
鳴謝
作者非常感謝中國國家自然科學(xué)基金會儀器基金會（ No.20027002 ） 。
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