ISSN 1009 - 3095 Journal of Zhejiang University SCIENCE V. 4 ,No.3 ,P. 300- 304 ,May - June , 2003300http ://www. zju. edu. cn/jzus ;http ://www. periodicals. com. cn ;jzus@ zju. edu. cnPredictive functional contROl( PFC ) and its application inchlorinated polyethylene processL Hong-lianf李鴻亮yl , sU Hong-y(蘇宏業) ,LIU Ju(劉軍尸, CHU Jiar(褚健)( 1 National Key Laboratory of Industrial Control Technology , Institute of Advanced Process Control ;Material and Chemical engineering Institute , Zhejiang University , Hongzhou 310027 , China )E-mail : hli @ ipe . zju. edu. cnReceived May .28 2002 ; revision accepted Oct. 12 2002Abstract : The main principle and the characteristic of Predictive Functional Control( PFC ) strategy are pre-sented in this paper and the corresponding control system aid design software APC- PFC is also introduced. Fora chlorinated polyethylene( CPE ) process , a design scheme of cascade predictive functional control system isdescribed and the control performance is improved obviously .Key words : Predictive control , Predictive functional control( PFC ) , Base functions , Chlorinated Polyethy-lene( CPE )Document code : ACLC number : TP 273.1INTRODUCTIONpolyethylene and the result is very nice.With the development of science and technol- THE PFC ALGORITHMogy,requirements for the satisfactory performanceof the control processes are largely enhanced.PFC is based on the same principle as that ofHowever,modern control theory based on theclassical predictive control strategy , i.e. use astate-space method cannot meet the requirementof the practical control problem due to the factmodel to predict the future output of a process ,that it is very diffcult to obtain the precise mathe-achieve optimization and feed- back correction.matical model of processes,especially for non-lin-The main difference between general predictiveear,uncertain , time-delay and time- varying pro-control strategy and PFC is that in PFC ,thecesses. Ordinary predictive control strategies canstructure of the control variables is considered assolve some of these control problems , but are usu-a linear combination of a set of base functionsally only limited to the slow processes because of( Richalet , 1987 ). The control variables can bethe complex on-line computation. Thus , Predic-obtained by calculating the weight coefficients oftive Functional Control( PFC )is used to deal withthe base functions 'linear combination.Thethe quick tracking control problems as a new kind choice of base functions is related to the charac-of predictive control method( Su , 2000 ).teristic of the process and the desired setpoint.PFC has been regarded as an effective controlThe key function of PFC is the selection ofmethod for rapid processes since it was presented at base functions ,predictive model ,reference tra-the beginning of the 1980' s. Recently , PFC has jectory and coincidence points.sucessfully been used in some practiced industrial 1. Predictive modelprocesses ,such as those for nonage robot , rocket ,PFC is a model-based predictive control strat-object dogging , reactor and heater ,etc .In this paper , the PFC algorithm is describedegy中國煤化工is often described bythe1quationand then a PFC aid design software package is in-0HCNMH Gtroduced. Finally , the PFC technology is appliedU( k-1)(1)to control a process for producing chlorinated Ym( h )=C Xm( h)Project ( No. 69974035 ) supported by the National Natural Science Foundation of ChinaA啊方數據pondencePredictive functional control( PFC ) and its application301Where X∈R"x1 is the state vector of the inter-Then the predictive output of the process isnal model process. Ym∈R'x1 is the output vectorY,(k+i)=Y(hi+i)+e(h:+i)(5)of the internal model process. U∈R'x1 is the where e( hi + i ) is the predicted difference be-control input vector of the system. A∈R"Xn ,B tween the process output and the sum of intermal∈R"xl and C∈R'xn are the cofficient matricesmodel output and disturbance model outputs , ob-tained through filtered observations on a past hori-of the discrete state space model .The model( 1 ) can be obtained by general i-zon ,by a polynomial extrapolationdentify methods because PFC is mainly used toe(k+i)=y,(h)-Y,(k)+2e(h)ideal with single input/ single output systems andpossesses strong robustness.where Ne is the order of the predicted difference2. Base functionspolynomial extrapolation. The coefficient of theOne feature of the PFC is that the control .polynomial extrapolation is e( h ),j= 1 .. ,N。.variables are expressed as the linear combinationy( k )is the process output at time hof a set of base functions5.Object function , coincidence points and control lawu(k+i)=2u(k:)f(i)(2)The goal of the optimization is to find a set ofcoefficients μ1川2... 1v such that the sum ofwhere fi( i ) is base function with corresponding the squares of the difference between processoutput when applied to a process , expressed bypredictive output and tracking trajectory at eachgn( i ),p( h )is the weighted coefficient( j=1,coincidence point is minimized , during the whole. J );J is the number of the base functions .optimizing period , so thatThe choice of these base functions depends onthe nature of the process and the setpoint. Gener-minZ(Y;(k+ h;)- Y(h+ h;)2 (6)i=1ally step , ramp , parabola .. are used .where: Y,( k.+ h;) is the predicted future pro-3. Reference trajectorycess output , Y( ht + h; )is the value of the ref-In PFC algorithm , in order to control the sys- erence trajectory , i = 1... ,n。and n, is thetem so that its output can reach the setpoint grad- number of the coincidence points .ually and avoid overshot or control variablesIf the calculation equation of the setpoint ischanging dramatically ,the following reference in polynomial formtrajectory is commonly used :y;(k+i)=d h+i)-a'(d(h)-yp(h)) (3)Qk;+h;)=>c(h:)hi,where ( k )is the desired setpoint ,y( k+i)is where N. is the order of the polynomial ,c h)isthe reference trajectory ,y,( k )is the system out- the coefficient of the polynomial.From the above equations , we can get theput ,a= e-3T/T, T, is the sample time , T is thecontrol lawresponse time of the corresponding reference tra-ma(N, ,N。)jectory. The tracking speed of the reference tra-U(h)= ko" ( C(k:)- Y( h))+ >jectory tending to the desired set-point value de-pends on the value of a.(c(k)-e(k))+hm.Xm(k)(7)4. Predictive output and auto-compensationwhereFrom system model( 1 ) , the predictive outputof the model at the moment h: + i is中國煤化工"IYm( k + i)= CA' Xm(h)+YHCNMH G之μ(h) g(i)]c[A-1]|j=1(4)k= v| :|i 1矯內數據s( i)」j=1302L Hongliang , SU Hongye et al.v=[f(0) ... f;(0)] M ;efficients ko , k; , him ,can be computed off-line ,M=(GGT)↓G;andCh),Y,(h),c(h),e(h)areknown.grK h|) ... g{ h,)]Here , state variable X( h ) , control variable U( k:)and predictive error between the process andG=Lghr( h) h, )」the model are needed to compute on-line. Obvi-ously , compared with the other predictive controlg以n)= CA- B(fC0...mB.mfC i-1);strategies , PFC has simpler algorithm and lessNe is the order of the predicted difference poly- computation.( Richalet ,1987 ;Didier,1991 ;nomial extrapolation , N, is the order of the refer-Ata-Doss et al. , 1991 ;Xi , 1993 ; Chu ,1995 ).The structure of the predictive functionalence trajectory .Where u h )is the control input signal .co- control is same as the structure of the model al-gorithmic control , and is shown in Fig.1.Base FunctionProcessControloutputinputSetpoint 廠ReferenceControllertrajectoryJDisturbance「Distur bancemodelInternaT| Calculating-9OfninecalculatingFig.1 Block diagram of the structure of the Predictive Functional Control methodwith industrial control problems conveniently , a .THE SOFTWARE PACKAGE OF APC-PFC .PFC aid design software package was developedand a man-machine interface of the APC-PFC isIn order to use the PFC algorithm to deal shown in Fig.2.AIBECudel AndonMadei SeleatPedtereaace leder口Sep Hiespense P HyepihetFig理loter Model口Pulse FenponeeDistutb Meitetp Bede F中國煤化工MYHCNMHGFig.2 The interface of APC-PFCPredictive functional control( PFC ) and its application303This software has been applied in many prac- process , and must react according to the giventical industrial processes. It can be realized in relationship among the temperature , time and to-DCS,PLC or industrial control computer based tal amount of chlorine. The property of the pro-on the fact that this software can form C+ + ,C cess varies greatly during reaction , so it is hardand EXE files , control by using traditional control strategiessuch as PID control strategy. In the past , manu-CHI ORINATED POL YETHYI ENE( CPE ) PROCESSal operation control was very difficult and trou-blesome,while PID control was troubled byovershot , vibration and low control precision .Chlorinated polyethylene( CPE ) is an impor-The flow sheet of the CPE process is showntant chemical engineering production. The chlo-in Fig.3.rinating procedure is a fitful and discontinuous1-Compressed mir2-Tail總鮮s3-Hydrochlotie ncid4-Polyethylene5-Chlorine gasSteam--國Pasty stock。Hot waterFig.3 The flow sheet of CPE ,From the raw material to the chlorinating temperature tracking .production , the process has four stages : adding Heat preservation : The main goal of this periodmaterial , exhaust,heating ,heat preservation. is to keep the temperature at a given area. ThisEach stage has different task and control feature. stage is the key for ensuring production quality ,Adding material : Adding the raw materials and the controller should guarantee the kettle( polyethylene mainly ) , churning fully ,increas- temperature inside the given the kettle temperature by steam.The production output after the above fourExhaust : When the kettle temperature reaches stages should be de-acidified , neutralized andT , add chlorine F to remove airs.dried to finally , yields the chlorinated polyethy-Heating : When the kettle temperature is T2 ,lene product.close the steam valve and add chlorine gas nor-PFC APPLICATION IN THE CHLORINATEDmally. This period may be divided into somestages , with each stage having diferent desired POLYETHYLENE PROCESStemperature-time-total value that will affect the中國煤化工ied to deal with thequality of production. In this period , the tradi-tional PID control may have large overshot and prac.MYH. CNMH Gf a chlorinatedabrupt transition due to the fact that the heating polyethylene process in H langzhou Electrochemi-stage is a heat absorbing process and that the cal Group Co. ,Ltd. The distributed control sys-kettle temperature is adjusted only by changing tem was Supcon JX-300 DCS , model identifica-chlorine, gas, gyantity. Moreover , vibration and tion and PFC controller were designed by APC-low precisroltx源e also the control problems of PFC software. The control framework is shown in304L Hongliang , SU Hongye et al.Fig.4.甲Fp _ I FeedingT。. FeedingReaction→q- -[PFCI] 8“PFC2valvefowkcitle|Fig.4 The control framework of cascade PFCThe inner loop of the control system was system , and the curve below is that of PFC. Thecomprised of PFC 1 controller and the feed flow ripples in the upper curve shows that the systemvalve. The outer loop was comprised of PFC 2 has a lot of disturbances. The PFC strategy leadscontroller , the inner loop output and the reactor to a more precision , strong robustness and goodkettle , which was used to regulate the set point tracking performance.of the feed flow so that the kettle temperaturetracked the desired reaction temperature .CONCLUSIONS .The PFC algorithm was programmed by sys-tem controlling language ( SCL ) of the JX-300DCS application module and was downloaded toThe PFC method and APC- PFC software arethe control station of DCS .introduced in this paper and applied to deal withThe transfer function of the inner loop pro- the control problem of chlorinated polyethylenecess can be obtained as G( s )=_1.72process. The actual control results indicated that17.635s + 1 compared to the tradition PID control strategy.e-1.02s1.66the PFC control algorithm has many more advan-,and outer loopas G(s)=35.338+1tages such as the rapid tracking , the higher pre-e-2.7*. The kettle temperature under PFC and cision , strong robustness , etc.PID control law is compared in Fig.5 , where thex-axis is the time ( minutes ).ReferencesThe curve above is the input of the PID controlAta-Doss ,S.A. , Fiani ,P. and Richalet ,J,, 1991. Han-dling Input and State Constraints in Predictive FunctionIDControl. Proceedings of the 30th Conference on Decisionand Control , Brighton , England ,p. 985 - 990.Chu ,J , 1995. The Base of Moderm Control Theory. Zhe-jiang University Press , Hangzhou( in Chinese ).PFCDidier, C. S., 1991. Computer aided design of weaponsystem guidance and control with predictive functionalcontrol technique. AGARD Conference : Software forGuidance of Control , Greece.13929a)Richalet ,J.,1987. Predictive functional control : Applica-tion to fast and accurate robots. Proc. of 10h IFAC. PIDworld Congress , Munich.Su ,H. Y. , Hu ,J.B. and Chu ,J. , 2000. Robust Stabi-lization of Uncertain Time-Delay Systems ContainingNonlinear Saturating Actuators. Joural of Zhejiang University SCIENCE ,1( 3 )241 - 248.Xi ,Y.G. , 1993. Predictive Control. National Defence In-dustrial Press , Beijing ,p.207- 214( in Chinese ).FC中國煤化工12:40 傳努(b)13:20 1.4013:29YHCNMHGTimeFig.5 Comparison of two control methods( a )Output of two control methods { b )Input of two controlmethods.

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