(过控)04_机理建模

1、本节内容在课程中的位置本节内容在课程中的位置n过程控制中，被控过程多种多样，如锅炉、过程控制中，被控过程多种多样，如锅炉、液体储罐、加热器、压力容器、球磨液体储罐、加热器、压力容器、球磨机机等等形形色色的生产设备。等等形形色色的生产设备。Fundamental modelsWhen I complete this chapter, I want to beable to do the following.Write balance equations using the integral methodsDetermine the state, input, and output variabl

2、es and the parameters for a particular model (set of equations)Determine the necessary information to solve a system of dynamic equationsLinearize a set of nonlinear equations to find the state space modelMajor sections of this chapternMaterial balances nMaterial and energy balancesnForm of dynamic

3、modelsnLinear models and deviation variablesOutline of the lesson.Purpose of development of dynamic process modelsn指导过程控制系统方指导过程控制系统方案设计；案设计；n系统调试和调节器参系统调试和调节器参数整定；数整定； n指导工艺生产设备的指导工艺生产设备的设计；设计；n先进控制理论的应用先进控制理论的应用和优化研究；和优化研究；n系统仿真，操作员前系统仿真，操作员前期或离线培训等。期或离线培训等。Reasons for modelingn Models are often u

4、sed forn(i) operator training. Process operators can learn the proper response to upset conditions, before having to experience them on the actual process.n(ii) process design. Can be used to properly design industrial process equipment for a desired production rate.n(iii) safety system analysis, or

5、n(iv) process control.No single model of a process exists!Improving or understanding industrial process operation is a major overall objective.Self-regulating system( )( )1pipkH sQssIntegrating system( )( )pipkH sQssInverse response process(1) ( )(1)pppksgsssn响应曲线在一段时间内变化方向与其他时间相反（非响应曲线在一段时间内变化方向与其他

6、时间相反（非最小相位系统）。最典型的是锅炉汽包液位的反向特最小相位系统）。最典型的是锅炉汽包液位的反向特性过程：性过程：n冷水增加会引起汽包内水的沸腾突然减弱，水中气泡迅速减冷水增加会引起汽包内水的沸腾突然减弱，水中气泡迅速减少，水位下降。少，水位下降。 n但液位终究会随着进水量的增加而增加，并呈现积分响应。但液位终究会随着进水量的增加而增加，并呈现积分响应。 Most widely used process model( )1pspkG sesn实践证明，多数被控过程具有如下特性：实践证明，多数被控过程具有如下特性：n1.被控参数的变化往往是不振荡的，单调的，有惯被控参数的变化往往是不振荡的

7、，单调的，有惯性；性；n2.存在纯滞后。存在纯滞后。n最常见的数学模型：最常见的数学模型：n工业过程中，此类被控过程非常多。许多高阶工业过程中，此类被控过程非常多。许多高阶环节也可化简为一阶惯性加纯滞后环节。环节也可化简为一阶惯性加纯滞后环节。 Integral balances mass or mass or energy inside theenergy inside thesystem at system at ttt mass or energy mass or energy entering the system _ leaving the system from to from t

8、o tttttt nAn integral balance is developed by viewing a system at two different “snapshots” in time.Integral balances Representing ,as and as Note that the system is perfectly mixed, inoutininoutininoutoutMVmFmFdVFFdt()ttttttinoutinoutttttttMMm dtmdtmmdtinoutdMmmdtSteady state orinoutininoutmmFF0ino

9、utdMmmdtSteady-state (稳态稳态) relationships are often used for process design and determination of optimal operating conditions.Gas surge drum (气体缓冲罐气体缓冲罐) examplenSurge drums are often used as intermediate storage (中间中间储藏储藏) capacity for gas streams that are transferred between chemical process units

10、.(/), ()idnd PVRTV dPPVnRTdtdtRT dtdPRTqqdtVwhere is the total amount of gas (moles)contained in the drum. represents the molecular weight, assuming constant.iidnMWq MWqMWdtnMWidnqqdtWhats kind of this system?？An integrating system!Outlet flow as a function of gas drum pressurenConsider the case whe

11、re the outlet molar flow rate is proportional (正比正比) to the difference in gas-drum pressure and the pressure in the downstream header piping, Ph. ()ihdPRTRTqPPdtVV()hqPPAt steady state, /0,()Solving for ,isshsisshsdP dtqPPPqPPWhats kind of this system?？A self-regulating system!An lsothermal (绝热绝热) c

12、hemical reactor exampleEthylene oxide () is reacted with water ( ) in continuously stirred tank reactor (CSTR) to form ethylene glycol ( ,). iABPABPdVFFdt环氧乙烷,连续搅拌化学反应器,乙二醇 (1)Component material balancesLet and represent the molar concentrations of and (moles/volume). (2) where and represent the rat

13、e ofAPAPAiAiAAPPPCCAPdVCFCFCVrdtdVCFCVrdtrr of species and per unit volume.generationAPAn lsothermal chemical reactor (cont.) where is the reaction rate constant and the minus signindicates that is consumed in the reaction, and Since AApAArkCkArkCdVCd (3)Combing (1),(2), and (3), we find ()Similarly

14、, AAiAAiAAiPPAdCdVVCtdtdtFdCCCkCdtVFdCCkCdtV Steady-state solutionLet 0(/),(/)(/) 1(/)(/)(/) 1Notice that the concentrations are a function of the (,/), which has units of inverse tiAPsAisAisAsssAissAisPssssdCdCdtdtFV CCCFVkkVFkCkVF CCFVkkVFspacevelocityFV空速me.Linear models and deviation variablesCo

15、nsider the stirred-tank heater model, when the volume, flowrate, and inlet temperature are constant at their steady-state values: ()sissspFdTQTTdtVVcDefine the following deviation variables ssuQQyTT1Then Or ssspppV dyyuF dtFcdyyk udt Whats kind of this process?？Linearization of nonlinear models,One

16、state variable:( )( )()()One state and one input:( , )( , )( , )(,)()() Output varlable:( , )( , )( , )(,)()sssssssssxssssx ux usssx uf xf xf xxxxf x uf x uf x uf x uxxuuxug x ug x uyg x ug x uxxx,()sssx uuuuA second-order reaction example2Consider a continuously stirred tank reactor(CSTR) witha sin

17、gle, second-order reaction. (,)()where the state variable is and the input variable is .AAAinAAAdCFf CFCCkCdtVCFWe want to get a linear model as the following form where AASSAASxaxbuycxduxCCuFFyxCC Whats the a, b, c and d?？Solution to the second-order reaction example,(,)2(,)(,)1(,)0AssAsssACFAsAAin

18、sAsACFAAAFf CFakCCVCCf CFbFVg CFcCg CFdF Generalization11111221111111111Consider the general nonlinear model with states, outputsand parameters( ,)( ,) ( ,)( ,nxnunpnxnunpnxnxnxnunpnxnunxnynpxf xxuuppxfxxuuppxfxxuuppyg xxuup122111111,)( ,) ( ,)npnxnunpnynynxnunppygxxuuppygxxuuppGeneralization,The li

19、near state space model iswhereIn future chapters we normally drop the prime() notation fordeviation variables anssssssssiiijijjjx ux uiiijijjjx ux uxAxBuyCxDuffABxuggCDxud assume that a state space model is always in deviation variable form.Jacketed(夹套夹套) heater exampleJacketed heaterThe rate of hea

20、t transfer from the jacket fluid to the vessel fluid is where is the overall heat transfer coefficient and is the areafor heat transfer.EnergjQUA TTUA12y balances on the vessel and jacket fluids result in the following equations. ()()( ,) ()()( ,ijjjijinPjjjinjjjjijinjjjPjdTFUATTTTf T T F F T TdtVV cdTFUATTTTf T T F F T TdtVVc)Jacketed heater11221234In deviation form:sjjsjjssiisjinjinsTTyxyxTTyxFFuFFuuTTuTTuWhats the A, B, C and D?？Solution to ja