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Process Control College of Automation Chongqing University1Dynamic ResponseOutline:轮廓⏹Brief Review of the Dynamic Response简要回顾动态响应⏹First Order Models for Processes一阶模型的过程⏹Seconds Order Model for Processes二阶模型过程⏹Models for Process with Dead-Time死区时间的过程模型⏹Higher Order Models and Approximation高阶模型和近似⏹Special Features of Lead-Lag Process滞后过程的特殊特色The First Order Model of a ProcessQ,C inC1V1Whereis time constantThe general form of the 1st order model一阶模型的一般形式Steady state gain稳态增益The Second Order Model of a ProcessWhereare time constantsThe general form of the 2st order modelQ,C inV 1C 1C 2V 22'''22121222()()indC dC C t C dtdtττττ+++=)(01222t bx y a dtdya dt y d a =++withWith an ≠ 0和零初始条件Analysis of the 1st Order ProcessStep responsetransfer functionConsider a step input, x(t) =Mu(t), and X(s) = M/sThe output isThe time domain function isAnalysis of the 1st Order Process Step response阶跃响应Property 1性质1y increases from 0 to a new steadystate M K, thus self-regulatingy增加从0到一个新的稳态MK,从而自我调节Analysis of the 1st Order Process Step responseProperty 2性质2Steady state gain K = y/M,The larger gain K, the moresensitive is the output to thechange in the input增益K越大，输出随输入变化就越敏感Analysis of the 1st Order Process Step responseProperty 3At t=τ, the output isy =0.632MKThe formula above can be used to estimate space timeτ上面的公式可以用来估计空间时间τAnalysis of the 1st Order ProcessStep responseThe time domain function is 时域功能Property 4The shorter the space time τ, the faster reaches the new steady state0.25, 0.5, 1, 2Analysis of the 1st Order ProcessImpulse response脉冲响应transfer function传递函数Consider an impulse input, x(t) =M (t), and X(s) = M 考虑一个脉冲输入The output is Inverse transform反变换The output increases instantaneously at time t = 0, and decays exponentially to zero.输出瞬间增加在时间t= 0，且呈指数衰减到零Analysis of the 1st Order ProcessIntegrating process: Non-self-regulating 整合过程：非自我调节a= 0Laplace transformTime domain时域Analysis of the 1st Order Process⏹Integrating process: Non-self-regulating☐With step response, the output is a ramp function阶跃响应，输出的是一个斜坡函数☐With impulse response▪The output will not return to its original steady state▪输出不会回到原来的稳定状态▪Output value is the accumulation of what is added▪输出值会累积增加⏹Example can be☐Charging a capacity充电容量☐Filling up a tank 填充的水池Example: Show that a storage tank with pumps at its inlet and outletis a integrating process 表明储罐泵在其进口和出口是一个整合过程Mass balance of a continuous flow mixed tankat constant density is :质量守恒方程，在密度不变的情况下whereq in and q are the flow rates of the inlet and outlet q in and q 是进口和出口的流动速率A is the cross-section 截面h is the liquid level 液位hExample (cont.)⏹At steady state, we can define deviation variables⏹在稳定状态下,我们可以定义偏差变量h’=h – h s, q’in =q in – q s, and q’ =q – q s⏹Mass balance becomes⏹The general solution一般解Example (cont.)⏹The transfer function⏹Step input in either q’in or q’ Leading to a ramp response, thus no steady state阶跃输入q‘in 或q’，导致斜坡响应，因此，没有稳定的状态⏹The tank will overflow, while outlet slows down ⏹容器将溢出,当出口关小Setting q’in=constant, the transfer function is⏹The tank will be drained, while outlet speeds up ⏹容器内液体将流干，当流出速度增加Example (cont.): Visualize the integrating process 可视化的积分过程 pump 泵q inqq inqNon-Self-RegulatingThe tank will overflow, while step-in occursOther Typical1st Order ProcessesE= Voltage, 电压z = Position,K’= Spring constant弹性系数,f = friction coefficient摩擦系数Other Typical 1st Order Processes An Extra Example (cont.):RC i iVccV V dtdV RC -=where τ = RC is time constant K = 1 is steady state gain x(t) = V s is the input )1(/τt s c e V V --=Charging: Discharging:τ/t s c e V V -=Other Typical 1st Order ProcessesAn Extra Example (cont.):RCi iV )1(/τt s c e V V --=Charging:Discharging:τ/t s c e V V -=Analysis of the 2nd Order ProcessCorresponding Laplace Transform相应的拉普拉斯变换Where 说明：damping ratio阻尼比natural period of oscillation自然振荡周期natural frequency固有频率Analysis of the 2nd Order Process Characteristic polynomial特征多项式The poles are 极点是：Noticing again that a stable process requires再一次注意到一个稳定的过程需要ζ>τ)0(i.e.,>Three Cases of the PolesCase 1. overdamped process 过阻尼过程In term of the two time constants 依据两个时间常数Time constant can be derived below 被推倒21ττ and 1>ζ21ττ and or,In the case of having real poles, we have 在实极点的情况下，我们有Three Cases of the PolesCase 1. overdamped process 过阻尼过程How about the forms of transfer function in term of ? 传递函数有哪种形式按照/1 and /121ττ-- 1>ζStep response in term of the time constant 阶跃响应下的时间常数τResponse is sluggish compared with underdamped or critically damped processes 响应比较缓慢与欠阻尼或临界阻尼的进程相比Three Cases of the Poles三种极点ζCase 1. overdamped process过阻尼1>可视为时间常数Three Cases of the PolesCase 3. underdamped process 欠阻尼 10<≤ζStep responseBeing rearranged as被调整为The real part determines the exponential decay, thus the amount of can be considered as the time constant 决定了指数衰减，从而可视为时间常数τζ-τζTwo conjugate poles are两个共轭极点是τζτζ21-±-j based on 基于 τζ-τζKey Features of Underdamped Process 欠阻尼过程的主要特点(2) making control system design specifications with respect to the dynamic response 制作动态响应的控制系统设计规范⑴ fitting experimental data in the measurements of natural period and damping factor ,把测量自然周期和阻尼因子拟合过后的实验数据Features Derived from the figure for:图的特征Key Features of Underdamped Process1. Overshoot超调⏹The overshoot increases as ζ becomes smaller⏹The OS becomes zero as ζ approaches 1⏹The time to reach the peak value is Peak Time峰值时间T p⏹The time to hit the final value of y(t) is Rise Time上升时间 t rKey Features of Underdamped Process2. Frequency and Period周期⏹Noting that（注意）T=2 T p⏹The unit of the frequency is radian/time频率的单位是弧度/时间 The relationship between frequency and periodKey Features of Underdamped Process3. Settling time 调节时间 T s⏹The dominant factor forcing theoscillation to decay to zero is震荡衰减到0的主导因素是：)/(t e τζ-in ⏹To settle with ±5% of the final value is T s =3/(ζ/τ)⏹±5%误差带所需要的调节时间 T=⏹To settle with ±2% of the final value is T s =4/(ζ/τ)n ω1Key Features of Underdamped Process 4. Decay Ratio 衰减率OS为超调（overshoot）⏹The decay ratio is the square of the overshoot⏹Both quantities are functions of ζ only这两个量只是ζ函数（调节时间和衰减率）Other Typical 2nd Order ProcessesE= Voltage,z = Position,K’= Spring constant,f = Friction CoefficientM = Massh = forceProcesses with Dead Time过程控制的延迟时间The time delay between the input and output in a process输入与输出的时间延迟⏹Being also called dead time or transport lag传输延迟⏹The Laplace transform of a time delay is an exponentialfunction指数函数Processes with Dead Time A Simple ExampleProcesses with Dead Time⏹The 1nd and 2nd order models have the s-domain function S域函数⏹Td是延迟时间and⏹Dealing with the exponential functions处理的指数函数⏹Estimation with Taylor series expansion泰勒级数展开估计Estimation with Padé approximation (higher accuracy) Padé逼近估计（精度更高）Processes with Dead Time⏹The 1nd order Padé approximation⏹The Denominator introduces a negative pole, probably impacting thecharacteristic polynomial of the original process介绍了负极分母,可能影响特征多项式的原工艺⏹The numerator has a positive zero, making the process unstable分子有一个积极的零,使过程不稳定⏹The 2nd order Padé approximation⏹Having two negative poles and at least one zero⏹有两个负极点和至少一个零点Processes with Dead TimeExample: Using the 1nd order Padé approximation帕德近似to plot the step response of the 1st process with dead time 使用的一介帕德近似逼近延迟时间绘制的第一过程的阶跃响应Padé approximationObservation: the approximation is acceptable at larger timescompared with the original transfer function.逼近的函数和原函数相比可以接受Processes with Dead TimeExample (cont.) Generating the required plot 生成需要的图形（MATLAB ）Pad é approximationProcesses with Dead TimeThe response of the dead time processProcesses with Dead TimeTwo plants have different intermediate variables but have the same input-output behavior!两个工厂有不同的中间变量,但有相同的投入产出的行为!Processes with Dead TimeTwo plants have different intermediate variables but have the same input-output behavior!Higher Order Process⏹All linearized higher order system can be broken down into the 1st and 2nd order units所有线性化高阶系统可以分成一阶和二阶单位⏹The complex process like two interacting tanks can be formulated in coupled differential equations复杂的过程，像两个相互作用的容器能制定耦合微分方程⏹All these problems are considered linear⏹所有这些问题都能被线性化Higher Order ProcessA series of well-mixed vessels where the volumetric flow rate, and the respective volumes are constant 一系列混合容器，其中体积流速，和各自的容量是恒定的n 1n n n c c tc τ-=-d dHigher Order Process⏹A series of well-mixed vessels (cont.)混合容器☐The steady state gain is unity in the process 在过程中稳态增益不变☐The more tanks in the series, the more sluggish is the response of the overall process 容器越多，整个响应过程的滞后越长☐Processes that are products of the 1st order functions are called as multicapacity processes 多容量过程☐If all of space time （空间时间关系）are equal, nτττ=== (21)Higher Order ProcessExample: showing how the unit step response C n (t) becomes more sluggish as n increases 显示单位阶跃响应Cn(t)随著n 增加变得更加缓慢Higher Order ProcessExample (cont.) the Matlab code for the plot 绘制图形的MATLAB 代码The response is obviously slower, as n increses The curves can be approximated by the 1st order model with dead time 这些特征曲线可近似为滞后的一阶模型3=τApproximation of Higher Order Process⏹Higher models☐Being factored into the form partial functions考虑部分函数的形式☐Time constants have a large enough difference时间常数有很大的的差异⏹The reduced-order model approximation☐Throwing away the small time scale terms☐扔掉小时间关系☐Retaining the ones with dominant poles (larger time constants)☐固定主导极点(大时间常数)。
Unit 1 Introduction to Process ControlIn recent years the performance requirements for process plants have become increasingly difficult to satisfy. Stronger competition, tougher environmental and safety regulations and rapidly changing economic conditions have been key factors in the tightening of plant product quality specifications. A further complication is that modern processes have become more difficult to operate because of the trend toward larger, more highly integrated plants with smaller surge capacities between the various processing units. Such plants give the operators little opportunity to prevent upsets from propagating from one unit to other interconnected units. In view of the increased emphasis placed on safe. efficient plant operation, it is only natural that the subject of process control has become increasingly important in recent years. In fact, without process control it would not be possible to operate most modern processes safely and profitably, while satisfying plant quality standards.近年来，对于过程系统的执行的必要条件越来越难满足了，在紧缩的工厂产品质量规范中，强大的竞争，严峻的环境和安全规范，快速变化的经济状况，这些重要因素都是我们必须考虑的。
目录第一篇 SPC概述 (1)1．1SPC定义 (1)1．2SPC主要用途 (1)第二篇 DOSOFTSPC产品介绍 (2)2．1D OSOFT SPC产品体系 (2)2．2D OSOFT SPC产品特点 (3)2．3D OSOFT SPC功能特色 (4)2．4D OSOFT SPC功能介绍 (6)2．4．1 DosoftSPC数据采集 (6)2．4．2 DosoftSPC过程监控 (8)2．4．3 DosoftSPC质量追溯 (9)2．4．4 DosoftSPC统计分析 (10)2．4．5 DosoftSPC质量改进 (17)2．5D OSOFT SPC操作流程 (24)2．6D OSOFT SPC软件优势 (25)第三篇常见问题 (26)第一篇SPC概述1．1 SPC定义SPC（Statistical Process Control）中文译名“统计过程控制系统”，是应用于企业质量管理的至为有效的方法和工具，六西格玛的核心工具之一。
它运用数理统计的方法，对过程进行监控，对检测所得的各种质量数据进行统计分析，保证过程的稳定，提高过程能力，帮助质量管理人员有效的分析和解决质量问题，不断提升品质，有效地减少不良品的产生，从而大幅降低企业的成本，提高企业的经济效益和核心竞争力。
1．2 SPC主要用途企业质量管理三境界：●质量检验阶段：企业只进行质量的检验，不进行分析●质量分析阶段：企业采用EXCEL等简单工具，进行部分，不定期的问题分析●质量控制阶段：建立质量控制平台，进行预警，监控，分析，控制的闭环控制系统。
1、采用国际标准的质量过程控制系统，建立了从数据采集，过程监控，图形分析，过程控制的闭环控制平台——提高管理水平，加强质量意识。
2、提供了基于网络和数据库的数据分析工具，改变传统手工的简单烦琐图形绘制——提高办公效率，降低劳动强度，创造个性化工作环境。
3、建立统一分析标准，固化先进管理模式，保存完整质量数据——避免人为因素，减少员工流失带来的损失，保证系统可持续稳定运行。
Intelligent process control using neural fuzzy techniquesChyi-Tsong Chen*,Shih-Tein PengDepartment of Chemical Engineering,Feng Chia University,Taichung 407,TaiwanAbstractIn this paper,we combine the advantages of fuzzy logic and neural network techniques to develop an intelligent control system for processes having complex,unknown and uncertain dynamics.In the proposed scheme,a neural fuzzy controller (NFC),which is constructed by an equivalent four-layer connectionist network,is adopted as the process feedback controller.With a derived learning algorithm,the NFC is able to learn to control a process adaptively by updating the fuzzy rules and the membership functions.To identify the input±output dynamic behavior of an unknown plant and therefore give a reference signal to the NFC,a shape-tunable neural network with an error back-propagation algorithm is implemented.As a case study,we implemented the proposed algorithm to the direct adaptive control of an open-loop unstable nonlinear CSTR.Some important issues were studied extensively.Simulation comparison with a conventional static fuzzy controller was also performed.Extensive simulation results show that the proposed scheme appears to be a promising approach to the intelligent control of complex and unknown plants,which is directly operational and does not require any a priori system information.#1999Elsevier Science Ltd.All rights reserved.Keywords:Intelligent process control;Neural fuzzy design techniques;Nonlinear unstable CSTR1.IntroductionConventional control theory is well suited for appli-cations where the processes can be reasonably described in advance.However,when the plant's dynamics is hard to characterize precisely or is subject to environmental uncertainties,one may encounter di culties in apply-ing the conventional controller design methodologies.Despite of the di culty in achieving high control per-formance,the ®ne-tuning of controller parameters is a tedious task that always requires experts with knowl-edge both in control theory and process information.Therefore,in recent years the control of systems with complex,unknown and uncertain dynamics has become a topic of considerable importance in the literature and several advanced strategies have been developed [1±3].Fuzzy logic control (FLC)has been suggested as an alternative approach for process systems in the presence of complex dynamics.Much progress has been made in both the theoretical research and the implementation to industrial control systems [4±6].Basically,the FLC techniques represent a means of both collecting humanknowledge and expertise and dealing with nonlinearities.However,the FLC techniques su er from problems such as (1)the derivation of fuzzy control rules is often time consuming and di cult;(2)the system perfor-mance relies signi®cantly on so-called process experts who may not be able to transcribe their knowledge into the requisite rule form;(3)there exists no formal fra-mework for the choice of the parameters of a fuzzy control system;(4)the static fuzzy controller has no mechanisms for adapting to real-time plant change.From a practical point of view,these di culties may inhibit the applicability of the fuzzy logic control under stringent conditions [3].To overcome the above-mentioned drawbacks,there is a growing interest in bringing the learning abilities of the neural networks to automate and realize the design of fuzzy logic control systems [7±13].Three categories of approaches have been proposed in the literature [14].Among them,one of the most popular approaches is to install the fuzzy logical system in architecture iso-morphic to the neural networks.In other words,special-type multi-layer neural networks,which are often called the fuzzy neural networks [15],are used to perform a function equivalent to the fuzzy logical system.A basic design concept of the fuzzy neural network based control system is the ®rst to use structurelearningJournal of Process Control 9(1999)493±5030959-1524/99/$-see front matter #1999Elsevier Science Ltd.All rights reserved.PII:S0959-1524(99)00014-1*Corresponding author.Tel.:+886-4-4517250,ext.3691;fax:+886-4-451-0890.E-mail address :ctchen@.tw (C.-T.Chen)algorithm to®nd appropriate fuzzy logic rules from sample data and then use parameter learning algorithm for the re®nement of the membership functions and other parameters.In principle,the combination of techniques from these two®elds reaps the bene®ts of both neural networks and fuzzy logical systems.The neural networks provide the connectionist structure (fault tolerance and distributed representation proper-ties)and learning ability to the fuzzy logical systems;the fuzzy logical systems provide a structural framework with high-level fuzzy IF±THEN rule thinking and rea-soning to the neural networks.This synergistic integra-tion of neural networks and fuzzy logical systems provides a new direction toward the realization of intelligent system for diverse®elds[12].In this paper we propose a novel and systematic neural fuzzy control system for the intelligent control of chemical processes having complex,unknown and uncertain dynamics.The designed fuzzy logical con-troller,which is called the neural fuzzy controller(NFC) throughout this paper,is implemented using an equiva-lent four-layered connectionist network.With a derived learning algorithm,the NFC is able to identify fuzzy rules of the controlled plant and has the capability of tuning membership functions automatically by merely observing the process output errors.To identify the input±output dynamic behavior of an unknown plant and therefore provide a reference signal for on-line tuning of the NFC,a shape-tunable neural network (MNN)[16]with an error back-propagation algorithm is implemented.The applicability and e ectiveness of the proposed scheme were demonstrated through the challenge problem of controlling a nonlinear and open-loop unstable CSTR.Some important issues of imple-menting the proposed scheme were studied.Further-more,extensive simulation comparisons of the proposed scheme with a conventional static fuzzy control system was also performed.2.An intelligent control system for complex processes 2.1.The control system structureThe proposed intelligent control system is schemati-cally shown in Fig.1,where a neural fuzzy controller (NFC)is adopted as the process feedback controller. The error and change-of-error terms,generating by the comparison of the process output with the desired setpoint,are mapping through a hyperbolic tangent function before feeding into the NFC.More precisely, the inputs to the NFC are obtained through the mappings of x1 1Àexp À 1e a 1 exp À 1e and x2 1Àexp À 2ce a 1 exp À 2ce ,where 1and 2are the pre-speci®ed parameters governing the slope of the hyperbolic tangent function.This e ort ensures the universe of discourse to lie in the range of[À1,1], which can facilitate the design of the neural fuzzy control system.Another important part in the scheme is the MNN-based estimator,which is designed to identify the input±output dynamic behavior of a controlled plant so as to provide a reference signal for the NFC parameter tuning.For completeness,in what follows we describe the proposed scheme through individual parts.2.2.The NFC and its associated learning algorithm2.2.1.The NFC structureFig.2depicts the NFC structure,which is a four-layer feedforward connectionist network to realize a simpli®ed Takagi and Sugeno's fuzzy inference system [17].The NFC,in essence,integrates the basic elements and functions of a conventional FLC(membership functions,fuzzy logic rules,fuzzi®cation,defuzzi®ca-tion,and fuzzy implication)into a connectionist struc-ture that has distributed learning ability to learn the membership functions and fuzzy logic rules.Let each input have n terms for fuzzy partition,that is,each input has n membership functions,then the input±output relations between layers are stated precisely as follows: .Layer1:Input layerThe input units in this layer are the transformed process output error x1and the transformed change-of-error x2,and the output nodes just494 C.-T.Chen,S.-T.Peng/Journal of Process Control9(1999)493±503transmit these input values to the next layer.For clarity of presentation,we express the input layer by snput unitXI 1 i x i Yi 1Y 2yutput unitX O 1 ij I 1i Y i 1Y 2Yj 1Y 2Y F F F Y n.Layer 2:Linguistic term layerThis layer receives the signals from the input layer and uses a Gaussian function as a member-ship function to determine the relative contributionof the observed signals.Thus,the input±outputrelationship of this layer is de®ned as follows:snput unitsXI 2 ijÀO 1 ij Àa ij22ijY i 1Y 2Yj 1Y 2Y F F F Y nyutput unitsX O 2 ij "A ij exp I 2ij Yi 1Y 2Yj 1Y 2Y F F F YnFig.1.The schematic diagram of the proposed neural fuzzy controlsystem.Fig.2.The structure of the proposed neural fuzzy controller.C.-T.Chen,S.-T.Peng /Journal of Process Control 9(1999)493±503495where a ij and b ij are,respectively,the center and the width parameters of the Gaussian function..Layer3:Rule layerLayer3implements the links relating precondi-tions to consequences.The connection criterion is that each rule node has only one antecedent link from a linguistic variable.Hence,we havesnput unitsX I 3 jÀ1 n l o 2 1j o 2 2l Y j 1Y2Y F F F Y n Yl 1Y2Y F F F Y nyutput units X o 3 i "i I 3 i Y i 1Y2Y F F F Y m n2.Layer4:Output layerAll consequence links are fully connected to the output nodes and are interpreted directly as the strength of the output action.This layer performs centroid defuzzi®cation to obtain the inference output,that issnput unitX I 4mp 1o 3 p w pyutput unitX o 4 uÃI 4 mp 1o 3 pApparently,the NFC presented is equivalent to a simpli®ed fuzzy inference system[17],where layers1 and2correspond to the antecedent part of the fuzzy control rules,and the layers3and4correspond to the conclusion part.2.2.2.A learning algorithm for the NFC parameter updatingOnce an NFC has been constructed,the learning aims at determining appropriate values for the parameters of the Gaussian(membership)functions,a ij and b ij,and the linking weights w j.The adjustment of these para-meters can be divided into two tasks,corresponding to the IF(antecedent)part and THEN(consequence)part of the fuzzy logic rules.In the antecedent part,we need to initialize the center and width for Gaussian functions. Since the®nal performance will depend mainly on learning and the universe of discourse normally lies in the range of[À1,1],we choose normal fuzzy sets in this paper.In the consequence part,the parameters are the linking weights(the output singletons).In general,by either extracting from process operating data or from available expert knowledge these initial singletons can be set accordingly.For the case that the process infor-mation and/or expert knowledge are unavailable or incomplete,one convenient method is to initialize these values randomly,as in the pure neural networks[13]. Instead of using random numbers,we suggest in this paper to initialize these singletons using Table1.It should be mentioned that the contents in Table1,which contains m(m n2and n 2N 1)fuzzy rules,are the normalized fuzzy singletons extracted from our experi-ences.These initial settings can generally give more meaningful and stable starting than that of using ran-dom numbers.After the initialization process,a gra-dient-descent-based back-propagation algorithm is employed to adjust the controller parameters.Based on minimizing the error function of E 12y dÀy 2,the NFC parameters can be updated by w) k 1 w) k Àd Ed w)Áw) k I a ij k 1 a ij k Àd Ed a ijÁa ij k PTable1The suggested initial linking weights for the proposed control system496 C.-T.Chen,S.-T.Peng/Journal of Process Control9(1999)493±503andb ij k 1 b ij k Àd Ed b ijÁb ij k Qfor ) 1Y 2Y F F F Y m ,i 1Y 2and j 1Y 2Y F F F Y n ,whereÁ1 k is de®ned by Á1 k 1 k À1 k À1 .In theupdating rules,the gradients d Ed w )and d E d a 1jcan be derived respectively byd E d w ) d E d y d y d u Ãd u Ãd w ) À y d Ày d y d u Ão 3 jm p 1o 3 pRandd E d a 1jd E d y d y d u à nl 1d u Ãd o 3j À1 n 1d o 3 j À1 n 1d o 2 1j d o 2 1j d I 2 1j d I 2 1jd a 1j À y d Ày d y d u Ã2 o 1 1j Àa 1j o 2 1j b 2 1j m p 1o 3 p 2 nl 1o 2 2l w j À1 n 1m p 1o 3p Àm p 1o 3p w p 23Y j 1Y 2Y F F F Y nSAlso,in a similar way,the required gradients d Ed a 2j ,d E d b 1jand d Ed b 2j can be obtained byd E d a 2j À y d Ày d y d u Ã2 o 1 2j Àa 2j o 2 2j b 22j m p 1o 3 p nl 1o 21l w l À1 n j m p 1o 3 p Àm p 1o 3p w p 23Y j 1Y 2Y F F F Y nTd E d b 1j À y d Ày d y d u Ã2 o 1 1j Àa 1j 2o 2 1j b 31j m p 1o 3 p nl 1o 22l w j À1 n l m p 1o 3 p Àm p 1o 3p w p 23Y j 1Y 2Y F F F Y nUandd E d b 2j À y d Ày d y d u Ã2 o 1 2j Àa 2j 2o 2 2j b 32j m p 1o 3 p 2 nl 1o 21l w l À1 n jm p 1o 3 p À m p 1o 3p w p 23Y j 1Y 2Y F F F Y nVThe only unknown in the proposed learning algorithmis d y ad u ÃÐthe gradient of the system output with respect to the control ually,this gradient depends on the operating point and cannot be deter-mined exactly,especially in a noisy and/or uncertain environment.To provide this gradient information,many schemes in the literature can be utlilized [18±20].In this paper,however,we attempt to develop an on-line gradient estimator based on using a shape-tunable neural network (MNN)[16].2.2.3.An MNN-based estimator and its associated learning algorithmThe feedforward MNN model,which is used to esti-mate the value of d y ad u Ã,is depicted in Fig.3.The input±output relationships of a three-layer MNN are de®ned as follows [16]:snput l yer X S 1jy k Àj 1 Y 14j 4qu k Àj q 1 Y q 14j 4m 1&Fig.3.The MNN-based estimator.C.-T.Chen,S.-T.Peng /Journal of Process Control 9(1999)493±503497ridden l yerX net 2im 1j 1~w2ij S 1j ~ 2i Y i 1Y 2Y F F F Y m 2S 2i 1Àe Ànet 2i1 e Ànet 2iY i 1Y 2Y F F F Y m 2yutput l yerX net 3m 2i 1~w3i S 2i ~ 3Y y~a 1Àe Ànet 3 1 e Ànet 3where m 1and m 2are,respectively,the numbers of inputand hidden layer nodes,and yis the MNN output.To enable the MNN to emulate the dynamic behavior of the plant and therefore to provide the required gradient information,a gradient-descent-based back-propaga-tion algorithm is also employed for parameter updating.Based on minimizing the error function of~E 12y À y 2,we have the updating rules for the MNN as follows:~w2ij k 1 ~w 2ij k ~ y À y 3~w 3i 2i S 1j ~ Á~w 2ij k W~w3i k 1 ~w 3i k ~ y À y 3S 2i ~ Á~w 3i k IH ~2i k 1 ~ 2i k ~ y À y 3~w 3i 2i ~ Á~ 2i k II ~ 3 k 1 ~ 3 k ~ y À y 3 ~ Á~ 3 k IPand~ak 1 ~a k ~ y À y y~a ~ Á~a k IQ where 2i and 3are given by 2i 12 1ÀS 2i 1 S 2iIR and3 12~a 1À y ~a 1y ~aISHere,it should be noted that the shape parameter of theoutput layer,~a,is adjusted along with the interconnec-tion weights and the bias.This e ort,allowing the output range of the MNN to be adjusted automatically,avoids the scaling procedure and prevents the MNN from saturation [16].After the MNN has been trained toemulate the plant,we have y%y .This means that d y ad u Ãcan be approximated by d yad u Ã.Consequently,by using the input±output relationships of the MNN,we get the required gradient information for the NFC as follows:d y d u Ã%d y d u Ãd y d net 3 m 2i 1d net 3d S 2i d S 2i d net 2i d net 2i d S 1Y q 1d S 1Y q 1d u Ã3K 3m 2i 1~w3i 2i ~w 2Y i Y q 1 IT3.A case study:controlling an open-loop unstablenonlinear CSTRIn the previous section,we have developed an intelli-gent control system for complex and unknown plants.For learning from process output errors,associated parameter tuning algorithms have been derived.To demonstrate the applicability and e ectiveness of the proposed scheme,in this section we shall implement the proposed scheme to the intelligent control of a non-linear CSTR.The comparison of the proposed scheme with a conventional static fuzzy logical controller will also be presented.The dynamic equations of the non-linear CSTR are given by [21] ~xÀ~x 1 D a 1À~x 1 exp ~x 21 ~x2a9IU~x2 À 1 ~x 2 BD a 1À~x 1 exp ~x 21 ~x2a9u IU where ~x1and ~x 2represent,respectively,the dimension-less reactant concentration and reactor temperature.The control input u is the dimensionless cooling jacket temperature.The physical parameters in the CSTR model equa-tions are D a ,9,B and which correspond to the Damkhler number,the activated energy,heat of reac-tion and heat transfer coe cient,respectively.Based on the nominal values of system parameters,D a 0X 072,9 20,B 8,and 0X 3,the open-loop CSTR exhi-bits three steady states ~x1Y ~x 2 A 0X 144Y 0X 886 , ~x1Y ~x 2 B 0X 445Y 2X 750 and ~x 1Y ~x 2 C 0X 765Y 4X 705 ,where the upper and lower steady states ~x1Y ~x 2 A and ~x1Y ~x 2 C are stable,whereas the middle one, ~x 1Y ~x 2 B ,is unstable [21].The control objective is to bring the non-linear CSTR from the stable equilibrium point ~x1Y ~x 2 A to the unstable one ~x1Y ~x 2 B .All of the results presented are based on reactor temperature ~x2control,that is y t ~x2 t .It is important to emphasize that the plant model (17)is merely used for the simulation of the498 C.-T.Chen,S.-T.Peng /Journal of Process Control 9(1999)493±503dynamics of the CSTR and is completely unknown to the NFC.In implementing the proposed scheme to this unstable CSTR,the structure of the NFC is arbitrary chosen to be of 2-14-49-1.In other words,each of the two input variables has seven linguistic variables (seven parti-tions),say {NB,NM,NS,ZO,PS,PM,PB},where terms NB,NM,F F F ,and PS are the abbreviations for the commonly used names of ``negative big'',``negative medium'',F F F ,and ``positive small'',respectively.The initial linking weights w j 0 are listed in Table 2,which was obtained from Table 1for n 7 N 3 .The initial membership function parameters are chosen normally as a i 1 0 Y a i 2 0 Y F F F Y a i 7 0 À1Y À23Y À13Y 0Y 13Y 23Y 1ÂÃand b ij 0 0X 25,for i 1Y 2and j 1Y 2Y F F F Y 7to cover the universe of discourse [À1,1]uniformly.The struc-ture of the MNN is selected to be of 4-5-1,that is q 2,m 1 4and m 2 5.The initial values of the MNNparameters,~w2ij ,~w 3i ,~ 2i and ~ 3,are selected randomly in the range of À0.01and 0.01,and the initial shape para-meter of the activated function in the output layer ischosen as ~a0 1,which is of the same shape as the activated function used in the hidden layer.The learningrate ~of 0.3is set for the MNN-based estimator and the momentum parameters are set to 0and ~0X 01for the controller and the estimator,respectively.Besides,the NFC parameters used are 1Y 2 10Y 0X 01 ,K 3 5and 0X 8.Having the previous preparations,we are ready to investigate the following issues:3.1.The e ects of sampling interval on system performanceThe e ect of the sampling time on performance of the proposed scheme is ®rst examined.Fig.4depicts thesimulation results of the process outputs,produced control inputs and the performance of the estimator for designated sampling times.From this ®gure,it is observed that the performance of the MNN-based esti-mator can be improved by reducing the sampling inter-val.Also observed is that a high-performance estimator can result in generating aggressive control inputs and in turn accelerating the control system response.However,Table 2The initial linking weights for the open-loop unstable CSTR (seven segments)Fig.4.The e ects of sampling interval on system performance.C.-T.Chen,S.-T.Peng /Journal of Process Control 9(1999)493±503499an extremely small sampling interval would lead to an oscillatory transient response,which may be undesirable and would require powerful computation ability.In our numerical experiments,the sampling interval represents a trade o between the speed of the transient response and the level of oscillation.As to this nonlinear and open-loop unstable CSTR,the suitable sampling inter-val may be in the range of[0.05,0.5].Based on these results,we use a sampling interval of0.1min for the later simulation studies.3.2.Parameter uncertaintiesAs previously stated,the performance of a conven-tional fuzzy logical controller(FLC)relies on the fuzzy rules that transcribed by experts.Fig.5shows that the performance of the FLC is comparable to the proposed scheme when the fuzzy rules are carefully chosen.To explore the plant uncertainty on the essential behavior of the control system,we assume that,after5min of operation,the values of the heat transfer coe cient, , and heat of reaction,B,are suddenly changed to0.35 and7.5,respectively.Fig.6shows obviously that,under the in¯uence of the parameter uncertainties,a large o set exists as the conventional FLC without modify-ing its rule base was applied.The reason for this is that the static FLC control system has no mechanism for adaptation to the real-time change.It therefore loses the ability to reject the sudden parameter variations exactly. In contrast,the proposed scheme has the ability of learning from the observed process output error by updating the fuzzy rules.As a result,the plant uncer-tainties were e ectively accommodated and an o set-free control performance was obtained.3.3.Unmeasured disturbance rejectionThe next issue to be examined is the disturbance rejection ability.For simulation,we assume that there exists a step feed temperature disturbance of amplitude 0.5,which was adding in the right hand side of the dynamic Eq.(17b)after5min.It is noted that the dis-turbance is assumed unmeasured and is completely unknown to the control system.The closed-loop response to this unmeasured disturbance was depicted in Fig.7.It can be seen from this®gure that the dis-turbance rejection ability by the NFC is very excellent, whereas the conventional FLC equipped with the ori-ginally unmodi®ed rule base is unable to bring the sys-tem back to the unstable operating point.Based on the above simulation results,the advantages of the pro-posed neural fuzzy control scheme over the conven-tional static fuzzy logic control strategy areevident.parison of the proposed scheme with a conventional fuzzycontrol system.The upper graph compares the system performance,whereas the lower one compares the produced controlinput.parison of the proposed scheme with a conventional fuzzycontrol system in the presence of parameter uncertainties.The uppergraph compares the system performance,whereas the lower one com-pares the produced control input.500 C.-T.Chen,S.-T.Peng/Journal of Process Control9(1999)493±5033.4.Handling hard input constraintTo have a further demonstration,we assume that there exists actuator saturation between the controller and the nonlinear CSTR.It is well known that the pro-blem of input hard constraints caused by the actuator saturation is presented in almost every chemical process.The presence of the input saturation will impose an extra nonlinearity on system.To examine the ability of the control system in handling this situation,we assume that the control input is constrained to lie in the range of [À2,2].The simulation results in Fig.8shows clearly that the proposed control strategy works well in the face of hard input constraint.The control input produced from the NFC switches between its extreme bounds initially to give a fast transient response and soon con-verges to its ®nal value.However,the static FLC was su ered from the existing extra nonlinearity,where a large o set is observed.3.5.Measurement noise and measurement delay Fig.9illustrates that the proposed scheme has the ability in handling the additional measurement delay,even though the delay was not taken into consideration in the design of the NFC control system.In contrast,the performance of the static FLC wassigni®cantlyparison of the proposed scheme with a conventional fuzzy control system in the face of unmeasured disturbance.The upper graph compares the system performance,whereas the lower one com-pares the produced controlinput.parison of the proposed scheme with a conventional fuzzy control system in the face of hard input constraint.The upper graph compares the system performance,whereas the lower one compares the produced controlparison of the proposed scheme with a conventional fuzzy control system in the presence of measurement delay.The upper graph compares the system performance,whereas the lower one compares the produced control input.C.-T.Chen,S.-T.Peng /Journal of Process Control 9(1999)493±503501a ected by the measurement delay,leading to an oscil-latory system output.Finally,the e ect of measurement noise on the control performance was evaluated.Tem-perature measurement noise was simulated by adding zero mean random numbers with standard deviation of 0.01.Fig.10shows that in the presence of the relatively large measurement noise,the proposed control scheme can still easily bring the nonlinear CSTR to its unstable equilibrium point and remain there.4.ConclusionsIn this paper,an intelligent control strategy has been proposed for the direct adaptive control of chemical processes in the presence of unknown dynamics,non-linearities and/or uncertainties.The main idea of the present approach is to combine the advantages of the fuzzy logic and neural network techniques.The fuzzy inference system,which is used to generate the appro-priate control inputs,is implemented with an equivalent connectionist network.With a derived learning algo-rithm,the fuzzy rules and membership functions are updated adaptively by merely observing the process output error.A shape-tunable neural network with back-propagation algorithm has been suggested as the estimator that is able to provide a reference signal to the controller.The e ectiveness and applicability of the proposed scheme have been demonstrated through thechallenge problem of controlling a nonlinear and open-loop unstable CSTR.Extensive comparisons of the proposed scheme with a static fuzzy controller have also been performed.Simulation results show that the proposed scheme is directly operational and does not require any a priori process information.Besides,the proposed scheme overcomes some substantial di culties arising from the conventional static fuzzy control systems,mainly due to its learning ability.It should also be mentioned that there is no real time constraintsÐcompared with the conventional PID controllers,where a constant sam-pling time must be guaranteed.In contrast,the pro-posed scheme can make e cient use of the available computing power.Despite of these advantages,some practical problems concerning with the implementation of the proposed neural fuzzy intelligent control scheme should be considered.Certainly,an intelligent control system using direct control by error back propagation can be very sensitive to dynamic properties of the plant.Also,it has been found that the performance of the MNN-based estimator depends heavily on the sampling time as well as the initial parameter values.Never-theless,the proposed intelligent control technique appears to be a promising approach for complex pro-cesses that cannot be controlled by conventional ones in a satisfactory manner.A detail investigation of the sta-bility issues of the proposed scheme was beyond the scope of this paper and should be preserved for future work.AcknowledgementsThe authors wish to acknowledge the valuable remarks and suggestions made by the reviewers.The ®nancial support from the National Science Council of the Republic of China under Grant NSC84-2214-E-035-005is also acknowledged.References[1]B.W.Bequette,Nonlinear control of chemical processes:areview,Ind.Eng.Chem.Res.30(1991)1391±1398.[2]D.E.Seborg,A perspective on advanced strategies for processcontrol,Modeling,Identi®cation and Control 15(1994)179±189.[3]G.Stephanopoulos,C.Han,Intelligent systems in process engi-neering:a review,Computers Chem.Engng.20(1996)743±791.[4]M.Sugeno,Industrial Applications of Fuzzy Control,ElsevierScience,New York,1985.[5]K.Tanaka,M.Sugeno,Stability analysis and design of fuzzycontrol systems,Fuzzy Sets and Systems 45(1992)135±156.[6]Y.L.Huang,L.T.Fan,A fuzzy-logic based approach to buildinge cient fuzzy rule based expert system,Computers Chem.Engng.17(1993)181±192.[7]J.S.Jang,Self-learning fuzzy controllers based on temporal backpropagation,IEEE Trans.Neural Network 3(1992)723±741.Fig.10.The performance of proposed scheme in the presence of measurement noise.502 C.-T.Chen,S.-T.Peng /Journal of Process Control 9(1999)493±503。
重⼤⾃动化过程控制_process_control_中⽂_翻译_第⼀章Process Control Systems过程控制系统College of Automation,Chongqing University过程控制⾃动化重庆⼤学1Outline of the IntroductionW hat Is Process Control?DefinitionA few examples and forms⼀些例⼦和形式W hat Does It Do?Differences from automatic control theory⾃动控制理论的差异?W hat to be controlled?How Does It Do?如何实现Formulating the problem制定问题Control Equipment and Process Equipment控制设备和⼯艺设备?M odeling the process of the Problem建模过程的问题Introduction to Process Control Operator’s View of Process Control操作员的观点的过程控制A Day in aLife of a PlantOperatorDefinitionThe technology ofcontrolling a series of events to transform a material into a desired end product is called process control.控制技术的⼀系列事件把资料达到所希望的最终产品,被称为过程控制Short examples:M aking of fire for cooking rice (primitive and modern)The fly-ball governor for steam engine control (1774)短的例⼦:让⽕煮⽶饭(原始的和现代)州长的fly-ball蒸汽发动机控制(1774)Tendency of industrial process controlbeing computerized,being automatized , andbeing instrumented w ith smart sensors and M EM S⼯业过程控制的趋势在计算机化,在潜意识中⾃动使⽤,被装备智能传感器和微机电系统(M EM S)A Few Examples1.Flow Control in Oil refinery Plant:Do w e run around the plant to adjust the valves w hen required?流量控制,是炼油⼚植物:我们到处跑植物调节阀门在需要的时候吗?A Few Examples2. pH ControlManual⼿册AutomatedpH controlA Few Examples:3. Room temperature controlA Few Example4. Watt Centralfugal Speed Governor ⽡特Centralfugal调速器A Few Examples5. Level Control液位控制A Few Examples6. Cross Direction ProceControl⼗字⽅向过程控制Several hundred sensors andactuators,M illisecond operation,Controlling paper thickness tow ithin microns!⼏百传感器和执⾏器,微操作,控制纸张厚度和在微⽶!A Few Examples7. Discrete M anufacturing Processes 离散型制造过程A Few Examples8. Typical continuous processes典型的连续过程A Few Examples9. Typical non-continuous processesA Few Examples10. A Semi-Continuous Process半连续过程How large shouldthe tank volume be?油箱体积是多⼤呢？Sample-Plant: M ill W ide Process Control轧机⼴泛的过程控制Sample Softw are: Honeyw ell Intellimap样品软件:霍尼韦尔IntellimapW hat Is Process Control?Summary of the Examples- Forms总结的例⼦-形式Discrete M anufacturing, M otion, and Packaging离散型制造、运动、和包装Robotic Assembly Line in Automotive Production机械的汽车⽣产流⽔线M etal Stamping for the discrete pieces of product 五⾦冲压为离散件产品Continuous Production of Fuels, Chemicals连续⽣产的燃料、化学品Room Temperature Control室温控制Nucleus Chemical Reactor核化学反应器Batch Production of intermediate/end products批量⽣产中间/终端产品Adhesives and gluesFood, Beverages, andM edicineW hat Is Process Control?Tedency: Being Compueterized, Automatized, and Instrumented by smart sensors and M EM S计算机化，⾃动化，和动态化由智能传感器和微机电系统Sensors, local indicators,and valves in the process传感器、当地的指标,和阀门在这个过程中Valve openingdetermined by thesignal from computerDisplays of variables, calculations, commands to valves andhistorical data are in the centralized control center.显⽰变量的影响,计算,命令对阀门和历史数据是在中央控制中⼼Differences from Automatic Control Theory⾃动控制理论的差异?Using Control Theory as a ToolSolving the Real-W orld Problems forM aintaining controlled variables at the desired values保持控制变量在期望值M anufacturing products w ith consistent quality w hen raw material properties change⽣产质量稳定的产品，原料性质改变时？Responding dangerous situations w ith given time危险的情况下和给定的时间响应Being Specialized by transducer作为专业的传感器Smart sensorsM EM S 微机电系统。
Lesson 4 Process Control1 Process-Control PrinciplesProcess Control is the active changing of the process based on the results of process monitoring. In process control, the basic objective is to regular the value of some quantity. To regulate means to maintain that quantity at some desired value regardless of external influences. The desired value is called the reference value or setpoint.Figure 5.9 shows the process to be used for this discussion. Liquid is flowing into a tank at some rate Qin and out of the tank at some rate Qout. The liquid in the tank has some height or level h. It is known that the flow rate out varies as the square root of the height, so the higher the level the faster the liquid flows out. If the output flow rate is not exactly equal to the input flow rate, the tank will either empty, if Qin > Qout, or overflow, if Qout < Qin.This process has a property called self-regulation. This means that for some input flow rate, the liquid height will rise until it reaches a height for which the output flow rate matches the input flow rate. A self-regulating system does nit provide regulation of a variable to any particular reference value. In this example the liquid level will adopt some value foe which input and output flow rates are the same and there it will stay. If the input flow rate changed, then the level would change also, so it is not regulated to a reference value.Suppose we want to maintain the level at some particular value H in Figure 5.9, regardless of the input flow rate, then something more than self-regulation is needed.Human-Aided ControlHuman-aided control shows a modification of the tank system to allow artificial regulation of the level by a human. To regulate the level so that in maintains the value H it will be necessary to employ a sensor to measure the level. This has been provided via a sight tube. The actual liquid level or height is called the controlled variable. In addition, a value has been added so the output flow rate can be changed by the human. The output flow rate is called the manipulated variable or controlling variable.Now the height can be regulated apart from the input flow rate using the following strategy: The person measures the height in the sight tube and compares the value to the setpoint. If the measured value is larger, the human opens the value a little to let the flow out increase, and thus the level lowers toward the setpoint. If the measured value is smaller than the setpoint, the person closes the value a little to decrease the flow out and allow the level to rise toward the setpoint.By a succession of incremental opening and closing of the value, the human can bring the level to the setpoint value H and maintain it there by continuous monitoring of the sight tube and adjustment of the value.Automatic ControlTo provide automatic control, the system is modified using machines, electronics, or computers to replace the operations of the human. An instrument called a sensor is added that is able to measure the value of the level and convert it into a proportional signal. The signal is provided as input to a machine, an electronic circuit, or a computer, called the controller. This performs the function of the human in evaluating the measurement and providing an output signal to change the value setting via an actuator connected to the valve by a mechanical linkage.2 Identification of ElementsThe elements of a process-control system are defined in terms of separate functional parts of the system.ProcessIn general, a process can consist of a complex assembly of phenomena that relate to some manufacturing sequence. Many variables may be involved in such a process, and it may be desirable to control all these variables at the same time. There are single-variable process, in which only one variable is to be controlled, as well as multivariable processes, in which many variables, perhaps interrelated, may require regulation.MeasurementClearly, to effect control of a variable in a process, we must have information on the variable itself. Such information is found by measuring the variable. In general, a measurement refers to the conversion of the variable into some corresponding analog of the variable, such as a pneumatic pressure, an electrical voltage, or a current. A sensor is a device that performs the initial measurement and energy conversion of a variable into analogous electrical or pneumatic information. Further transformation or signal conditioning may be required to complete the measurement function. The result of the measurement is a representation of the value in some forms required by the other elements in the process-control operation.ControllerThe next step in the process-control sequence is to examine the error and determine what action, if any, should be taken. This part of the control system has many names; however, controller is the most common. The evaluation may be performed by an operator, by electronic signal processing, by pneumatic signal processing, or by a computer. The controller requires an input of both a measured indication of the controlled variable and a representation of the reference value of the variable, expressed in the same terms as the measured value.Control ElementThe final element in the process-control operation is the device that exerts a direct influence on the process; that is, it provides those required changes in the controlled variable to bring it to the setpoint. This element accepts an input from the controller, which is then transformed into some proportional operation performed on the process.3 Process-Control Block DiagramTo provide a practical, working description of process control, it is useful to describe the elements and operations involved in more generic terms. Such a description should be independent of a particular application and thus be applicable to all control situations. A model may be constructed using blocks to represent each distinctive element. The characteristics of control operation then may be developed from a consideration of the properties and interfacing of these elements. Figure 5.10 shows a general block diagram. The controlled variable in the process is denoted by e in this diagram, and the measured representation of the controlled variable is labeled b. The controlled variable setpoint is labeled r, for reference.The error detector is a subtracting-summing point that outputs an error signal e=r-b to the controller for comparison and action.The purpose of a block diagram approach is to allow the process-control system to be analyzed as the interaction of smaller and simpler subsystems. If the characteristics of each element of the system can be determined, then the characteristics of the assembled system can be established by an analytical marriage of these subsystems. The historical development of the system approach in technology is dictated by this practical aspect: first, to specify the characteristics desired of a total system and, then, to delegate the development of subsystems thatprovide the overall criteria..4 Control System EvaluationA process-control systems is used to regulate the value of some process variable. When such a system is in use, it is natural to ask, “How well is it working?” This is not an easy question to answer, because it is possible to adjust a control system to provide different kinds of response to errors. This section discusses some methods for evaluating how well the system is working.The variable used to measure the performance of the control system is the error, which is the difference between the constant setpoint or reference value r and the controlled variable c(t).Since the value of the controlled variable may vary in time, so may the error.In principle, the objective of a control system is to make the error exactly zero, but the control system responds only to errors. Conversely, if the error were zero and stayed zero, the control system would be doing nothing and would not be needed in the first place. Therefore, this objective can never be perfectly achieved, and there will always be some errors. The question of evaluation becomes one of how large the error is and how it varies in time.The purpose of the control system is to regulate the value of some variables. This requires that action be taken on the purpose itself in response to a measurement of the variable. If this is not done correctly, the control system can cause the process to become unstable. In fact, the more tightly we try to control the variable, the greater the possibility of an instability.The first objective, then, simply means that the control system must be designed and adjusted so the system is stable. Typically, as the control system is adjusted to give better control, the likelihood of instability also increases.。
