UNDERSTANDING DYNAMIC PROCESS BEHAVIOR FOR
Control StationInnovative Solutions from the Process Control ProfessionalsPractical Process Controlusing Loop-Pro SoftwareDouglas J. CooperPractical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
Practical Process Control Using Loop Pro Copyright 2005 by Control Station, Inc.All rights reserved. No portion of this book may be reproduced in any formor by any means except with explicit, prior, written permission of the author.Doug Cooper, professor of chemical engineering at the University of Connecticut, has been teachingand directing research in process control since 1985. Doug's research focuses on the development ofadvanced control strategies that are reliable, and perhaps most important, easy for practitioners touse. He strives to teach process control from a practical perspective. Thus, the focus of this book is onproven control methods and practices that practitioners and new graduates can use on the job.AuthorProf. Douglas J. CooperChemical Engineering Dept.University of Connecticut, Unit 3222Storrs, CT 06269-3222Email: cooper@engr.uconn.eduPublisherControl Station, Inc.One Technology DriveTolland, CT 06084Email: cooper@controlstation.comWeb: www.controlstation.comPractical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
Table Of ContentsPagePractical Control81. Fundamental Principles of Process Control1.1 Motivation for Automatic Process Control1.2 Terminology of Control1.3 Components of a Control Loop1.4 The Focus of This Book1.5 Exercises88101112132. Case Studies for Hands-On and Real-World Experience2.1 Learning With a Training Simulator2.2 Simulating Noise and Valve Dynamics2.3 Gravity Drained Tanks2.4 Heat Exchanger2.5 Pumped Tank2.6 Jacketed Reactor2.7 Cascade Jacketed Reactor2.8 Furnace Air/Fuel Ratio2.9 Multi-Tank Process2.10 Multivariable Distillation Column2.11 Exercises1515151516171819192122233. Modeling Process Dynamics - A Graphical Analysis of Step Test Data3.1 Dynamic Process Modeling for Control Tuning3.2 Generating Step Test Data for Dynamic Process Modeling3.3 Process Gain, KP, From Step Test Data3.4 Overall Time Constant, τP , From Step Test Data3.5 Apparent Dead Time, θP , From Step Test Data3.6 FOPDT Limitations - Nonlinear and Time Varying Behaviors3.7 Exercises24242626283032354. Process Control Preliminaries4.1 Redefining “Process” for Controller Design4.2 On/Off Control – The Simplest Control Algorithm4.3 Intermediate Value Control and the PID Algorithm373738395. P-Only Control - The Simplest PID Controller5.1 The P-Only Controller5.2 The Design Level of Operation5.3 Understanding Controller Bias, ubias5.4 Controller Gain, KC , From Correlations5.5 Reverse Acting, Direct Acting and Control Action5.6 Set Point Tracking in Gravity Drained Tanks Using P-Only Control5.7 Offset - The Big Disadvantage of P-Only Control5.8 Disturbance Rejection in Heat Exchanger Using P-Only Control5.9 Proportional Band41414242434444454648Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
5.10 Bumpless Transfer to Automatic5.11 Exercises48486. Automated Controller Design Using Design Tools6.1 Defining Good Process Test Data6.2 Limitations of the Step Test6.3 Pulse, Doublet and PRBS Test6.4 Noise Band and Signal to Noise Ratio6.5 Automated Controller Design Using Design Tools6.6 Controller Design Using Closed Loop Data6.7 Do Not Model Disturbance Driven Data!6.8 FOPDT Fit of Underdamped and Inverse Behaviors5151525254555960627. Advanced Modeling of Dynamic Process Behavior7.1 Dynamic Models Have an Important Role Beyond Controller Tuning7.2 Overdamped Process Model Forms7.3 The Response Shape of First and Second Order Models7.4 The Impact of KP, τP and θP on Model Behavior7.5 The Impact of Lead Element τL on Model Behavior6464656667708. Integral Action and PI Control8.1 Form of the PI Controller8.2 Function of the Proportional and Integral Terms8.3 Advantages and Disadvantages to PI Control8.4 Controller Bias From Bumpless Transfer8.5 Controller Tuning From Correlations8.6 Set Point Tracking in Gravity Drained Tanks Using PI Control8.7 Disturbance Rejection in Heat Exchanger Using PI Control8.8 Interaction of PI Tuning Parameters8.9 Reset Time Versus Reset Rate8.10 Continuous (Position) Versus Discrete (Velocity) Form8.11 Reset Windup7272727475757679808181829. Evaluating Controller Performance9.1 Defining “Good” Controller Performance9.2 Popular Performance Criteria83838310. Derivative Action, Derivative Filtering and PID Control10.1 Ideal and Non-interacting Forms of the PID Controller10.2 Function of the Derivative Term10.3 Derivative on Measurement is Used in Practice10.4 Understanding Derivative Action10.5 Advantages and Disadvantages of PID Control10.6 Three Mode PID Tuning From Correlations10.7 Converting From Interacting PID to Ideal PID10.8 Exploring Set Point Tracking Using PID Control10.9 Derivative Action Dampens Oscillations10.10 Measurement Noise Hurts Derivative Action10.11 PID With Derivative Filter Reduces the Impact of Noise10.12 Four Mode PID Tuning From Correlations10.13 Converting From Interacting PID with Filter to Ideal PID with Filter8686878788898990919293949596Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
10.14 Exploring Set Point Tracking Using PID with Derivative Filter ControlPractical Theory969911. First Principles Modeling of Process Dynamics11.1 Empirical and Theoretical Dynamic Models11.2 Conserved Variables and Conservation Equations11.3 Mass Balance on a Draining Tank11.4 Mass Balance on Two Draining Tanks11.5 Energy Balance on a Stirred Tank with Heater11.6 Species (Component) Balance on a Stirred Tank with Reaction11.7 Exercises99999910010310410610812. Linearization of Nonlinear Equations and Deviation Variables12.1 The Linear Approximation12.2 Linearization for Functions of One Variable12.3 Linearization for Functions of Two Variables12.4 Defining Deviation Variables12.5 Deviation Variables Simplify the Equation Form12.6 Exercises11011011111211311411613. Time Domain ODEs and System Behavior13.1 Linear ODEs13.2 Solving First Order ODEs13.3 Deriving "τp 63.2% of Process Step Response" Rule13.4 Solving Second Order ODEs13.5 The Second Order Underdamped Form13.6 Roots of the Characteristic Equation Indicate System Behavior13.7 Exercises11711711711912112612713014. Laplace Transforms14.1 Laplace Transform Basics14.2 Laplace Transform Properties14.3 Moving Time Domain ODEs into the Laplace Domain14.4 Moving Laplace Domain ODEs into the Time Domain14.5 Exercises13313313513814114315. Transfer Functions15.1 Process Transfer Functions15.2 Controller Transfer Functions15.3 Poles of a Transfer Function and Root Locus15.4 Poles as Complex Conjugates15.5 Poles of the Transfer Function Indicate System Behavior15.6 Exercises14414414614815015115316. Block Diagrams16.1 Combining Transfer Functions Using Block Diagrams16.2 The Closed Loop Block Diagram16.3 Closed Loop Block Diagram Analysis16.4 Simplified Block Diagram155155158159161Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
16.5 The Padé Approximation16.6 Closed Loop Analysis Using Root Locus16.7 Exercises17. Deriving PID Controller Tuning Correlations17.1 The Direct Synthesis Design Equation17.2 Deriving Controller Tuning Correlations Using Direct Synthesis17.3 Internal Model Control (IMC) Structure17.4 IMC Closed Loop Transfer Functions17.5 Deriving Controller Tuning Correlations Using the IMC Method17.6 ExercisesCombining Theory and Practice16116216616816817017317417517818018. Cascade Control18.1 Architectures for Improved Disturbance Rejection18.2 The Cascade Architecture18.3 An Illustrative Example18.4 Tuning a Cascade Implementation18.5 Exploring the Jacketed Reactor Process18.6 Single Loop Disturbance Rejection in the Jacketed Reactor18.7 Cascade Disturbance Rejection in the Jacketed Reactor18.8 Set Point Tracking Comparison of Single Loop and Cascade Control18.9 Exercises18018018018118418418518719219319. Feed Forward Control19.1 Another Architecture for Improved Disturbance Rejection19.2 The Feed Forward Architecture19.3 An Illustrative Example19.4 Feed Forward Control Design19.5 Feed Forward Control Theory19.6 Limits on the Form of the Feed Forward Model19.7 Feed Forward Disturbance Rejection in the Jacketed Reactor19.8 Static Feed Forward Control19.9 Set Point Tracking Comparison of Single Loop and Feed Forward Control19419419419619819820020220620720. Multivariable Controller Interaction and Loop Decoupling20.1 Multivariable Process Control20.2 Control Loop Interaction20.3 Decouplers are Feed Forward Controllers20.4 Distillation Study - Interacting Control Loops20.5 Distillation Study - Decoupling the Loops20920921021121421821. Modeling, Analysis and Control of Multivariable Processes21.1 Generalizing 2x2 Multivariable Processes21.2 Relative Gain as a Measure of Loop Interaction21.3 Effect of KP on Control Loop Interaction21.4 Effect of τP on Control Loop Interaction21.5 Effect of θP on Control Loop Interaction21.6 Decoupling Cross-Loop KP Effects223223224224228230232Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
21.7 Decoupling Cross-Loop τP Effects21.8 Decoupling Cross-Loop θP Effects23523622. Model Based Smith Predictor For Processes with Large Dead Time22.1 A Large Dead Time Impacts Controller Performance22.2 Predictive Models as Part of the Controller Architecture22.3 The Smith Predictor Control Algorithm22.4 Exploring the Smith Predictor Controller23823823923924123. DMC - Single Loop Dynamic Matrix Control23.1 Model Predictive Control23.2 Dynamic Matrix Control23.3 The DMC Process Model23.4 Tuning DMC23.5 Example Implementation23.6 Chapter Nomenclature23.7 Tuning Strategy for Single Loop DMC248248248251252253260262Appendix A: Derivation of IMC Tuning CorrelationsA.1 Self Regulating ProcessesA.1.a Ideal PID ControlA.1.b Interacting PID ControlA.1.c Ideal PID with Filter ControlA.1.d Interacting PID with Filter ControlA.2 Non-Self Regulating ProcessesA.2.a Ideal PID ControlA.2.b Interacting PID ControlA.2.c Ideal PID with Filter ControlA.2.d Interacting PID with Filter Control263263263265267269272272274276278Appendix B: Table of Laplace Transforms282Appendix C: DMC Controller Tuning GuidesC.1 DMC Tuning Guide for Self Regulating (Stable) ProcessesC.2 DMC Tuning Guide for Integrating (Non-Self Regulating) Processes283283284Appendix D: PID Controller Tuning GuidesD.1 PID Tuning Guide for Self Regulating (Stable) ProcessesD.2 PID Tuning Guide for Integrating (Non-Self Regulating) Processes285285286Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
Practical Control1. Fundamental Principles of Process Control1.1 Motivation for Automatic Process ControlSafety FirstAutomatic control systems enable a process to be operated in a safe and profitable manner. Theyachieve this by continually measuring process operating parameters such as temperatures, pressures,levels, flows and concentrations, and then making decisions to, for example, open valves, slow downpumps and turn up heaters so that selected process measurements are maintained at desired values.The overriding motivation for modern control systems is safety, which encompasses thesafety of people, the environment and equipment. The safety of plant personal and people in thecommunity is the highest priority in any plant operation. The design of a process and associatedcontrol system must always make human safety the prime objective.The tradeoff between safety of the environment and safety of equipment is considered on acase by case basis. At the extremes, a nuclear power plant will be operated to permit as much as theentire plant to be ruined rather than allowing significant radiation to be leaked to the environment. Onthe other hand, a fossil fuel power plant may be operated to permit an occasional cloud of smoke tobe released to the environment rather than permitting damage to a multimillion dollar process unit.Whatever the priorities for a particular plant, safety of both the environment and the equipment mustbe specifically addressed when defining control objectives.The Profit MotiveWhen people, the environment and plant equipment are properly protected, control objectives canfocus on the profit motive. Automatic control systems offer strong benefits in this regard. Plant-widecontrol objectives motivated by profit include meeting final product specifications, minimizing wasteproduction, minimizing environmental impact, minimizing energy use and maximizing overallproduction rate.Process: Gravity Drained TankController: Manual Modeoperating constraintMore ProfitableMore ProfitableOperationOperation704.4604.24.050poor control meanslarge variability, sothe process must beoperated in a lessprofitable region3.8403.630process variable6080100Time (mins)120140Figure 1.1 - Process variability from poor control means lost profits8Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
Product specifications set by the marketplace (your customers) are an essential priority ifdeviating from these specifications lessens a product's market value. Example product specificationsrange from maximum or minimum values for density, viscosity or component concentration, tospecifications on thickness or even color.A common control challenge is to operate close to the minimum or maximum of a productspecification, such as a minimum thickness or a maximum impurities concentration. It takes more rawmaterial to make a product thicker than the minimum specification. Consequently, the closer anoperation can come to the minimum permitted thickness constraint without going under, the greaterthe profit. It takes more processing effort to remove impurities, so the closer an operation can come tothe maximum permitted impurities constraint without going over, the greater the profit.All of these plant-wide objectives ultimately translate into operating the individual processunits within the plant as close as possible to predetermined values of temperature, pressure, level,flow, concentration or other of the host of possible measured process variables. As shown in Fig. 1.1,a poorly controlled process can exhibit large variability in a process measurement over time. Toensure a constraint limit is not exceeded, the baseline (set point) operation of the process must be setfar from the constraint, thus sacrificing profit.Process: Gravity Drained TankController: Manual Modeoperating constraintMore ProfitableMore ProfitableOperationOperation4.270604.0tight control permitsoperation near theconstraint, whichmeans more profit503.8process variable403.6303.480100120Time (mins)140160Figure 1.2 - Well controlled process has less variability in process measurementsFigure 1.2 shows that a well controlled process will have much less variability in themeasured process variable. The result is improved profitability because the process can be operatedcloser to the operating constraint.Automatic Process ControlBecause implementation of plant-wide objectives translates into controlling a host of individualprocess parameters within the plant, the remainder for this text focuses on proven methods for theautomatic control of individual process variables. Examples used to illustrate concepts are drawnfrom the Loop Pro software package.The Case Studies module presents industrially relevant process control challenges includinglevel control in a tank, temperature control of a heat exchanger, purity control of a distillation columnand concentration control of a jacketed reactor. These real-world challenges will provide hands-onexperience as you explore and learn the concepts of process dynamics and automatic process controlpresented in the remainder of this book.9Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
1.2 Terminology of ControlThe first step in learning automatic process control is to learn the jargon. We introduce some basicjargon here by discussing a control system for heating a home as illustrated in Fig. 1.3. This is arather simple automatic control example because a home furnace can only be either on or off.As we will explore later, the challenges of control system design increase greatly whenprocess variable adjustments can assume a complete range of values between full on and full off. Inany event, a home heating system is easily understood and thus provides a convenient platform forintroducing the relevant terminology.The control objective for the process illustrated in Fig. 1.3 is to keep the measured processvariable (house temperature) at the set point value (the desired temperature set on the thermostat bythe home owner) in spite of unmeasured disturbances (heat loss from doors and windows opening;heat being transmitted through the walls of the house).To achieve this control objective, the measured process variable is compared to thethermostat set point. The difference between the two is the controller error, which is used in acomputation by the controller to compute a controller output adjustment (an electrical or pneumaticsignal).thermostatcontrollerset lfuel flowvalveheat loss(disturbance)furnaceFigure 1.3 - Home heating control systemThe change in the controller output signal causes a response in the final control element (fuelflow valve), which subsequently causes a change in the manipulated process variable (flow of fuel tothe furnace). If the manipulated process variable is moved in the right direction and by the rightamount, the measured process variable will be maintained at set point, thus satisfying the controlobjective. This example, like all in process control, involves a measurement, computation and action:MeasurementComputationActionhouse temperature, THouseis it colder than set point ( TSetpoint THouse 0 )?open fuel valveis it hotter than set point ( TSetpoint THouse 0 )?close fuel valveNote that computing the necessary controller action is based on controller error, or the differencebetween the set point and the measured process variable.10Practical Process Control by Douglas J. CooperCopyright 2005 by Control Station, Inc.All Rights Reserved
1.3 Components of a Control LoopThe home heating control system of Fig. 1.3 can be organized in the form of a traditional feedbackcontrol loop block diagram as shown in Fig. 1.4. Such block diagrams provide a general organizationapplicable to most all feedback control systems and permit the development of more advancedanalysis and design methods.controllererrorSet Point -controlleroutputsignalmanipulatedfuel flow tofurnaceThermostatFuel ValvehousetemperatureHome HeatingProcessHeat LossDisturbancehouse smitterFigure 1.4 - Home heating control loop block diagramFollowing the diagram of Fig. 1.4, a sensor measures the measured process variable andtransmits, or feeds back, the signal to the controller. This measurement feedback signal is subtractedfrom the set point to obtain the controller error. The error is used by the controller to compute acontroller output signal. The signal causes a change in the mechanical final control element, which inturn causes a change in the manipulated process variable. An appropriate change in the manipulatedvariable works to keep the measured process variable at set point regardless of unplanned changes inthe disturbance variables.The home heating control system of Fig. 1.4 can be further generalized into a block diagrampertinent to all control loops as shown in Fig. 1.5. Both these figures depict a closed loop systembased on negative feedback, because the controller works
17. Deriving PID Controller Tuning Correlations 168 17.1 The Direct Synthesis Design Equation 168 17.2 Deriving Controller Tuning Correlations Using Direct Synthesis 170 17.3 Internal Model Control (IMC) Structure 173 17.4 IMC Closed Loop Transfer Functions 174 17.5 Deriving Controller
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