PRACTICE OF A CARL& A. SMIT. B. Co

Transcription

1 PRACTICE OF A CARL& A. SMIT B. Co

2 SELECTED TABLES AND FIGURES TYPICAL RESPONSES Common input signals 13 Stable and unstable responses 34 First-order step response 42 First-order ramp response 44 First-order sinusoidal response 45 Lead-lag step response Lead-lag ramp response 48 Second-order step response TRANSFORMS transforms 15 z-transforms and modified z-transforms 607 TUNING FORMULAS On-line quarter decay ratio 306 Open-loop quarter decay ratio 320 Minimum error integral for disturbance 324 Minimum error integral for set point 325 Controller synthesis (IMC) rules 345 Computer PID control algorithms 666 Dead time compensation algorithms 675 INSTRUMENTATION ISA standard instrumentation symbols and labels Control valve inherent characteristics Control valve installed characteristics Flow sensors and their characteristics Temperature sensors and their characteristics Classification of filled-system thermometers Thermocouple voltage versus temperature Valve capacity (Cv) coefficients BLOCK DIAGRAMS Rules 98 Feedback loop 254 Unity feedback loop 257 Temperature control loop 261 Flow control loop 268 Pressure control loop 281 Level control loop 333 Multivariable (2 X 2) control loop 565 Decoupled multivariable (2 X 2) system 566 Sampled data control loop 630 Smith predictor 679 Internal Model Control (IMC) 680 Dynamic Matrix Control (DMC) 689

3 Principles and Practice of Automatic Process Control Second Edition Carlos A. Smith, Ph.D., P.E. University of South Florida Armando B. Corripio, Ph.D., P.E. Louisiana State University John Wiley Sons, Inc. New York Chichester Weinheim Brisbane Singapore Toronto

4 This work is dedicated with all our love to The for all his daily blessings made this book possible our God, The Smiths: Cristina, A. Jr., Tim, Cristina M., and Sophia C. Livingston, and Mrs. Rene M. Smith, my four grandsons: Nicholas, Robert, Garrett and David and to our dearest homeland, Cuba

5 Preface This edition is a major revision and expansion to the first edition. Several new subjects have been added, notably the z-transform analysis and discrete controllers, and several other subjects have been reorganized and expanded. The objective of the book, however, remains the same as in the first edition, to present the practice of automatic process control along with the fundamental principles of control theory. A significant number of applications resulting from our practice as part-time consultants have also been added to this edition. Twelve years have passed since the first edition was published, and even though the principles are still very much the same, the tools to implement the controls strategies have certainly advanced. The use of computer-based instrumentation and control systems is the norm. Chapters 1 and 2 present the definitions of terms and mathematical tools used in process control. In this edition Chapter 2 stresses the determination of the quantitative characteristics of the dynamic response, settling time, frequency of oscillation, and damping ratio, and de-emphasizes the exact determination of the analytical response. In this way the students can analyze the response of a dynamic system without having to carry out the time-consuming evaluation of the coefficients in the partial fraction expansion. Typical responses of first-, second-, and higher-order systems are now presented in Chapter 2. The derivation of process dynamic models from basic principles is the subject of Chapters 3 and 4. As compared to the first edition, the discussion of process modelling has been expanded. The discussion, meaning, and significance of process nonlinearities has been expanded as well. Several numerical examples are presented to aid in the understanding of this important process characteristic. Chapter 4 concludes with a presentation of integrating, inverse-response, and open-loop unstable processes. Chapter 5 presents the design and characteristics of the basic components of a control system: sensors and transmitters, control valves, and feedback controllers. The presentation of control valves and feedback controllers has been expanded. Chapter 5 should be studied together with Appendix C where practical operating principles of some common sensors, transmitters, and control valves are presented. The design and tuning of feedback controllers are the subjects of Chapters 6 and 7. Chapter 6 presents the analysis of the stability of feedback control loops. In this edition we stress the direct substitution method for determining both the ultimate gain and period of the loop. Routh s test is deemphasized, but still presented in a separate section. In keeping with the spirit of Chapter 2, the examples and problems deal with the determination of the characteristics of the response of the closed loop, not with the exact analytical response of the loop. Chapter 7 keeps the same tried-and-true tuning methods from the first edition. A new section on tuning controllers for integrating processes, and a discussion of the Internal Model Control (IMC) tuning rules, have been added. Chapter 8 presents the root locus technique, and Chapter 9 presents the frequency response techniques. These techniques are principally used to study the stability of control systems. V

6 vi Preface The additional control techniques that supplement and enhance feedback control have been distributed among Chapters 10 through 13 to facilitate the selection of their coverage in university courses. Cascade control is presented first, in Chapter 10, because it is so commonly a part of the other schemes. Several examples are presented to help understanding of this important and common control technique. Chapter 11 presents different computing algorithms sometimes used to implement control schemes. A method to scale these algorithms, when necessary, is presented. The chapter also presents the techniques of override, or constraint, control, and selective control. Examples are used to explain the meaning and justification of them. Chapter 12 presents and discusses in detail the techniques of ratio and feedforward control. Industrial examples are also presented. A significant number of new problems have been added. Multivariable control and loop interaction are the subjects of Chapter 13. The calculation and interpretation of the relative gain matrix (RGM) and the design of couplers, are kept from the first edition. Several examples have been added, and the material has been reorganized to keep all the dynamic topics in one section. Finally Chapters 14 and 15 present the tools for the design and analysis of data (computer) control systems. Chapter 14 presents the z-transform and its use to analyze sampled-data control systems, while Chapter 15 presents the design of basic algorithms for computer control and the tuning of sampled-data feedback controllers. The chapter includes sections on the design and tuning of dead-time compensation algorithms and model-reference control algorithms. Two examples of Dynamic Matrix Control (DMC) are also included. As in the first edition, Appendix A presents some symbols, labels, and other notations commonly used in instrumentation and control diagrams. We have adopted throughout the book the ISA symbols for conceptual diagrams which eliminate the need to differentiate between pneumatic, electronic, or computer implementation of the various control schemes. In keeping with this spirit, we express all instrument signals in percent of range rather than in or psig. Appendix B presents several processes to provide the student/reader an opportunity to design control systems from scratch. During this edition we have been very fortunate to have received the help and encouragement of several wonderful individuals. The encouragement of our students, especially Daniel Palomares, Denise Farmer, Carl Thomas, Gene Daniel, Samuel bles, Dan Logue, and Steve Hunter, will never be forgotten. Thanks are also due to Dr. Russell Rhinehart of Texas Tech University who read several chapters when they were in the initial stages. His comments were very helpful and resulted in a better book. Professors Ray Wagonner, of Missouri and G. David Shilling, of Rhode Island, gave us invaluable suggestions on how to improve the first edition. To both of them we are grateful. We are also grateful to Michael R. Benning of Exxon Chemical Americas who volunteered to review the manuscript and offered many useful suggestions from his industrial background. In the preface to the first edition we said that To serve as agents in the training and development of young minds is certainly a most rewarding profession. This is still our conviction and we feel blessed to be able to do so. It is with this desire that we have written this edition. Tampa, Florida, 1997 Baton Rouge, Louisiana, 1997

7 Contents Chapter 1 Introduction l-l A Process Control System 1 Important Terms and the Objective of Automatic Process Control Regulatory and Servo Control 4 Transmission Signals, Control Systems, and Other Terms 5 Control Strategies Feedback Control Feedforward Control 7 Background Needed for Process Control 9 Summary 9 Problems Chapter 2 Mathematical Tools for Control Systems Analysis 2-1 The Transform Definition of Transform Properties of the Transform Solution of Differential Equations Using the Transform Transform Solution Procedure Inversion by Partial Fractions Expansion Handling Time Delays Characterization of Process Response Deviation Variables Output Response Stability Response of First-Order Systems Step Response Ramp Response Sinusoidal Response Response with Time Delay Response of a Lead-Lag Unit Response of Second-Order Systems Overdamped Responses Underdamped Responses Higher-Order Responses Linearization Linearization of Functions of One Variable Linearization of Functions of Two or More Variables Linearization of Differential Equations Review of Complex-Number Algebra Complex Numbers Operations with Complex Numbers vii

8 viii Contents 2-8 Summary 74 Problems 74 Chapter 3 First-Order Dynamic Systems Processes and the Importance of Process Characteristics Thermal Process Example 82 Dead Time 92 Transfer Functions and Block Diagrams Transfer Functions Block Diagrams 96 Gas Process Example 104 Chemical Reactors Introductory Remarks Chemical Reactor Example 111 Effects of Process Nonlinearities 114 Additional Comments 117 Summary 119 Problems Chapter 4 Higher-Order Dynamic Systems 4-1 Noninteracting Systems Noninteracting Level Process Thermal Tanks in Series Interacting Systems Interacting Level Process Thermal Tanks with Recycle Nonisothermal Chemical Reactor Response of Higher-Order Systems Other Types of Process Responses Integrating Processes: Level Process Open-Loop Unstable Process: Chemical Reactor Inverse Response Processes: Chemical Reactor Summary Overview of Chapters 3 and Problems 183 Chapter 5 Basic Components of Control Systems 5-1 Sensors and Transmitters Control Valves The Control Valve Actuator Control Valve Capacity and Sizing Control Valve Characteristics Control Valve Gain and Transfer Function Control Valve Summary Feedback Controllers Actions of Controllers

9 Types of Feedback Controllers Modifications to the PID Controller and Additional Comments Reset Windup and Its Prevention Feedback Controller Summary 244 Summary 244 Problems 245 Contents ix 238 Chapter 6 Design of Single-Loop Feedback Control Systems The Feedback Control Loop Closed-Loop Transfer Function Characteristic Equation of the Loop Steady-State Closed-Loop Gains Stability of the Control Loop Criterion of Stability Direct Substitution Method Effect of Loop Parameters on the Ultimate Gain and Period Effect of Dead Time Routh s Test Summary 290 Problems 290 Chapter 7 Tuning of Feedback Controllers Quarter Decay Ratio Response by Ultimate Gain 304 Open-Loop Process Characterization Process Step Testing Tuning for Quarter Decay Ratio Response Tuning for Minimum Error Integral Criteria Tuning Sampled-Data Controllers Summary of Controller Tuning 330 Tuning Controllers for Integrating Processes Model of Liquid Level Control System Proportional Level Controller Averaging Level Control Summary 337 Synthesis of Feedback Controllers Development of the Controller Synthesis Formula Specification of the Closed-Loop Response Controller Modes and Tuning Parameters Summary of Controller Synthesis Results Tuning Rules by Internal Model Control (IMC) 350 Tips for Feedback Controller Tuning Estimating the Integral and Derivative Times Adjusting the Proportional Gain 354 Summary 354 Problems 355

10 x Contents Chapter 8 Root Locus Some Definitions 368 Analysis of Feedback Control Systems by Root Locus Rules for Plotting Root Locus Diagrams 375 Summary 385 Problems Chapter 9 Frequency Response Techniques 9-1 Frequency Response Experimental Determination of Frequency Response Bode Plots Frequency Response Stability Criterion Polar Plots Nichols Plots Pulse Testing Performing the Pulse Test Derivation of the Working Equation Numerical Evaluation of the Fourier Transform Integral Summary 434 Problems 434 Chapter 10 Cascade Control 10-1 A Process Example Stability Considerations Implementation and Tuning of Controllers Two-Level Cascade Systems Three-Level Cascade Systems Other Process Examples Further Comments 452 Summary 453 Problems 454 Chapter 11 Override and Selective Control 11-1 Computing Algorithms Scaling Computing Algorithms l-l.2 Physical Significance of Signals Override, or Constraint, Control Selective Control Summary 479 Problems 479 Chapter 12 Ratio and Feedforward Control 12-1 Ratio Control Feedforward Control

11 The Feedforward Concept Block Diagram Design of Linear Feedforward Controllers Lead/Lag Term Back to the Previous Example Design of Nonlinear Feedforward Controllers from Basic Process Principles Some Closing Comments and Outline of Feedforward Controller Design Three Other Examples Summary 526 Problems 527 Chapter 13 Multivariable Process Control Loop Interaction Pairing Controlled and Manipulated Variables Calculating the Relative Gains for a 2 X 2 System Calculating the Relative Gains for an X System Decoupling of Interacting Loops Decoupler Design from Block Diagrams Decoupler Design for X Systems Decoupler Design from Basic Principles Multivariable Control vs. Optimization Dynamic Analysis of Multivariable Systems Signal Flow Graphs (SFG) Dynamic Analysis of a 2 X 2 System Controller Tuning for Interacting Systems Summary 592 Problems 592 Contents xi Chapter 14 Mathematical Tools for Computer Control Systems Computer Process Control 600 The z-transform Definition of the z-transform Relationship to the Transform Properties of the Calculation of the Inverse z-transform 613 Pulse Transfer Functions Development of the Pulse Transfer Function Steady-State Gain of a Pulse Transfer Function Pulse Transfer Functions of Continuous Systems Transfer Functions of Discrete Blocks Simulation of Continuous Systems with Discrete Blocks 627 Sampled-Data Feedback Control Systems Closed-Loop Transfer Function Stability of Sampled-Data Control Systems 632 Modified z-transform Definition and Properties of the Modified z-transform 639

12 xii 14-6 Contents Inverse of the Modified z-transform Transfer Functions for Systems with Transportation Lag Summary 645 Problems Chapter 15 Design of Computer Control Systems 15-1 Development of Control Algorithms Exponential Filter Lead-Lag Algorithm Feedback (PID) Control Algorithms Tuning of Feedback Control Algorithms Development of the Tuning Formulas Selection of the Sample Time Feedback Algorithms with Dead-Time Compensation The Dahlin Algorithm The Smith Predictor Algorithm Design by Internal Model Control Selection of the Adjustable Parameter Automatic Controller Tuning Model-Reference Control Summary 695 Problems 696 Appendix A Instrumentation Symbols and Labels Appendix B Case Studies 707 Case 1: Ammonium Nitrate Prilling Plant Control System 707 Case 2: Natural Gas Dehydration Control System 709 Case 3: Sodium Hypochlorite Bleach Preparation Control System 710 Case 4: Control Systems in the Sugar Refining Process 711 Case 5: CO, Removal from Synthesis Gas 712 Case 6: Sulfuric Acid Process 716 Case 7: Fatty Acid Process 717 Appendix C Sensors, Transmitters, and Control Valves C-l Pressure Sensors 721 c-2 Flow Sensors 723 c-3 Level Sensors 733 c - 4 Temperature Sensors 734 c-5 Composition Sensors 742 C-6 Transmitters 743 C-6.1 Pneumatic Transmitter 743 C-6.2 Electronic Transmitter 745 C-7 Types of Control Valves 745 C-7.1 Reciprocating Stem 745 C-7.2 Rotating Stem

13 Contents xiii c-9 Control Valve Actuators 750 Pneumatically Operated Diaphragm Actuators 750 C-8.2 Piston Actuators 750 C-8.3 Electrohydraulic and Electromechanical Actuators 751 C-8.4 Manual-Handwheel Actuators 751 Control Valve Accessories 752 C-9.1 Positioners 752 C-9.2 Boosters 753 C-9.3 Limit Switches 753 Control Valves-Additional Considerations 753 C Viscosity Corrections 753 C-lo.2 Flashing and Cavitation 756 Summary 760 Index 763

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15 Chapter 1 Introduction The purpose of this chapter is to present the need for automatic process control and to motivate you, the reader, to study it. Automatic process control is concerned with maintaining process variables, temperatures, pressures, flows, compositions, and the like at some desired operating value. As we shall see, processes are dynamic in nature. Changes are always occurring, and if appropriate actions are not taken in response, then the important process variables-those related to safety, product quality, and production rates-will not achieve design conditions. This chapter also introduces two control systems, takes a look at some of their components, and defines some terms used in the field of process control. Finally, the background needed for the study of process control is discussed. In writing this book, we have been constantly aware that to be successful, the engineer must be able to apply the principles learned. Consequently, the book covers the principles that underlie the successful practice of automatic process control. The book is full of actual cases drawn from our years of industrial experience as full-time practitioners or part-time consultants. We sincerely hope that you get excited about studying automatic process control. It is a very dynamic, challenging, and rewarding area of process engineering. l-l A PROCESS CONTROL SYSTEM To illustrate process control, let us consider a heat exchanger in which a process stream is heated by condensing steam; the process is sketched in Fig The purpose of this unit is to heat the process fluid from some inlet temperature up to a certain desired outlet temperature T(t). The energy gained by the process fluid is provided by the latent heat of condensation of the steam. In this process there are many variables that can change, causing the outlet temperature to deviate from its desired value. If this happens, then some action must be taken to correct the deviation. The objective is to maintain the outlet process temperature at its desired value. One way to accomplish this objective is by measuring the temperature T(t), comparing it to the desired value, and, on the basis of this comparison, deciding what to do to correct any deviation. The steam valve can be manipulated to correct the deviation. That is, if the temperature is above its desired value, then the steam valve can be 1

16 2 Chapter 1 Introduction Condensate return Figure Heat exchanger. throttled back to cut the steam flow (energy) to the heat exchanger. If the temperature is below the desired value, then the steam valve can be opened more to increase the steam flow to the exchanger. All of this can be done manually by the operator, and the procedure is fairly straightforward. However, there are several problems with such manual control. First, the job requires that the operator look at the temperature frequently to take corrective action whenever it deviates from the desired value. Second, different operators make different decisions about how to move the steam valve, and this results in a less than perfectly consistent operation. Third, because in most process plants there are hundreds of variables that must be maintained at some desired value, manual correction requires a large number of operators. As a result of these problems, we would like to accomplish this control automatically. That is, we would like to have systems that control the variables without requiring intervention from the operator. This is what is meant by automatic process control. To achieve automatic process control, a control system must be designed and implemented. A possible control system for our heat exchanger is shown in Fig Steam return Figure l-l.2 Heat exchanger control system.

17 1-2 Important Terms and the Objective of Automatic Process Control 3 pendix A presents the symbols and identifications for different devices.) The first thing to do is measure the outlet temperature of the process stream. This is done by a sensor (thermocouple, resistance temperature device, filled system thermometer, thermistor, or the like). Usually this sensor is physically connected to a transmitter, which takes the output from the sensor and converts it to a signal strong enough to be transmitted to a controller. The controller then receives the signal, which is related to the temperature, and compares it with the desired value. Depending on the result of this comparison, the controller decides what to do to maintain the temperature at the desired value. On the basis of this decision, the controller sends a signal to the final control element, which in turn manipulates the steam flow. This type of control strategy is known as feedback control. Thus the three basic components of all control systems are 1. Sensor/transmitter Also often called the primary and secondary elements. 2. Controller The brain of the control system. 3. Final control element Often a control valve but not always. Other common final control elements are variable-speed pumps, conveyors, and electric motors. These components perform the three basic operations that must be present in every control system. These operations are 1. Measurement(M) Measuring the variable to be controlled is usually done by the combination of sensor and transmitter. In some systems, the signal from the sensor can be fed directly to the controller, so there is no need for the transmitter. 2. Decision On the basis of the measurement, the controller decides what to do to maintain the variable at its desired value. 3. Action (A) As a result of the controller s decision, the system must then take an action. This is usually accomplished by the final control element. These three operations, M, D, and A, are always present in every type of control system, and it is imperative that they be in a loop. That is, on the basis of the measurement a decision is made, and on the basis of this decision an action is taken. The action taken must come back and affect the measurement; otherwise, it is a major in the design, and control will not be achieved. When the action taken does not affect the measurement, an open-loop condition exists and control will not be achieved. The decision making in some systems is rather simple, whereas in others it is more complex; we will look at many systems in this book. 1-2 IMPORTANT TERMS AND THE OBJECTIVE OF AUTOMATIC PROCESS CONTROL At this time it is necessary to define some terms used in the field of automatic process control. The controlled variable is the variable that must be maintained, or controlled, at some desired value. In our example of the heat exchanger, the process outlet temperature, T(t), is the controlled variable. Sometimes the term process variable is also used to refer to the controlled variable. The set point (SP) is the desired value of the controlled variable. Thus the job of a control system is to maintain the controlled variable at its set point. The manipulated variable is the variable used to maintain the controlled variable at its set point. In the example, the steam valve position is the

18 4 Chapter 1 Introduction manipulated variable. Finally, any variable that causes the controlled variable to deviate from the set point is known as a disturbance or upset. In most processes there are a number of different disturbances. In the heat exchanger shown in Fig , possible disturbances include the inlet process temperature, the process flow, the energy content of the steam, ambient conditions, process fluid composition, and fouling. It is important to understand that disturbances are always occurring in processes. Steady state is not the rule, and transient conditions are very common. It is because of these disturbances that automatic process control is needed. If there were no disturbances, then design operating conditions would prevail and there would be no need to monitor the process continuously. The following additional terms are also important. Manual control is the condition in which the controller is disconnected from the process. That is, the controller is not deciding how to maintain the controlled variable at set point. It is up to the operator to manipulate the signal to the final control element to maintain the controlled variable at set point. Closed-loop control is the condition in which the controller is connected to the process, comparing the set point to the controlled variable and determining and taking corrective action. Now that we have defined these terms, we can express the objective of an automatic process control system meaningfully: The objective of an automatic process control system is to adjust the manipulated variable to maintain the controlled variable at its set point in spite of disturbances. Control is important for many reasons. Those that follow are not the only ones, but we feel they are the most important. They are based on our industrial experience, and we would like to pass them on. Control is important to 1. Prevent injury to plant personnel, protect the environment by preventing emissions and minimizing waste, and prevent damage to the process equipment. SAFETY must always be in everyone s mind; it is the single most important consideration. 2. Maintain product quality (composition, purity, color, and the like) on a continuous basis and with minimum cost. 3. Maintain plant production rate at minimum cost. Thus process plants are automated to provide a safe environment and at the same maintain desired product quality, high plant throughput, and reduced demand on human labor. 1-3 REGULATORY AND SERVO CONTROL In some processes, the controlled variable deviates from set point because of disturbances. Systems designed to compensate for these disturbances exert regulatory control. In some other instances, the most important disturbance is the set point itself. That is, the set point may be changed as a function of time (typical of this is a batch reactor where the temperature must follow a desired profile), and therefore the controlled variable must follow the set point. Systems designed for this purpose exert servo control. Regulatory control is much more common than servo control in the process

19 1-4 Transmission Signals, Control Systems, and Other Terms tries. However, the same basic approach is used in designing both. Thus the principles in this book apply to both cases. 1-4 TRANSMISSION SIGNALS, CONTROL SYSTEMS, AND OTHER TERMS Three principal types of signals are used in the process industries. The pneumatic signal, or air pressure, normally ranges between 3 and 15 psig. The usual representation for pneumatic signals in process and instrumentation diagrams is The electrical signal normally ranges between 4 and 20 Less often, a range of to 50 1 to 5 V, or 0 to 10 V is used. The usual representation for this signal in is a series of dashed lines such as The third type of signal is the digital, or discrete, signal (zeros and ones). In this book we will show such signals as (see Fig. which is the representation proposed by the Instrument Society of America (ISA) when a control concept is shown without concern for specific hardware. The reader is encouraged to review Appendix A, where different symbols and labels are presented. Most times we will refer to signals as percentages instead of using psig or That is, 0%- 100% is equivalent to 3 to 15 psig or 4 to 20 It will help in understanding control systems to realize that signals are used by devices-transmitters, controllers, final control elements, and the like-to communicate. That is, signals are used to convey information. The signal from the transmitter to the controller is used by the transmitter to inform the controller of the value of the controlled variable. This signal is not the measurement in engineering units but rather is a psig, volt, or any other signal that is proportional to the measurement. The relationship to the measurement depends on the calibration of the sensor/transmitter. The controller uses its output signal to tell the final control element what to do: how much to open if it is a valve, how fast to run if it is a variable-speed pump, and so on. It is often necessary to change one type of signal into another. This is done by a transducer, or converter. For example, there may be a need to change from an electrical signal in milliamperes to a pneumatic signal in pounds per square inch, gauge (psig). This is done by the use of a current (I) to pneumatic (P) transducer (I/P); see Fig The input signal may be 4 to 20 and the output 3 to 15 psig. An to-digital converter (A to D) changes from a or a volt signal to a digital signal. There are many other types of transducers: digital-to-analog (D to A), current (P/I), voltage-to-pneumatic (E/P), pneumatic-to-voltage (P/E), and so on. The term analog refers to a controller, or any other instrument, that is either pneumatic or electrical. Most controllers, however, are computer-based, or digital. By computer-based we don t necessarily mean a main-frame computer but anything starting from a microprocessor. In fact, most controllers are microprocessor-based. Chapter 5 presents different types of controllers and defines some terms related to controllers and control systems. Figure I/P transducer.

20 6 Chapter 1 Introduction 1-5 CONTROL STRATEGIES Feedback Control The control scheme shown in Fig. l-l.2 is referred to as feedback control and is also called afeedback control loop. One must understand the working principles of feedback control to recognize its advantages and disadvantages; the heat exchanger control loop shown in Fig. l-l.2 is presented to foster this understanding. If the inlet process temperature increases, thus creating a disturbance, its effect must propagate through the heat exchanger before the outlet temperature increases. Once this temperature changes, the signal from the transmitter to the controller also changes. It is then that the controller becomes aware that a deviation from set point has occurred and that it must compensate for the disturbance by manipulating the steam valve. The controller signals the valve to close and thus to decrease the steam flow. Fig shows graphically the effect of the disturbance and the action of the controller. It is instructive to note that the outlet temperature first increases, because of the increase in inlet temperature, but it then decreases even below set point and continues to oscillate around set point until the temperature finally stabilizes. This oscillatory response is typical of feedback control and shows that it is essentially a trial-and-error operation. That is, when the controller notices that the outlet temperature has increased above the set point, it signals the valve to close, but the closure is more than required. Therefore, the outlet temperature decreases below the set point. Noticing Fraction of valve opening Figure Response of a heat exchanger to a disturbance: feedback control.

21 1-5 Control Strategies 7 the controller signals the valve to open again somewhat to bring the temperature back up. This trial-and-error operation continues until the temperature reaches and remains at set point. The advantage of feedback control is that it is a very simple technique that compensates for all disturbances. Any disturbance affects the controlled variable, and once this variable deviates from set point, the controller changes its output in such a way as to return the temperature to set point. The feedback control loop does not know, nor does it care, which disturbance enters the process. It tries only to maintain the controlled variable at set point and in so doing compensates for all disturbances. The feedback controller works with minimum knowledge of the process. In fact, the only information it needs is in which direction to move. How much to move is usually adjusted by trial and error. The disadvantage of feedback control is that it can compensate for a disturbance only after the controlled variable has deviated from set point. That is, the disturbance must propagate through the entire process before the feedback control scheme can initiate action to compensate for it. The job of the engineer is to design a control scheme that will maintain the controlled variable at its set point. Once this is done, the engineer must adjust, or tune, the controller so that it minimizes the amount of trial and error required. Most controllers have up to three terms (also known as parameters) used to tune them. To do a creditable job, the engineer must first know the characteristics of the process to be controlled. Once these characteristics are known, the control system can be designed and the controller tuned. Process characteristics are explained in Chapters 3 and 4, Chapter 5 presents the meaning of the three terms in the controllers, and Chapter 7 explains how to tune them Feedforward Control Feedback control is most common control strategy in the process industries. Its simplicity accounts for its popularity. In some processes, however, feedback control may not provide the required control performance. For these processes, other types of control strategies may have to be designed. Chapters 10, 11, 12, 13, and 15 present additional control strategies that have proved profitable. One such strategy is ward control. The objective of feedforward control is to measure disturbances and compensate for them before the controlled variable deviates from set point. When forward control is applied correctly, deviation of the controlled variable is minimized. A concrete example of feedforward control is the heat exchanger shown in Fig Suppose that major disturbances are the inlet temperature, and process To implement feedforward control, these two disturbances must first be measured, and then a decision must be made about how to manipulate the steam valve to compensate for them. Fig shows this control strategy. The feedforward controller makes the decision about how to manipulate the steam valve to maintain the controlled variable at set point, depending on the inlet temperature and process flow. In Section 1-2 we learned that there are a number of different disturbances. The feedforward control system shown in Fig compensates for only two of them. If any of the others enter the process, this strategy will not compensate for it, and the result will be a permanent deviation of the controlled variable from set point. To avoid this deviation, some feedback compensation must be added to feedforward control; this is shown in Fig Feedforward control now compensates for the major

22 Chapter 1 Introduction SP Steam Feedforward controller TT 10 stream Y Condensate return Figure l-s.2 Heat exchanger feedforward control system. T while feedback control compensates for all other disturbances. Chapter 12 presents the development of the feedforward controller. Actual industrial cases are used to discuss this important strategy in detail. It is important to note that the three basic operations, M, D, A, are still present in this more advanced control strategy. Measurement is performed by the sensors and transmitters. Decision is made by both the feedforward and the feedback controllers. Action is taken by the steam valve. The advanced control strategies are usually more costly than feedback control in return Figure Heat exchanger feedforward control with feedback compensation.

23 Problems 9 hardware, computing power, and the effort involved in designing, implementing, and maintaining them. Therefore, the expense must be justified before they can be implemented. The best procedure is first to design and implement a simple control strategy, keeping in mind that if it does not prove satisfactory, then a more advanced strategy may be justifiable. It is important, however, to recognize that these advanced strategies still require some feedback compensation. 1-6 BACKGROUND NEEDED FOR PROCESS CONTROL To be successful in the practice of automatic process control, the engineer must first understand the principles of process engineering. Therefore, this book assumes that the reader is familiar with the basic principles of thermodynamics, fluid flow, heat transfer, separation processes, reaction processes, and the like. For the study of process control, it is also fundamental to understand how processes behave dynamically. Thus it is necessary to develop the set of equations that describes different processes. This is called modeling. To do this requires knowledge of the basic principles mentioned in the previous paragraph and of mathematics through differential equations. transforms are used heavily in process control. This greatly simplifies the solution of differential equations and the dynamic analysis of processes and their control systems. Chapter 2 of this book is devoted to the development and use of the transforms, along with a review of complex-number algebra. Chapters 3 and 4 offer an introduction to the modeling of some processes. 1-7 SUMMARY In this chapter, we discussed the need for automatic process control. Industrial processes are not static but rather very dynamic; they are continuously changing as a result of many types of disturbances. It is principally because of this dynamic nature that control systems are needed to continuously and automatically watch over the variables that must be controlled. The working principles of a control system can be summarized with the three letters M, D, and A. M refers to the measurement of process variables. D refers to the decision made on the basis of the measurement of those process variables. Finally, A refers to the action taken on the basis of that decision. The fundamental components of a process control system were also presented: sensor/ transmitter, controller, and final control element. The most common types of pneumatic, electrical, and digital-were introduced, along with the purpose of transducers. Two control strategies were presented: feedback and feedforward control. The advantages and disadvantages of both strategies were briefly discussed. Chapters 6 and 7 present the design and analysis of feedback control loops. PROBLEMS l-l. For the following automatic control systems commonly encountered in daily life, identify the devices that perform the measurement (M), decision (D), and action

24 10 Chapter 1 Introduction (A) functions, and classify the action function as On/Off or Regulating. Also draw a process and instrumentation diagram (P&ID), using the standard ISA symbols given in Appendix A, and determine whether the control is feedback or forward. (a) House air conditioning/heating (b) Cooking oven (c) Toaster (d) Automatic sprinkler system for fires (e) Automobile cruise speed control Refrigerator 1-2. Instrumentation Diagram: Automatic Shower Temperature Control. Sketch the process and instrumentation diagram for an automatic control system to control the temperature of the water from a common shower-that is, a system that will automatically do what you do when you adjust the temperature of the water when you take a shower. Use the standard ISA instrumentation symbols given in Appendix A. Identify the measurement (M), decision (D), and action (A) devices of your control system.

25 Chapter Tools for Control Systems Analysis This chapter presents two mathematical tools are particularly useful for analyzing process dynamics and designing automatic control systems: transforms and linearization. Combined, these two techniques allow us to gain insight into the dynamic responses of a wide variety of processes and instruments. In contrast, the technique of computer simulation provides us with a more accurate and detailed analysis of the dynamic behavior of specific systems but seldom allows us to generalize our findings to other processes. transforms are used to convert the differential equations that represent the dynamic behavior of process output variables into algebraic equations. It is possible to isolate in resulting algebraic equations what is characteristic of the process, the from what is characteristic of the input forcing functions. Because the differential equations that represent most processes are nonlinear, linearization is required to approximate nonlinear differential equations with linear ones that can then be treated by the method of transforms. The material in this chapter is not just a simple review of transforms but is a presentation of the tool in the way it is used to analyze process dynamics and to design control systems. Also presented are the responses of some common process transfer functions to some common input functions. These responses are related to the parameters of the process transfer functions so that the important characteristics of the responses can be inferred directly from the transfer functions without having to invert them each time. Because a familiarity with complex numbers is required to work with transforms, we have included a brief review of complex-number algebra as a separate section. We firmly believe that a knowledge of transforms is essential for understanding the fundamentals of process dynamics and control systems design. 2-1 THE TRANSFORM This section reviews the definition of the transform and its properties. 11

26 12 Chapter 2 Mathematical Tools for Control Systems Analysis Definition of the Transform In the analysis of process dynamics, the process variables and control signals are functions of time, The transform of a function of time, f(t), is defined by the formula = = (2-1.1) where F(s) = the transform off(t) = the transform variable, time- The transform changes the function of time, into a function in the transform variable, F(s). The limits of integration show that the transform contains information on the function for positive time only. This is perfectly acceptable, because in process control, as in life, nothing can be done about the past (negative time); control action can affect the process only in the future. The following example uses the definition of the transform to develop the transforms of a few common forcing functions. The four signals shown in Fig are commonly applied as inputs to processes and instruments to study their dynamic responses. We now use the definition of the transform to derive their transforms. (a) UNIT STEP FUNCTION This is a sudden change of unit magnitude as sketched in Fig. representation is Its algebraic = 0 Substituting into Eq yields = 0 0

27 2-1 The Transform H I -1.0, I t=t 0 I I I I I I Figure Common input signals for the study of control system response. (a) Unit step function, u(t). (b) Pulse. (c) Unit impulse function, (d) Sine wave, sin A PULSE OF MAGNITUDE HAND DURATION T The pulse sketched in Fig b is represented by t t T Substituting into Eq yields = dt = He- dt 0 H = 0 - H = A UNIT IMPULSE FUNCTION This function, also known as the Dirac delta function and represented by is

28 14 Chapter 2 Mathematical Tools for Control Systems Analysis sketched in Fig. It is an ideal pulse with zero duration and unit area. All of its area is concentrated at time zero. Because the function is zero at all times except at zero, and because the term in Eq. 1.1 is equal to unity at = 0, the transform is dt 1 Note that the result of the integration, is the area of the impulse. The same result can be obtained by substituting = l/t in the result of part (b), so that HT = 1, and then taking limits as T goes to zero. A SINE WAVE OF UNITY AMPLITUDE AND FREQUENCY The sine wave is sketched in Fig and is represented in exponential form by sin = 2i where i = is the unit of imaginary numbers. Substituting into Eq. 1.1 yields i O - l- + o - 1 2i iw 2i The preceding example illustrates some algebraic manipulations required to derive the transform of various functions using its definition. Table 1.1 contains a short list of the transforms of some common functions Properties of the Transform This section presents the properties of transforms in order of their usefulness in analyzing process dynamics and designing control systems. Linearity and the real differentiation and integration theorems are essential for transforming differential equations into algebraic equations. The final value theorem is useful for predicting the final