process dynamics, mo de lin g, an d control TOPICS IN CHEMICAL ENGINEERING A Series of Textbooks and Monograph s SERIES EDITOR ASSOCIATE EDITORS KEITH E GUBBINS Cornell University MARK A BARTEAU University of Delaware KLAVS F JENSEN Massachusetts Institute of Technology DOUGLAS A LAUFFENBURGER University of lllinois MANFRED MORARI California Institute of Technology W HARMON RAY University of Wisconsin WILUAM B RUSSEL Princeton University SERIES TITLES Receptors: Models for Binding, Trafficking, and Signalling D Lauffenburger and f Lindennan Process Dynamics, Modeling, and Control B Ogunnaike and W H Ray process dynamics, modeling, and control BABATUNDE A OGUNNAIKE E I DuPont de Nemours, Experimental Station, and Adjunct Professor, Department of Chemical Engineering University of Delaware W HARMON RAY Department of Chemical Engineering University of Wisconsin New York Oxford OXFORD UNIVERSITY PRESS 1994 Oxford University Press Oxford New York Athens Auckla nd Bangkok Bombay Calcutt a Cape Town Dares Salaam Delhi Florence Hong Kong Istanbu l Karachi Kuala Lumpu r Madraa Madrid Melbourne Mexloo City Nairob i Paris Singap ore Taipei Tokyo Toront o and aasoda ted compan ies in Berlin Ibadan Copy right@ 1994 by Oxford University Press, Inc Publish ed by Oxford Univer sity Press, Inc., 200 Madiso n Avenue , New York, New York 10016 Oxford is a registe red tradem ark of Oxford Unlvem ty Press All righta reserve d No part of this publica tion may be reprodu ced, stored In a retrieva layatem , or transm itted, In any form or by any means, electronic, mec:hanlcal, photoco pying, reoordlng, or othenv lae, withou t the prior permis sion of Oxford Univer sity Press Ubrary of Congress Cataloglng-ln-Publlcalion Data Ogunn alke, Babatu nde A (Babatu nde Ayodeji) Proceas dynami cs, modeli ng, and contro l/ Babatu nde A Ogunnllike, W Harmo n Ray p em -(Topi cs in chemical enginee ring) Includes Indexes 1SBN 0-19-509119-1 Chemic al process control I Ray, W Harmo n (Wiilis Harmo n), 1940U Title m Series: Topics In chemical enginee ring (Oxford Univer sity Press) TP155.75.036 1994 660'.2815 -dc20 94-28307 Printed in the United States of America on add-fre e paper To Anna and "the boys" (Damini and Deji), Agbaja owo ni n'gberu d'ori; and To decades of superb graduate student teachers, the heart of process control at Wisconsin CCONTJENTS part I INTRODUCTION Chapter Introductory Concepts of Process Control 1.1 1.2 1.3 1.4 1.5 1.6 The Chemical Process An Industrial Perspective of a Typical Process Control Problem Variables of a Process The Concept of a Process Control System Overview of Control System Design Summary Chapter Introduction to Control System Implementation 2.1 Introduction 2.2 Historical Overview 2.3 Basic Digital Computer Architecture 2.4 Data Acquisition and Control 2.5 Some Examples 2.6 Summary vii 5 13 15 19 30 35 35 36 38 46 56 61 viii CONTEN TS par tll PROCE SS DYNAMICS Chapter Basic Elements of Dynamic Analysis 3.1 3.2 3.3 3.4 3.5 Introduction Tools of Dynamic Analysis The Laplace Transform Characteristics of Ideal Forcing Functions Summary Chapter The Prcxess Model 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 The Mathematical Description of Chemical Processes Formulating Process Models State-Space Models Transform-Domain Models Frequency-Response Models Impulse-Response Models Interrelationships between Process Model Forms The Concept of a Transfer Function Summary Chapter Dynamic Behavior of Linear Low Order-Systems 5.1 5.2 5.3 5.4 5.5 5.6 First Order Systems Response of First-Order Systems to Various Inputs Pure Gain Systems Pure Capacity Systems The Lead/La g System Summar y Chapter Dynamic Behavior of Linear Higher Order Systems 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Two First-Order Systems in Series Second-Order Systems Response of Second-Order Systems to Various Inputs N First-Order Systems in Series The General Nth-Order System Higher Order Systems with Zeros Summary 67 67 68 71 80 86 89 89 92 104 108 110 111 115 128 134 139 139 142 153 157 161 166 175 175 183 188 200 204 205 211 ix CONTENTS Chapter Inverse-Response Systems 225 225 7.1 Introduction 229 7.2 Inverse Response in Physical Processes 7.3 Dynamic Behavior of Systems with Single, Right-Half Plane 231 Zeros 7.4 Dynamic Behavior of Systems with Multiple, Right-Half 237 Plane Zeros 240 7.5 Summary Chapter Time-Delay Systems 8.1 8.2 8.3 8.4 8.5 8.6 8.7 An Introductory Example The Pure Time-Delay Process Dynamic Behavior of Systems with Time Delays The Steam-Heated Heat Exchanger Rational Transfer Function Approximations Model Equations for Systems Containing Time Delays Summary Chapter Frequency-Response Analysis 9.1 9.2 9.3 9.4 9.5 9.6 Introduction A General Treatment Low-Order Systems Higher Order Systems Frequency Response of Feedback Controllers Summary VChapter 10 10.1 10.2 10.3 10.4 10.5 ,' Chapter 11 11.1 11.2 11.3 11.4 11.5 11.6 245 245 249 252 257 261 265 267 275 275 277 288 295 305 306 Nonlinear Systems 311 Introduction: Linear and Nonlinear Behavior in Process Dynamics Some Nonlinear Models Methods of Dynamic Analysis of Nonlinear Systems Linearization Summary 312 313 314 320 326 Stability 333 Introductory Concepts of Stability Stability of Linear Systems Stability of Nonlinear Systems Dynamic Behavior of Open-Loop Unstable Systems Stability of Dynamic Systems under Feedback Control Summary 333 337 343 349 353 355 1246 APPENDIXD or l(tl = W'M"'"o ll(t) = (D.SS) This is often written: l'"o (D.86) where the matrix e"', defined as: (D.87) is called the mtltrix exponential of AI It is very important to note that Eqs (0.86) and (0.87) provide the general solution to any set of homogeneous equations Eq (0.78) provided A has distinct eigenvalues Example 0.14 SOLUTION OF UNEAR MATRIX DIFFERENTIAL EQUATIONS To illustrate the solution of linear, constant coeffiaent, homogeneous differential equations, let us consider the system: (0.88) where Observe that A is the same matrix we have analyzed in Examples 0.10, 0.11, and D.12sowealready know llse~genvalues, At•.!:!• and modal matrix, M Thus, we have that Using Eq (D.87) we have that -'1#-$t/2e2'] 6+ rcl(t): ll(to> ="o (0.89) is straightforward Here u (t), d(t) represent control variables and distutbances respectively When the mab'kes A, B, rare constlmt mab'ices, a derivation rompletely similar to the one just given leads to the solution: ll(t) s ,.W-•ol:ro+ J,ACI-~[Ba(1)+rd(1)]dr (0.90) 'o when! the matrix exponentials, eA(t-~l, ~·~,may be evaluated using the relation Eq (0.87) l!umple 0.15 SOLtmON OF LINEAR NONHOMOGENEOUS MATRIX OIFFEREN11AL EQUATIONS To illustrate the solution of nonhomogeneous equations using Eq (0.90), let us suppose we have a syolem Eq (0.89) wilh A lite aame as lite last """"'f'le: and lnaddltlonaaaume "t • t1z • O,d •l (aaJNtantdlstwbanee)an d lhat t0 = In this case Eq (0.90) talcea lite lonn: x(l) = ,.V"o + J .,AU-~rc!(l)dr Substituting for ,AI, and ,.V"o calculated in lite Example 0.14, we obtain the solution: 1248 APPENDIXD x(t) = or For the situation where the matrices A, B, r may themselves be functions of time, the solution requires a bit more computation In this case: x(t) = •ll(:r,to) "o + r ~(t, to) ~('l;toT1 [Bu("' + rd("'1d-r (D.91) 'o ~(t, ~) is an n x n time-varying matrix known as the fundamental matrix solution which may be found from: Here dCP(t,t0 ) -;It = A(t)~(t, t ); ~(t0 ,fo) =I (D.92) Because A(t), B(t), r(t) may have arbitrary time dependence, the fundamental matrix solution is usually obtained by numerical methods Nevertheless, once ~(t,fo) is determined, the solution x(t), may be readily calculated for a variety of control and disturbance inputs, u(t ), d(t), using Eq (D.91) D.12 SUMMARY · In this appendix, the techniques of matrix algebra have been reviewed These methods find particularly useful application in providing very general solutions to sets of linear algebraic and linear ordinary differential equations The importance of matrices as a tool for analyzing the dynamics of physical processes should not be undervalued by the reader As an aid to further study, a bibliography is provided below REFERENCES AND SUGGESTED FURTHER READINGt J Wiley, New York (1967), Kreysig, E., Advanced Engineering Mathematics (2nd ed.), Chap.7 Amundson, N R., Mathematical Methods in Chemical Engineering, Prentice-Hall, Englewood Oiffs, NJ (1966) Wylie, C R., Advanced Engineering Mathematics, J Wiley, New York (1966) Duncan, W J., A R Collar, and R.Q Frazer, Elementary Matrices, Cambridge University Press (1963) Bellman, R., Introduction to Matrix Analysis, McGraw-Hill, New York (1.960) Gantmacher, F R., 1'he Theory of Matrices, (Vols and 2), Chelsea Publishing Company, New York (1960) +Listed in increasing order of depth ;i ~ AJPJPENDKX E COM PUT ER-A IDED CON TRO L SYSTEM DES IGN The calculations required for the analysis of process dynamic s, the fitting of models to experime ntal data, and the creation of control system designs can be quite tedious and challeng ing Fortunat ely, there are a host of interacti ve Comput er-Aided Design (CAD) package s which will carry out these calculations with no program ming effort required by the user These packages are available for reasonab le fee, and thus should be used by students and others studying the material in this book Some of the more widely used packages are listed in Table E.l below Reviews of the field of compute r-aided design and a discussio n of these and other CAD program s can be found in Refs [1-3] a 1249 APPENDIX E 1250 Table E.L Some Computer-Aided Analysis and Control System Design Packages ACSL Scope Primarily Simulation cc Comprehensive CONSYD Comprehensive Ctrl-C Model-C Comprehensive EASY5 Comprehensive Program MATLAB with Control System, Robust Control, and System Identification Toolboxes MATRIX-X Comprehensive Comprehensive TUTSIM Primarily Simulation UC-SIGNAL UC-ONLINE Primarily Simulation Source Mitchell and Gauthier Assoc 200 Baker Avenue Concord MA 01742 Systems Teclmology, Inc 13766 S Hawthorne Blvd Hawthorne CA 90250 Prof W Harmon Ray Dept of Chemical Eng University of Wisconsin 1415 Johnson Drive Madison WI 53706 Systems Control Teclmology 1801 Page Mill Road P Box 10180 Palo Alto, CA 94303 Boeing Computer Services P.O Box24346 Seattle WA 98124 Mathworks, Inc• 24 Prime Park Way Natick, MA 01760 Integrated Systems, Inc 3260 Jay Street Santa Clara CA 95054 Tutsim Products 200 Calif Ave., #212 Palo Alto CA 94306 University of California Office of Tech Licensing Berkelev, CA REFERENCES Chen, Z.-Y (Ed.)., Computer-Aided Design in Control Sytems, Proceedings 4th IPAC Symposium, Pergamon Press, New York (1988) Holt, B R., et al., "CONSYD- Integrated Software for Computer-Aided Control System Design and Analysis," Comput Chern Eng., 11, 187 (1987) Linkens, D A (Ed.), CAD fur Control Systems, Marcel Dekker, New York (1993) author in de x A Abramowit z, 1207 Aitolahti, 1029 Albert, 62 Altpeter, 620 Alvarez, 807 Amundson, 1248 Ardell, 1146 Aris, 401 Arkun,328 , 1029,1030 Arnold, K ].,401 Arnold, V.I., 328 Arulalan, 1028 Ash, 980 AstrOm, 558, 586, 639, 877, 943, 980 Ayral, 1029 B Baker, 1094 Bard, 401 Beck, 401 Bellman, 1248 Beudat, 450 Berry, 717 Bhat, 1095 Biegler, 1028, 1094 Simonet, 1030 Bird, 135, 212 Bischoff, 401 Bode, 167, 620 Bodson, 639 Bongiorno, 1031 Box, 843, 1028, 1059 Boyce, 1174 Bracewell, 135, 450 Bristol, 764, 807 Brogan, 10 Brosilow, 1028 Brown, D W., 1060 Brown,] W., 1174 Bruns, 808 Bryson, 1094 Buckley, 31, 1146 c Cadzow, 943 Caldwell, 1028, 1029 Camp, 1031 Caracotsios, 401 Carbonell, 1095 Carnahan, 1175 Ceaglske, 31 Champetier, 639 Chang,102 Chen, 1250 Chien, 1146 Churchill, 1174, 1207 Cinar, 1147 Clarke, 1028 Coddington, 1174 Coggan,62 Cohen,557 Collar, 1248 Congalidis, 1146 Conle, 1178 Considine, 557 Coon,557 Copson, 1174 Corripio, 240, 557 Coughanow r, 31, 268, 355 Cozewith, 1146 Crosier, 1059 Cutler, 808, 1028 D de Boor, 1175 DelToro, 31 1251 Deshpand~980, 1028,1146 DiPrima, 1174 Doss, 1059 Downs, 807, 1059 Doyle, F.J., 1147 Doyle,] c., 8C8, 1094 Driver, 1174 Duncan, 1248 E Eckman,31 Economou, 1028 Edgar, 980 Engell, 1146 English, 1059 Erickson, 1028 Eykhoff, 450 F Flannery, 1175 Francis, 808 Frank, 676, 1028 Franks, 401 Franklin, 877, 943, 980 Frazer, 1248 Friedly, 327, 401 G Gagnepain, 764 Gantmacher, 1248 Garcia, 676, 807, 1028, 1030, 1094 Gay, 1094 Gear, 1175 Georgiou, 1029 Georgakis, 1029 Gerstle, 1029 Gillette, 1030 1252 Goldberg, 1174 Golubitzky, 327 Gould, 1030 Greenberg, 1174 Grosdidier, 764, 1029 Grossmann, 1094 Guckenheimer, 327, 355 Gumowski, 1146 H Hagglund, 558 Halm,355 Hanus,586 Harris, 1059, 1060 Harrison, 62 Hashinloto, 1030, 1031 Hawkins, 1028 Henrici, 1175 Henrotte, 586 Hernandez, 1029, 1030 Hillier, 1094 Hirnrnelblau, 401 Ho, 1094 Hofhnan, 1060 Hokanson, 1029 Holmes, 327, 355 Holt, 764, 1250 Hoo, 639 Hopf,315 Hopfield, 1095 Hornbeck, 1175 Horowitz, 1029 Hubele, 1059 Hulburt, 807 Hummel, 1030 Hunt, 328, 639 Hunter, 1059, 1060 I Iinoya, 620 Ince, 1174 Iooss, 327, 355 Isermann, 980 Isidori, 328 J Jabr, 1031 Jazwinski, 1094 Jenkins, 843, 1028, 1059 Jensen, 807 Jeron1e, 808, 1146 Joseph, 327, 355 INDEX K Kaiser, 1030 Kantor, 639 Kaspar, 1146 Keats, 1059 Kinnaert, 586 Klatt, 1146 Koppel, 31, 268, 355, 764 Kramer, 1094 Kravaris, 328 Kresta, 1059 Kreyszig, 1174, 1248 Krishnan1urthi, 1059 Kuo, 980, 1175, 1207 L Landau, 639 Lapidus, 401, 450 Lasdon, 1094 Lau, 807 Lecamus, 1030 Lectique, 1029 Lee, J H., 1029, 1030 Lee, P L., 676, 1029 Lee, w.,31 Lemaire, 764, 808, 1147 LeRoux, 1030 Levinson, 1174 Lieberman, 1094 Lightfoot, 135, 212 Linkens, 1250 Littnaun, 1030 Longwell, 327 Lopez, 557 Lucas, 1059 Luther, 1175 Luyben,31,240 ,327,401, 717, 1029, 1146 Lyung, 450 M Maarleveld, 1147 Maciejowski, 808 Marlin, 1059 Martens, 943 Martin, 1028, 1029 MacGregor, 1029, 1059, 1060, 1146 Mahrnood,808,1029 Marchetti, 1029 Marquardt, 1094 Mason, 1029 McAuley, 1146 McAvoy, 764, 807, 1029, 1095, 1146 Matsko, 1029 Maurath, 1029 Meadows, 1029 Mehra, 808, 1029, 1030 MellichaD1p,62,980, 1029 Meyer, 328, 639 Michalski, 1095 Mitchell, 1095 Milne-Thon1pson, 1174 Mohtadi, 1028 Monopoli, 639 Montague, 1095 Moore, 807, 1094 Morari, 557, 620, 676, 717, 764, 808, 980, 1028, 1029, 1030, 1094, 1147 Moreau, 1030 Morris, 1095 Morshadi, 1029 Murrill, 557 Muske, 1029, 1030 N Narenda, 639 Newell, 676, 1029 Newton, 1030 Nichols, 557 Niederlinski, 764 Niida, 1094 Nisenfeld, 1146 Nygardas, 620 Ogata, 877, 943, 980, 1207 Ogunnaike, 450, 639, 764, 808, 1030, 1146, 1147 Olmo, 1030 Ohshlrna, 1030 Otto, 1028, 1030 Owen, 1095 p Page, 1060 Palsson, 1028 Papon,1030 Parher, 31 Pearson, 1147 Penlidis, 1146 Piovoso, 1095 I INDEX 1253 Pouliq uen, 1030 Powell , 877, 943 Prett, 807, 1029, 1030, 1094 Propoi , 1030 Q Qin, 1095 R Radem acher, 1147 Ragaz zi, 980 Ramake~808,1028, 1030 ' Ranz, 401 Rao, 1028 Rault, 1029, 1030 Rawlin gs, 1028, 1029, 1030 Ray, 31, 62, 401, 557, 676, 717, 764, 808, 1028, 1094, 1095, 1146, 1147 Rebou let, 639 Redhe ffer, 1174 Richalet, 1030 Richar ds, 1146 Ricker , 1030 Rijnsd orp, 1147 Rivera , 557, 1030 Robert s, 1060 Roffe!, 1060 Rosenbrock, 808 Ross, 1059 Rouha ni, 1030 Routh, 504 Rovira , 557 s Sastri, 1059 Sastry , 639 Schaeffer, 327 Schork , 1030 Schule r, 1147 Scott, 1095 Schwe dock, 1147 Seborg , 764, 980, 1028, 1029, 1031 Seema nn,114 Seinfeld, 401, 450 Semin o,558 Shewa rt, 1060 Shinskey,240,586,8~/, 1147 Shunta , 1146 Sim, 1030 Simminger, 1030 Skoges tad, 557, 1030, 1147 Smith, C A., 240, 557 Smith, C L., 557 Smith, c R., 808 Smith, J M., 620, 1030, 1031 Smith, R E., 557, 1095 Sokolnikoff, 1174 Stein, 1094 Stepha nopou los, 212, 1095 Stephe nson, 1174 Stewar t, 135, 212, 401 Stone, 1095 Su, 328,63 Subrarnarrian, 1030 Sulliva n, 676, 1029 T Takam atsu, 1030 Tanne nbaum , 808 Taylor , 1094 Tessie r, 1029 Testud , 1029, 1030, 1031 Teukb lsky, 1175 Tham, 1095 Truxal , 31 Tsing, 1031 Tu, 1031 Tuffs, 1028 Tyreus , 764 u Umeda ,1094 v Vanhamliki, 1029 Vellering, 1175 Venka tsubra manian , 1095 Verhey , 1174 Vinant e, 717 Vogel, 980 w Waller , 620 Wassick, 1031 Weber ,31 Weekman,31 Wethe rill, 1060 Whale n, 1031 Wilkes, 1175 Williams, 31, 1031 Winde s, 1147 Witten mark,5 86,639 ,877, 943, 980 Wood, 717 Woodb urn, 807 Wylie, 1174, 1248 y Yamamoto, 1031 Yeo, 1031 Yocum, 1028 Youla, 1031 Yuan, 1031 z Zadeh , 1031 Zafirio u, 558, 620, 676, 717, 808, 980, 1029, 1031, 1094 Zames , 1031 Zhang , 1147 Zhao, 1028 Ziegler, 557 subject index A abnormality detection, 1088 ACSL, 1250 actuators, 49 adaptive control, 628 AID converter, 43 alarm interpretatio n, 1088 aliasing, 826 amplitude ratio, see also magnitude ratio, 152, 281 analog ruters, 51 analog input/ output, 44 analog-to-digital converter, 43 antiresetlYin dup,585 ARIMA model, 1051 ARMAX model, 999 artificial intelligence, 1091 auctioneerin g control, 582 autoregressive moving average (ARMA) model, 999 autotuning, 555 B biological systems: anaerobic digester, 310, 405 anaesthesia control, 814 bioreactor, 357 cardiovascul ar regulator, 563, 770 hemodynamics model, 222 human pupil servomechanism, 509 immunology, 243 respiratory process, 220 "black box" models, 410 block diagrams, 463, 824, 927 Bode diagram, 153, 281 asymptotic consideration s, 306 classical controllers, 305 for feedback controller design,549 first-order system, 285 inverse-respo nse system,302 lead/lag system, 294, 300 pure capacity system, 291 second-order system,298 time-delay system, 303 Bode plot, see Bode diagram Bode stability criterion, 549 boiler, 229, 562, 811 bounded-input, boundedoutput stability, 337 Bristol array, see relative gain array (RGA), c capillary, 154 cascade control, 12, 567 catalytic reactors, 231, 1105 cc, 1250 chemical process, defini lion, objectives of operation, variables of, 13 chemical reactors, 101, 138, 141, 171, 217, 252, 271, 313, 315, 331, 358, 365, 381, 395, 407, 456, 583, 591, 641, 681, 816, 984, 1067, 1138 1255 closed loop, block diagram, 463, 824, 926 characteristic equation, 486 performance criteria, 520 stability, 486 transfer functions, 468 multiloop systems, 724 Ctrl-C, 1250 Cohen and Coon tuning rules, 537 comparator, 465, 927 complex variables, 1155 complex s- plane, Nyquist map of, 286 complex z- plane, 902 computer control system, 36-61 computer-aid ed control system design, 1249 computer control, see digital computer control, condition number, 803, 1241 CONSYD, 1250 control limits (in SPC), 1037 control system synthesis, case studies of, 1097 controllabilit y, 686 controller, 16, 465, 518, 927 controller design, 21 commercial, 518 choosing controller parameters, 524 controller type, 523 conventional feedback, 461 model-based, 645 performance criteria, 520 principles, 519 via optimization , 522 1256 troller tuning, auto tuning, 555 Cohen and Coon rules, 536 direct synthesis, 526, 538 internal model control, 529, 539 pole placement, 529 stability margins, 530, 552 with approximate models,532 with frequency response models,541 without a model, 555 time-integral rules, 525, Ziegler-Nichols approximate model rules, 536 Ziegler-Nichols stability margin rules, 553 control valve, 514 control variables, 13 comer frequency, 289 crisis management, 1088 critical gain, see also ultimate gain, 531 critically damped response, 191 crossover frequency, 550 crude oil, boiling point curve,8 CUSUM charts, 1040 cyclopentanol, 1138 D D I A converter, see digitalto-analog converter Dahlin controller, 973 damping coefficient, 184 data acquisition, 43, 47 deadbeat control, 971 dead time, see time delay, decay ratio, 520 decoupling, 773 design,776 dynamic, 777 feasibility of, 792 generalized, 781 limitations of, 785 partial, 788 simplified, 778 steady-sta te (static), 790 time scale, 755 INDEX delta function, Dirac, 82 Kroneker, 887 derivativ eaction,4 68 derivative time constant, 468 desired reference trajectory, see reference trajectory, deviation variable(s), 23 difference equations, 1166 differential equations, 1162, 1169 difficult dynamics, controller designs fur, 599 digital compulel', architecture, 38 capabilities, 38 peripherals, 38 digital computer control, 37, 821, 951 digital controller, 951 advanced, 966 poles and zeros of, 954 PID,960 digital filters, 829 digital input/output, 44 Dirac delta function, 82 direct digital control (DOC), 52 Direct Synthesis Control, 526, 538, 970, 978 discrete-time models, 107, 832, 873 backward shift form, 893 forward shift form, 894 poles and zeros, 898, 906 discrete-time systems analysis, 835, 847 block diagram 918 discretization, 835 dynamics, 883 identification, 838 relation to continuous systems, 901, 918 stability, 933, 937 distillation columns, 7, 32, 138, 172, 230, 369, 420, 442,507,5 62,565,59 0, 711, 719, 733, 749, 760, 766, 783, 791, 798, 810, 845, 982, 1097 distributed control system {DCS),54 distributed paramete r controllers, 1083 distributed paramete r systems, 106, 376, 1083 disturban ce variables, 13 DMC, see Dynamic Matrix Control, drug ingestion, 137, 215 Dynamic Matrix Control, 1000, 1012 ·Dynamic Matrix Identification, 1013 dynamic flowsheet simulation, 1089 E EASY 5,1250 economic forecasting, 220 electronic controllers, 37 empirical process models, see also process identification, 409-450 equal-percentage valve, 514 E~,seeexponentiaily weighted moving average, expert systems, 1091 exponentially weighted moving average, (EWMA), 1043 F fault detection, see also abnormality detection, feedback control, 12, 17 adaptive, 628 basic loop elements, 463, 514, 927 PID,467 tuning rules, 525 feedforward control, 12, 18, 571, 968 filter(s), analog, 51 digital, 829 final control element, 16, 465, 927 first order hold, 831 first order system, 139-154, 884, 912 ~; INDEX first order plus time delay model,253 approximation of higher order dynamics, 256 characte rization of process reaction curve, 533 use in controller design, 536 flow controller, 12 Fourier transform, 1178 frequency: comer,2 89 crossover, 550 Nyquist , 828 resonan t, 298 sampling, 827 frequency response analysis , 275-307 applicat ion in controller design,541 Bode/N yquist plots, 286305 identifica lion, 436 models, 110 pulse testing, 437 furnace, 8, 33, 269, 505, 581 G gain margin, 552 gasoline blending, 219,743 gain scheduling, 628 gas storage tank, 56 general ized inverses, 1227 Generic Model Control, (GMC), 671 grade transitions, 1089 grindin g circuit, 789, 810 H heatexc hanger, l07,257 , 273, 310, 377, 506, 560, 588, 596, 681, 986 heating tank, 14, 85, 95, 462 Heaviside function, 80 higher order systems, 205211 holds,8 30 Honeyw ell Multiva riable Predictive Control, (HMPC ),l016 Horizon Predictive Control, (HPC), 1016 1257 I IDCOM, 1008, 1011 ideal forcing functions, impulse,82 ramp,83 realization of, 85 rectangular pulse, 81 sinusoidal, 85 step, 80 ill-conditioning, condition number, 803 degeneracy,798 SVD, tool for detecting, 806 impulse,B2 impulse response function, in model predictive control, 1008 moments from data, 427 impulse response identification, 422 impulse response model, 111, 833 ingot, 388, 1084 input variable(s), 13 input/ output interfaces, 42 input/o utput pairing, 735 instrumentation, 47 interaction, 735 integral action, 467 interaction compensators, see decouplers, Internal Model Control, (IMC), 529, 539, 665 inverse response cornpensation,613 inverse response systems, 225-240, 608 controller designs for, 608 main characteristics, 226 physical examples, 229231 J Jury array, 938 Jury stability test, 938 K Kalman filter, 1064 L Laplace transfon n, application to the solution of differential equations, 77, 1185 defmiti on,71,1 180 inversion, 73, 1180 tables, 1193 lead/lag systems, 161-166 lime kiln, 818 lineariz ation, approximate, 626 exact, by variable transformation, 632 liquid/l iquid extraction, 405 loop pairing, 683, 727, 735-758 lumped parameter systems, 368 M magnih lderatio ,288 manipu lated variables, 13 manometer, 185 manual control, 10 MATLAB, 1250 matrices, 1209-1248 MATRIX-X, 1250 measuring device, 465, 927 methanol oxidation, 1107 MIMO systems, see multiinput-multi-output systems, minimum variance control, 1052 Model Algorithmic Control (MAC), see also IDCOM, 1008, 1011 model-based control, 645 MODEL-C, 1250 model identification, (see process identification), model predictive control, (MPC), 991 applications of, 995 commercial software packages for, 1011 model forms for, 997 nonline ar, 1020 model reference adaptive control, 629 1258 MPC, see model predictive control, multi-input, multi-output (MIMO) systems, 683-807 multidelay compensator, 1103 multiloop control systems, controller designs for, 723 ·controller tuning, 759 multiple input, single-output systems, 582 multivariable block diagrams, '775 multivariable control, block diagram, 712, 775 controller design, 759, 773 decoupling, 716 input/output pairing, 683, 727, 735 interactions, 686, 724 process models, 688 multivariable dynamics, 694, 890 multivariable identification, 447 multivariable system poles, 703 multivariable system zeros, 704 N NARMA(X), models, see nonlinear ARMA models, neural networks, 1091 Niederlinski index, 738 nonlinear ARMA (NARMA) models, 1026 nonlinear control, 625 nonlinear MPC, 106, 1020, 1026 nonlinear systems, 311-327 controller design philosophies, 625 dynamic response, 326 methods of dynamic analysis, 314 stability, 343 nonminirnum phase systems, 601 INDEX Nyquist diagram 286, 543 Nyquist frequency, 828 Nyquist plot, see Nyquist diagram, Nyquist stability criterion, 543 observability, 686 observers, 1064 offset, 25, 485 oil refinery, 1086 on-line optimization, 1086 open loop, control strategy, 18 stability, 333 open loop unstable systems, 617 optimal control, 674 optimization, 1086 Optimum Predictive Control, (OPC), 1014 output variable(s), 13 overdamped response, 191 overdefined systems, 1227 override control, 581 overshoot, 520 p P controller, see proportional controller, P &: I diagram, 59, 1149 packed bed reactors, 406, 1105 Pade approximations, for time delays, 261 paper machine, 982 parallel computing, 1093 parameter estimation, basic principles of, 381 differential equation models,384 partial decoupling, 788 PO controller, see proportional-plusderivative controller, pendulum, 335 performance criteria, 520 phase angle, 'Zl7 phase lag, 277 phase lead, 292 phase margin, 552 PI controller, see proportional-plusintegral controller, PID controller, see proportional-plusintegral-plusderivative controller, pipe, 246, 561 plant/model mismatch, 1070 pneumatic transmission, 37 pole placement, for continuous controller design,529 for discrete controller design,978 poles, closed loop, 496, 935 transfer function, 132, 933 pollution control, 216, 217, 331 polymerization, p~,58,270,332, 357, 456, 589, 640, 766, 844, 949, 987, 1039, 1113, 1122 predictive control, see model predictive control, Predictive Control, (PC), (commercial software package), 1015 pressing iron, 172 process and instrumentation diagrams, seeP&: I diagrams, process characterization cube, 1133 process dynamics, main objectives, 65 definition, 67 process identification, 409-450 frequency response, ~ impulse response, 422 multivariable, 447 pulse testing, 437 step response, 417 process model, formulation of, 92, · 363-401 interrelationships between various forms, 115, 128 various forms of: state-space, 104 INDEX frequency response, 99 impulse response, 100 transfer function, 128, 131 transform domain, 98, 108 process reaction curve, 533 process variability, 1070 product quality, specifications, product ion rate, proport ional band, 467, 518 proport ional controller, 467, 474 proport ional-pl usderivative controller, 468 proportional-plus-integral controller, 467, 478 proportional-plus-integralplus-derivative controller, 468, 518 pulse testing, 437 comparison with direct sine wave testing, 436 input characteristics, 441 multivariable, 447 pulse transfer function model,867 pure capacity system, 157-161 pure gain system, 153-157 pure time delay process, limit of infinite number of first order systems in series, 262 physical example of, 245, 252, 257 transfer function of, 249 pyrolysis fractionator, 169, 589 Q quality control, see statistical process control, quality control charting, 1037 quarter- decay ratio, 531 quick-opening valve, 514 R ramp function, 83 1259 ratio control, 579 realization, 117 rectangular pulse, 81 reference trajectory, in controller design by direct synthesis, 648 for model predictive control, 996 regulatory control, 19 relative gain array (RGA), 728 relay controller, 555 reset rate, 468 reset windup , see also antireset windup , 585 resonance, 298 reverse action, in controller hardwa re, 517 ringing, 972 rise time, 520 robust controller design, 1069 robust performance, 1070 robust stability, 1070 root locus, 496 Routh stability test, 489 s safety, sample-and-hold, see also zero-order hold, 824 effective time delay contributed by, 832 sampled data system, 821 block diagram analysis for, 917 closed loop block diagrams, 927 stability of, 933, 937 sampler, 823 scrubber, 454, 559 second order system, 183205, 913 selective control schemes, 581 self-tuning regulator, 630 sensors, 16 serial correlation, 1046 serial transmission, 43 servo control, 19 set-point, 19 set-point tracking, see servo problem, set-poin t trajectory, see reference trajectory, settling time, 520 Shewar t (quality control) chart, 1037 signals, analog voltage, 51 analog current, 51 digital, 52 signal conditioning, 49, 829 amplification, 50 multiplexing, 50 filtering, 51 single-i nput multiple-output systems, 581 singula r value decomposition (SVD), 806 singula r values, 803 sinusoid al inputs, 84 SISO systems, see singleinput-single-output systems Smith predictor,605 SPC, see statistical process control, split-range control, 583 spring-s hock absorber, 185, 193 stability , 333-355 definiti ons,335 discrete time, 933 linear, 337 multivariable syst!!rns, 710 nonline ar, 343 open loop, 349 closedl oop,353 ,486 stability criteria, bilinear, 937 Bode,54 direct substitu tion, 494 Jury,93 Nyquist, 543 root locus, 496 Routh,4 89 stagewise processes, 369 state estimation, 1063 state-space model, 104 state variables, 13 statistical process control, 1033 steady state decoupler designs, 790 1260 step response , idealize d input, 80 identific ation, 433, 533, 1013 first order system, 143 higher order systems , 204 inverse respons e system, 226 lead/lag system, 164 nonline ar systems , 312 pure capacity system, 159 pure gain system 155 second order system 188 system with multiple right half plane zeros, 237 stochast ic process control, 1050 storage tank, 136, 171 structur al instabil ity (of multiloo p systems ), 738 supervi sory control, 52 SVD, see singula r value decomposition, T INDEX time series, 997, 1051 transfer function , in generali zed view of modelin g, 128 properti es, 132, 893 traditio nal, 132 transform domain model form, 108, 893 poles of, 132, 898 zeros of, 132, 898 transmit ters, 16 TUTSIM, 1250 u UC-ONUNE, 1250 UC-SIGNAL, 1250 ultimate gain 531 ultimate period, 531 underda mped response, 191 underde fined systems , 1227 unstable system, 617 v valve, see control valve, Tank, 21, 33, 140, 146, 158, Vogel-E dgar controll er, 975 163, 176, 313, 318, 323, Volterra series models, 330, 348, 353, 358, 404, 1026 452, 521, 571, 579, 584, 588, 592, 627, 636, 642, w 684,746 ,800,84 0,880 tempera ture controll er, 12 water heater, 136, 168, 403 tempera ture measurement, Western Electric rules, 1039 16 theoreti cal process models, 363-401 thermom eter, 403 z-transf orms, 848 time delay compen sation, applicat ion in discrete 604 time control, 859 time delay systems , 245-268, applicat ion to the 603 solution of difference approxi mations for, 261 equatio ns,873, 1199 controll er designs for, defirriti on,849, 1194 603 effect of samplin g on, 857 dynami c response s, 250, inversio n, 854, 860, 1194 254 relation to Laplace models for, 246, 265 transfor m, 859 physica l example , 246, tables, 861, 1202 252 zeros, time domain models, 832 effect of samplin g on, 906, time-int egral criteria (IAE, 909 ISE, ITAE, ITSE), 525, effect on step response , 537 206-211, 231-239 time scale decoupl ing, 755 right half plane, 231 z zero-ord er hold (ZOH), 830, 869 Ziegler- Nichols tuning rules, 536, 553 ... Receptors: Models for Binding, Trafficking, and Signalling D Lauffenburger and f Lindennan Process Dynamics, Modeling, and Control B Ogunnaike and W H Ray process dynamics, modeling, and control BABATUNDE... of Process Dynamics, Modeling, and Control c~ntained in the iiJkbmin~apters Thus this chapter is an introductory oveAAew of process control and how it is practiced in the chemical process industry... accordingly The process control engineer requires a thorough understanding of the process itself as well as a proper understanding of the principles of Process Dynamics and Control in order to accomplish