Index

Accumulation, 53Accuracy:

numerical integration, 83-84sensor, 383, 772-773

Adaptive tuning:expert system, 528gain scheduling, 518, 529, 709, 715input conversion, 519reasons for, 512-517relay auto-tuning, 527selection of method, 529valve characteristic, 520-525

Alarms, 795, 890Aliasing:

antialiasing filter, 393due to sampling, 362, 989

Amplitude:amplitude ratio, 121-123, 316,412,

988-989response to sine, 121iSee also Frequency response)

Analog:computation, 257signals, 212-215, 358-359

Anti-reset windup, 399-402, 604-605,715

Array isee Relative gain array)Averaging filter, 394Averaging level control, 563-564,

569-570

B

Bandwidth, 419Benefits, control, 28-35,423^125Blending:

controllability, 627, 637gasoline, 866interaction, 632loop pairing, 663model, 621operating window, 625

1004

Index

Blending—Cont.optimum, 866-870tuning for, 646-648

Block diagrams:algebra, 116,118,143,244cascade, 463definition of, 115feed forward, 489multiloop, 630IMC, 592,994reduction to transfer function, 116,244series, 143single-loop, 243,974Smith predictor, 600

Bode:cascade, 468closed-loop, 412-415generalized plots, 323-326key aspects of plots, 328plot, 123stability criterion, 313-317

limitations of, 316Boiler:

control of, 27,474efficiency of, 32-34optimization of, 861-865iSee also Steam system)

Bounded input-output stability, 304,307-308

Cascade:block diagram, 463degrees of freedom, 460-461design criteria for, 461examples:

chemical reactor, 471-473distillation, 690-691fired heater, 473heat exchanger, 458-460

levels of, 473performance, 462-468primary variable, 460secondary variable, 460terminology, 460transfer functions, 462tuning, 469

Cause-effect relationship, 6-7,114, 651Centralized control, 617,727

Characteristic, valve:examples, 520-525inherent, 520specifying for linearizing loopgain, 524

Characteristic equation:definition, 309, 630relation to stability, 309-310,316,643,

987Characteristic polynomial:

definition of, 108,932relation to stability, 109roots of, 109,932

Checklist, for design, 820-822Chemical reactor, packed bed:

cascade, 471-473feedforward, 495-497inferential, 549-552variable structure, 713-714

Chemical reactor, stirred tank, 62,72,84-86

isothermal, 62,72nonisothermal:

cascade design, 475-476control design, 835control performance, 438-440linearized, 900model for, 85, 897-901multiple input-output, 163-165operating window, 781-783recycle, with, 785selecting variables, 216-218signal select, 710-712transfer function, 902

series:block diagram, 944inverse response, 944-945model, 64-67,943-944transfer function, 944

stability, without control, 902-906steady-states:

calculating, 902-904multiple, 905stabilizing via control, 905

Combustion:benefits for, 32-34excess oxygen control, 27fuel control, 500-501iSee also Fired heater)

Complex numbers:magnitude, 122,316-317,936-937phase angle, 122, 316-317,936-937polar form, 122, 316-317,936-937

Composition control:blending and mixing, 270,282,

512-519,646-648chemical reactor, 37,216,438,475,835flash, 23,537-544,768, 802-803iSee also Distillation)

Computation:analog, 257-258digital, 358-362

Computer:analog, 257-258digital, 358-362

control implementation, 365-367,974,983-989

simulation, 82-84,422-425iSee also Digital control)

Computer-aided calculations, 82-84,421-422

Conservationcomponent, 53energy, 53, 898material, 53

Constitutive relationships, 54Constraints, 26

control, 715-720hard or soft, 767-770valve position control, 718-719iSee also Operating window)

Continual improvement, 859Continuous cycling, 342-343Continuous-flow stirred tank (CST):

chemical reactor:heat-integrated, 785with recycle, 155-157iSee also, Chemical reactor, stirred

tank)heater, 76-80, 253-257,458-461,

483̂ 186mixer, 186-187, 223-225, 270, 512

Continuous-time variables, 98,212Control:

algorithms:DMC, 735-748IMC, 590-600lead/lag, 485^86PID, 252Smith predictor, 600-603

approaches, 228automated vs. manual, 228-231benefits, 28-35,425definition, 6design, 216-218, 823, 834feedback, 6-7,212,243

Control—Cont.feedforward, 488objectives, seven categories, 20-25,

768, 838iSee also Model predictive control)

Control design form, 768, 838Control objectives, 20,216, 269, 768Control performance:

best possible, 426-427,490control system factors, 433-440economic analysis, isee Benefits,

control)faction dead time, 279,426-429factors affecting, 444by frequency response, 412-415measures, 219-223, 240-241multivariable systems:

disturbance type, 667,677-679interaction, 616iSee also Relative disturbance gain)

process factors, 425-432robust, 268-269,411by simulation, 422

Control system:hierarchy, 829layout, 9-10, 212-213, 359-361

Control valve:characteristic, 520dynamics, 776failure position, 777range, 776selection, 217

Controlled variable:selection of, 7-8, 225,536,771-773,

775, 787, 840Controller:

dimensionless gain, 397error, 242-243execution frequency, 370, 373flowchart, 403frequency response of, 325-326location, 9-10manipulated variable, 217measured variable, 216nonlinear, 517, 567performance isee Control performance)sense switch, 396-397tuning:

Ciacone, 278-286comparison, 347dynamic matrix, 750fine, 289-293goals, 268-269

1005

Index

1006

Index

Controller—Cont.tuning—Cont.

IMC, 598Lopez, 287multiloop, 638-646robustness, 268-269,338-341Ziegler-Nichols, 329-330,347

Corner frequency, 323Critical frequency, 315Crossover frequency, 315CST isee Continuous-flow stirred tank)

D

Damping:coefficient, 138-139critically, 139overdamped, 139underdamped, 139

Dead time:Bode plot, 324compensation, 600computer programming, 922definition, 103discrete, 977effect on performance, 426-427effect on stability, 334-337frequency response, 318Pade* approximation, 913

Decay ratio, 220Decentralized control, 616-617Decoupling:

application criteria, 690designs:

calculated controlled variables,685-686

calculated manipulated variables,684-685

explicit controller calculations,686-689

performance, 689-690sensitivity to errors, 689-690iSee also Interaction)

Degrees of freedom:in control design, 217,460-461,708,

711,778effect of control, 254,778in modelling, 54-55

Derivative:approximation, 366definition of, 56filter, 402

Derivative—Cont.Laplace transform of, 101mode:

behavior, 249-252frequency response, 326noise transmission, 252, 292-293

time, 250z-transform, 978

Design, control:control design form (CDF), 768-769,

838-839controllability, 780-781degrees of freedom, 778dynamics:

disturbance, 444feedback, 444

loop pairing, 695operating window, 624-626,681,781,

788-789procedure, integrated, 834process decomposition, 831sequence of steps, 823temporal hierarchy, 825

Detuning factor, 678Deviation variables, 71,111Diagnostic:

model, 183tuning, 290

Difference equations:controllers, 367,493,595,994-995discrete models:

approximate, 923empirical, 188exact, 923,986

Differential equations:discrete form, 188,923,986linearization of, 70-72numerical solution:

error control, 84Euler, 83,423Runge-Kutta, 84

solution by:integrating factor, 895Laplace transforms, 102

Digital control:computing network, 359dynamic matrix control, 735internal model control, 595lead/lag, 493performance of PID, 367-369ringing, 370-371,982,992sampling:

hold, types of, 364-366period selection, 369

Digital control—Cont.sampling—Cont.

simulation, 423tuning modifications for, 370

Dimensional analysis, tuning, 278-286Direct-acting feedback, 396Distillation:

cascade control, 690composition control of:

inferential, 545-549interaction in, 637operating window, 625-626relative disturbance gain (RDG),

679-680tuning for, 648

decoupling control, 689dynamic matrix control of, 746-747,

754-756feedforward control of, 500-501industrial case study, 949-960modelling of:

empirical, 62,622-623fundamental, 157-163

regulatory control of:energy balance, 664material balance, 665

Distributed control system:advantages of, 361structure of, 359

Disturbance:causes, 7interaction effects isee Relative

disturbance gain)models, 220,224,415,444,496,666response, closed-loop:

frequency response, 412-418simulation, 422-425

Dominant variable, 779, 827Draining tank, 75-77,106-107Drawings, 12-13

instrument symbols, 889-892process equipment, 892-894valve symbols, 892

Dynamic compensation, 551Dynamic matrix control (DMC):

approximate inverse for, 729controller formulation, 737-738discrete step process model, 730-734feedback signal, 740-742future prediction, 735horizon, 737model, step-weight, 730move suppression, 743

Dynamic matrix control (DMC)—Cont.multivariable formulation, 744—748predictive structure, 728single-variable formulation, 738tuning, 750

Dynamics:dead time, 103, 140, 324, 328first-order systems, 57,137, 323, 328integrating process, 140-141, 564-566,

325,328recycle systems, 155, 840second-order systems, 138-140, 324,

328series systems, 143,328staged systems, 157iSee also Modelling procedure)

1007

Index

Economic value of control, 28-35Electrical circuit, 137, 138Emergency control systems, 20, 230-231,

794-799Empirical modelling:

dead time, 144,179-181,190diagnostics, 61, 183, 194experimental design for, 181, 188multivariable systems:

open-loop, 197,622partial closed-loop, 629, 670

process reaction curve, 179signal-to-noise, 182six-step procedure, 176statistical method, 188use in control analysis, 280, 338-343

Energy balance:in modelling, 53-54, 898strategy in distillation, 664

Energy reduction, control systems for, 23,716-717,791,861-866

Environmental protection, 21, 768, 797Equal-percentage characteristic, 521Equilibrium, ideal stage, 159Equilibrium, phase, 159, 538Error:

measures of control performance, 219in sensor measurement, 383, 773variable used by controller:

model predictive, 585, 741proportional-integral-derivative,

242-243

1008

Index

Euler:identity, 934numerical integration, 83

Evaporator, 676Evolutionary operation, 871Experimental modelling isee Empirical

modelling)Exponential filter:

analog, 390,393digital, 392,988predictive control, 593principle, 389

External feedback, 399External variable, 54,

Factor, partial fractions, 107,931Factorization, model, 590Feasible region isee Operating window)Feedback control:

block diagram for, 243,463,586,630components of loop, 212-213compared with feedforward, 488definition, 6negative, 6performance isee Control performance)pluses and minuses, 229positive, 142selecting variables in, 216-218,438,

536, 775, 779, 828iSee also PID; IMC; DMC)

Feedforward control:algorithms for:

digital, 492-493general derivation, 485lead/lag, 485-486transfer function, 488

block diagram for, 489design criteria for, 487

goal, 484digital implementation, 492examples:

chemical reactor, 495distillation, 501fired heater, 499-500heat exchanger, 497-498

feedback:combined with, 486,497comparison with, 488

Feedforward control—Cont.perfect, 484performance guidelines:

dynamic behavior, 491model error, 490

stability, effect on, 488,502tuning, 493

Fieldbus, 375Filtering:

algorithms:continuous, 390discrete, 392,988

aliasing in, 393low-pass, 390perfect, 390performance, effect on, 391reasons for, 389z-transform, 979

Final control element, 5,10,212-213,226, 438, 776-777

Final value theorem, 104,979Fine tuning, 289-293Finite difference, 366-367,493,923Fired heater:

cascade control, 494feedforward, 522-524industrial case study, 961-972loop pairing, 694-695outlet temperature control, 29

First-order system:continuous, 137discrete approximation, 922dynamic behavior, 59,137-138

Bode diagram, 323example systems, 137frequency response, 328time-domain responses, 136

series of:interacting, 145-148noninteracting, 143-145transfer function for, 144

Flash process:alarms for, 795-796control design for, 802control objectives for, 20-25,768-769controllability of, 787-788degrees of freedom, 787-788dynamic response of, 803inferential control of, 537-541operating window, 788-789safety control, 794-799

Flow:control, 13measurement, 387ratio, 499,684value, 80

Forcing function, 895Frequency distribution, 31-35Frequency response, 121

amplitude ratio, 121-122of basic systems, 323-326, 328Bode plot, 123closed-loop control performance,

412^20computer program for, 317,421direct evaluation, 122phase angle, 121,123of series systems, 144, 316-317shortcut from transfer function, 122in stability analysis:

Bode stability, 314-316transient, complete, 119-120

Furnace isee Fired heater)

Heat exchanger—Conf.cascade, 458dynamic model, 76-80feedback control transient, 256feedforward, 486linearizing characteristic, 523-524refrigeration, 475, 884-885steam condensing, 777stirred tank, 76-80

Heaviside, 932Hierarchy, 476, 826, 829High signal select, 713Histogram, 29-31Hold:

first order, 364zero-order, 364

Holdup time, 562Horizon:

input, 749output, 749

Hydrocracker control, 753

1009

Index

G

Gain:controller:

feedback, 245,587feedforward, 485nonlinear, 567

frequency dependent, 315margin, 338process, 87

disturbance, 224feedback, 224,254multivariable process, 627

steady-state, 58Gain scheduling, 518,529

H

Heat exchanger:with bypass:

feedback control, 784model, 76-80, 939-942numerator zero, 941recycle systems, 785transient response, 942

Identification isee Empirical modelling)IMC isee Internal model control)Impulse function, 101Inferential control:

block diagram, 537design criteria, 542design procedure, 543examples:

chemical reactor, 549-552combustion, 552-554distillation, 545-549flash process, 537-541

goal, 536multiple correlated measurements, 554

Initialization:controller, 245,402filtering, 392

Input:terminology for control, 6terminology for modelling, 53typical time functions, 220-222

Input-output isee Cause-effectrelationship)

Input processing:conversion, 212-213, 387filtering, 389

1010

Index

Input processing—Cont.units, 388validity, 387

Integral:Laplace transform of, 102numerical approximation, 366z-transform, 978

Integral stabilizability, 692Integral error measures:

IAE, integral of absolute value, 219IE, integral of error, 219,677ISE, integral of squared, 219ITAE, integral of product of time and

absolute, 219Integral mode:

advantage/disadvantage, 249equation for explicit mode, 248implicit isee Model predictive control)tuning constant, 248iSee also Anti-reset windup)

Integral windup isee Anti-reset windup)Integrating factor, 58, 895Integrating process:

dynamic behavior, 136general form, 140-141levels, 564stability, 307-308iSee also Level control)

Integrity, 637,672,692Interacting series, 145-148Interaction:

block diagram, 624controllability, effect on, 627,651

iSee also Decoupling)definition, 620integrity, effect on, 672-674,692, 850measure of isee Relative gain array)modelling:

empirical, 622fundamental, 621

operating window, effect on, 624-626,789

performance, feedback control:loop pairing, 671-681tuning, 682-683

stability, effect on, 638transfer function, 629-630tuning, 641-646iSee also DMC)

Internal model control (IMC):digital form, 595,994filter for, 593model inverse, approximate, 590,994performance, 597

Internal model control (IMC)—Cont.structure, 592tuning:

for IMC controller, 598for PID controller, 609

Inventories:control of isee Level)models for, 564-565reasons for and against, 562-563sizing, 562,572-574

Inverse:approximate, 590exact model, 588,729-730feedback as, 588

Inverse Laplace transform, 99Inverse response:

control performance, 430-431,444,996-1000

multivariable systems, 669-671open-loop, 152-155,943-946

ISE isee Integral error measures)ITAE isee Integral error measures)

Jacketed reactor, 476

Lag isee First-order system)Laplace transform:

applications:solving ODE, 102transfer function, 111

of common functions, 100definition of, 98of derivatives, 101of integrals, 102partial fractions, 107,931-935properties, 98-99

Lead:lead/lag algorithm, 485-486,595,687,

923time constant, 152

Least squares:as approximate inverse, 737assumptions in, 191

Least squares—Cont.in design of dynamic matrix control,

737-738empirical modelling, 188-190solution of linear problem, 191

Level:control of:

linear PI, 566nonlinear PI, 567

control objectives, averaging and tight,563-564

controller tuning, 568draining tank, 75-77inventory size, 572process model for:

non-self-regulating, 140, 565self-regulating, 75-77

sensors, 577series processes, 574-576

Limit cycle, 906Linear operator, 70Linear programming, 866-868Linearity, definition of, 70Linearization, 71-72

control loop, 517-529effect on stability analysis, 275, 284,

513-517Taylor's series, 71

Load isee Disturbance)Long-time behavior, 109, 119-121, 306,

936-937Low-pass filter, 390Low signal select, 710-713Lumped-parameter model, 47,53

M

Manipulated variable, 207,212, 218,226,243,276

Manual operation, 228Mass, conservation of, 53Master controller isee Cascade)Material, conservation of, 53Maximum deviation, 221Maximum overshoot, 220Measured variable:

accuracy, 383 iSee also Filtering)linearity, 387range, 383-384reproducibility, 383sensor dynamics, 212-216, 773

MIMO isee Interaction, Multiloopcontrol; Multivariable control)

Mixing process, with dead time:control of, 270-277,413-415model of, 271

Mixing process, three-tank:adaptive tuning for, 517-519control of:

derivative-only, 249-251integral-only, 248internal model, 595proportional-integral-derivative,

282-285, 330-332proportional-only, 245-248

mismatch from true process:due to nonlinearity, 283-285,

512-517effect on control performance,

431̂ *32effect on stability, 345-346

model of:empirical, 186fundamental, 223-224input-output, 223

Model predictive control (MPC):for cascade control, 606dead time, 606error, feedback, 585with feedforward control, 607filter for robustness, 592-593internal model control (IMC), 590perfect control, 587-588process inverse:

approximate, 590exact, 587-588

saturation of final element, 604Smith predictors, 600structure, 586transfer function, 592two-degree-of-freedom, 594zero-offset requirements, 587, 593, 601iSee also DMC)

Modelling procedure, 50approximate, 909empirical, 175fundamental, 53linearized, 71

Moments:definition, 909for impulse response, 910use in correlations, 281,286-287, 336,

598use in modelling, 912

Monitoring, 23, 799

1011M MIndex

1012H88HSIndex

Move suppression factor, 743,749Multiloop control:

block diagram for, 624,630comparison with single-loop, 616control performance:

input forcing, 663-669interaction, 628interactive dynamics, 669-671operating condition, 663

controllability, 626,651,780-781decoupling:

lead/lag, 687model sensitivity, 689

loop pairing, 671relative disturbance gain (RDG),

677-681tuning, 646-649,682iSee also Control design, Interaction)

Multivariable control:centralized:

model inverse for, 729,738structure, 728

iSee also Dynamic matrix control;Multiloop control)

N

Negative feedback, 6,141-142,207,242Niederlinski criterion, 692,694-695Noise:

effect on tuning, 275-276,292,915-920

frequency content, 423-425signal-to-noise ratio, 182iSee also Filtering)

Noninteracting series systems, 143Nonlinear:

control, 517, 520,570process, effect on operating window,

625-626,782,789process, effect on performance,

283-285,512saturation, 399-402,604,707,717iSee also Linearization)

Normal distribution, 30Numerical solution methods:

for algebraic equations, 902-903for differential equations, 82-84

Numerical solution methods—Cont.frequency response, 317,421for integrals, 366,917

Nyquist, 314

O

Objective function, 271, 736, 743, 864,866,917

Objectives, control, 20,268, 768, 838Offset, steady-state:

definition, 218, 240with feedback control, 246,249, 251with feedforward control, 488integral mode, 249,587level control, 571

On-off control:heating, 5,230model, 67-69

One-way decoupling, 690One-way interaction, 631, 636-637Open-loop operation, 228Open-loop transfer function:

G0lCs),316terminology, 328

Operability, 778Operating window, 26-27,226,440,

625-626,720-721,789Optimization:

constraints, 868control methods for:

control design, 861direct search, 870model-based, 866

in controller tuning:control objectives, 268,917correlations from, 281,284,598

plant economics:effect of variance, 31,33profit contours, 31,43

Order of system, 112Ordinary differential equations, 47,56,

102Output:

meaning for control, 6meaning for modelling, 53

Overdamped, 138-139Overshoot, 219-220

Packed bed:cascade control, 471-473empirical model, 202feedforward control, 495-497

Pade* approximation, 913Pairing, loop, 671Partial control, 779, 827Partial fraction expansion, 107,932-935

980Performance, isee Control performance)Period of oscillation, 121, 222, 315, 330

343Periodic behavior, 5, 67, 343, 906pH control, 527, 776Phase angle, 121-123Phase equilibrium:

in distillation, 159in flash process, 538K values for, 538relative volatility, 159

Phase margin, 340Physical realizability, 496,588PI, PID isee

Proportional-integral-derivativecontroller)

Pneumatic:control valve, 213controller, 257signal transmission, 212-213, 891

Polar form:complex numbers, 122, 316-318,421frequency response for series systems,

317Poles:

definition of, 113effect of control on, 247, 254-256, 259,

313effect on dynamic response, 109, 113,

310effect of process design on, 141-142,

151,155,157,425,440,564, 785,902,906

effect on stability, 109, 310Position (full) form of digital controller,

367Predictive control isee Model-predictive

control)Primary controller isee Cascade control)

Process dynamics:effect on control performance, 415,

426,438, 440, 663, 694effect on stability, 334effect of zeros, 152,939empirical modelling of, 196fundamental modelling of, 53linearized models, 74recycle process structures, 155series process structures, 152,939staged process structures, 157

Process examples, guide, 925-929Process reaction curve, 179, 187Product quality, 23, 768Profit function isee Objective function)Proportional:

controller mode, 245tuning constant, 245

Proportional band, 398Proportional-integral-derivative (PID)

controller:in adaptive control, 517in cascade control, 458,468̂ 169derivative mode, 250

effect on offset, 251effect on stability, 326

digital form of controller, 367-369frequency response, of controller,

366-367initialization, 245,402integral mode:

effect on dynamic response, 249effect on offset, 249effect on stability, 325, 336-337windup, 399

mode selection, 436output limits, 403proportional mode:

effect of dynamic response, 245,272effect on offset, 245effect on stability, 246

tuning:Ciancone, 281,286IMC, 609Lopez, 287multiloop, 641-646selection, 347Ziegler-Nichols, 329, 347

Proportional-only control, 245, 571Pulse, input function, 64, 101

1013

Index

1014

Index Quadratic dynamic matrix control, 751Quick-opening valve, 521

R

Ramp:input function, 93output response, 93

Random variable, normal distribution, 30Ratio control:

effect on stability, 519as feedforward, 499flow ratio, 499reset by feedback, 519,684

Reactor isee Chemical reactor)Realizable, 496,588Real-time operating system, 360Real-time optimization isee Optimization)Reconstruction of signal, 362Recycle:

advantages of, 155-157,785alternative source/sink, 832control of systems with, 785,832,

845-846effect of dynamic response, 156-157effect on stability, 156

Refrigeration, 475,885Regression isee Least squares)Relative disturbance gain (RDG):

integral error measure, 677loop pairing, 678-679tuning factor, 678

Relative gain array (RGA):calculation, 634control integrity, 637,672definition:

dynamic, 637steady-state, 633-634

interpretations, 636loop pairing, 672-674,695properties, 633-636stability, 637

Relative volatility, 159Reproducibility, sensor, 383,773Reset isee Integral)Reset time, 398

Reset windup isee Anti-reset windup)Resonant frequency, 414Reverse-acting feedback, 396Ringing controller, 368,992Rise time, 219Robustness:

importance, 241,512performance, 268-269,919stability, 338,345tuning, 268,919

Root locus, 312Runge-Kutta numerical integration, 83

Safety, 20-21alarms, 795basic process control, 794failure position of final elements, 386good practices, 797safety interlock system (SIS), 796safety valves, 797

Sampling isee Digital control)Saturation of controller output, 398,604,

707, 717Second-order system, 138-139Secondary controller isee Cascade)Select, signal:

degrees of freedom, 710design criteria, 715tuning, 714iSee also Constraints, control)

Selection of variables:controlled variables, 216,773,827-828manipulated variables, 216,226,438measured disturbances, 487secondary cascade, 461

Self-regulation, 141Sense isee Controller sense switch)Sensor:

accuracy, 383cost, 772-773dynamics, 215,773flow, 387identification symbols, 889level, 892noise, 276, 389,424, 879range or span, 383reliability, 387

Sensor—Cont.reproducibility, 383,773signal transmission, 890temperature, 388,536

Separable differential equation, 58, 895Set point, 218,242-243,458, 586Settling time, 220Shannon's sampling theorem, 362Signal:

conversion, 212analog to digital (A/D), 359digital to analog (D/A), 359electronic to pneumatic, 212

digital transmission, 373dynamics, 213electrical transmission, 212pneumatic transmission, 212ranges, 213

Signal-to-noise, 182Signal select, 710Simulation:

closed-loop system, 423,916performance measures, 917process dynamics, 83-84iSee also Digital control)

Sine input:amplitude ratio, 121-123first order, 123flow attenuation, 572typical input forcing, 136iSee also Frequency response)

Single-input single-output (SISO) iseeSingle-loop control)

Single-loop control, 5-6,208,218,243SIS isee Safety)Slave controller, 460Smith predictor:

system structure, 600tuning, 602zero offset, 601iSee also Model predictive control)

Snowball effect, 847Split range:

degrees of freedom, 706design criteria, 709tuning, 708iSee also Constraints, control)

Spring and dashpot, 137-138Stability:

analysis:Bode, 314-317complex plane plots isee Root locus)

Stability—Cont.analysis—Cont.

Nyquist, 314pole calculation, 308-313root locus, 312-313simulation, 248

chemical reactor, 902-906definition, bounded input-output,

303-304effect of controller tuning, 312effect of process dynamics, 334effect of sampling period, 367-370feedforward, 488of linearized system, 305-308margin, 338-340multiloop, 630,638

Staged systems isee Distillation)Standard deviation:

of averages, 394of data set, 30from set point, 221,466

Statistical modelling, 189Statistical process control:

capability index, 880-881goal of preventing disturbances, 876Shewart chart, 876specification limit, 881

Steady state:error (offset), 240feedforward control, 488operating window, 625-626

Steam heat exchanger:bypass, 784condensing, 777

Steam system:boiler, 27, 862header, 862turbines, 885

Steam trap, 777Step:

input function, 58, 136-138,162Laplace transform, 99test isee Process reaction curve)

Stiffness, 84Stirred tank (CST):

chemical reactor, 62,72, 85,438, 835,897

heat exchanger, 76-80,458,486, 523,939-943

mixer:one-tank, 52, 270,415

1015

Index

Stirred tank (CST)—Cont.mixer—Cont.

three-tank, 186,223,282,422-424,512,595-596

series reactors, 64,430,943typical assumptions, 52,899

Stochastic control performance, 293,424,879

Superposition, 70Surge tank, 119,562,572System definition, 52Systems analysis, 135

Tuning, feedback controller:digital PID control, 370dynamic matrix control, 750effect of process on, 281, 334,564-566,

645internal model control, 598multiloop PID, 645,682objectives isee Control, objectives)Smith predictor, 602stability margin:

gain margin, 338phase margin, 340iSee also Proportional-integral-

derivative, tuning)Tuning, feedforward controller, 496

Target, 585-586Taylor series approximation, 71Temperature control:

distillation, 545fired heater, 26,31,473,500,552,961flash drum, 21,538, 802stirred tank, 252-523

Three-mode controller iseeProportional-integral-derivativecontroller)

Time constant:empirical estimation, 179-180relation to process, 74,137,271,900,

942,944series of, 143-145

Time delay isee Dead time)Thermocouple, 388, 526Thermowell, 940Transfer function:

closed-loop, 244,462,488,586,629-630

controller, 252-253definition, 111, 118,983disturbance process, 224,415,666feedback process, 224,270-271, 622,

666instrument, 213matrix of, 624poles of, 113,255,259,312-313zeros of, 113,152

Transient isee Dynamics)Transmission interaction, 629Transportation delay, 103-104Tray, distillation, general balances, 159

uUltimate controller gain, 330,993Ultimate period, 330Underdamped process, 85,138-139,

253-256, 899-903Unstable systems:

closed-loop system, 308-317process without control, 307-308,

899-907Unsteady-state isee Dynamics)Utility systems:

fuel gas system, 501,810-811hot oil, 885steam system, 862iSee also Refrigeration)

vValidation, model, 60-61Valve:

automated control:capacity, 217,226, 385,438^141,

625-626characteristic, 520dynamic response, 213failure position, 386pneumatic power, 212-213range, 385

manual, 228, 892positioner, 474

Valve—Cont.safety relief, 797stem, 81, 213,474,520

Valve position controller, 718Variable:

continuous, 98dependent, 56,254deviation,71, 111discrete, 188-189, 365, 973external, 56,254manipulated, 5,208, 213,217

Variable structure:constraint control, 715multiple controllers, 716signal select, 710split range, 706valve position control, 718

Variance:definition, 30measure of performance, 221-222

Velocity form, controller, 367

wWeir, 159Wild stream, 499, 684Windup, reset isee Anti-reset windup)

1017

Index

z-transform, 973-975table, 975

Zero, sensor signal, 388Zero-order hold, 364,985Zeros of transfer function:

cancellation of pole and zero, 113effect on dynamic response, 152,943effect on stability, 113

Ziegler-Nichols:closed-loop tuning, 329, 342-343open-loop tuning, 347process reaction curve, 179-180