INDEX

Acceleration constant:

definition of, 280

determination from Bode diagram, 536

relationship to poles and zeros, 286–287

Accuracy, static, 277–288

ACET program, description of, 463

Ackermann’s formula for design using pole placement, 611–617

application example of, 613–617

Adaptive control systems, 252–254

human, 6

pitch flight, 589–591

Adjoint matrix, definition of, 104

Aeronautical control systems, 1

Aircraft:

adaptive pitch flight control of, 589–591

attitude control system for, 16

autopilots for, 14–16

Bell Boeing V-22 Osprey military tilt rotor, 16–17

Bell Boeing 609 commercial tilt rotor, 17

equations for landing phase, 172–173

examples of, 14–20

F-15 Eagle, 18–20

F-22 Raptor, 18–20

guidance system for, 14–15

instrument landing system for, 172–173

MD-11, 14–16

nose-wheel steering system for, 500

simulator for, 17–19, 266

UH-60 Black Hawk combat assault helicopter, 17–18

wind-shear detection for, 14

Airline reservation system, control of, 33

Amplidyne, 202

Analog computer, 94–101, 116–118, 133–134

Analogy circuit concept, 221–224

Analog-to-digital converters, 683–695

Analytic functions:

definition of, 41

derivative of, 40

example of, 41–42

Angle of departure, 418–420

Antennas of tracking radars, mechanical resonance of, 981–983

Antiskid control system, 7

Antisubmarine warfare system, control of, 33

Aquatic control system, 26

modeling equations for, 177–178

Armature-controlled dc servomotor, 198–202

decreasing time constant of, 230

elimination of disturbances with, 231–232

with back emf for stabilization, 231

Asymptotic stability, definition of, 236

Attitude control:

aircraft, 14–16

rocket, 501

space vehicle, 10–11

Automatic floor scrubbers, control of, 34

Automatic inventory control, 314–315

Automatic warehousing, 7, 314–315

Automation, 7

Automobile, model of leasing agency of, 35

Autopilots, 1, 14–16

control of airplane’s roll using, 1018–1020

Back emf, 230–231

Backlash, 275–277, 296

Band-pass network, circuit for, 79–81

Band-rejection network, circuit for, 79–81

Bandwidth:

definition of, 295–296

effect of compensation on, 532, 567–579

effect of noise on, 532

BASIC computer program, Bode diagram from, 386–389

Bioengineering control systems, 1

Biomedical control systems, 23–25

Block diagram, 82–86

reduction techniques, 83–84

Bode-diagram method, 362–398, 525–548

approximate closed-loop response, 541–548

approximate phase-shift from, 544–548

break frequency of, 368

compensation using, 528–541

computer programs for obtaining, 380–385

examples of, 372–380, 528–541

MATLAB used to obtain, 380–385

relationship to Nyquist diagram, 374–375

Bode’s theorems:

first theorem, 525–527

second theorem, 526–528

Boston elbow, 23–25

Branches, 86

Break-away point, 415–418

Break frequency, definition of, 368

Break-in point, definition of, 415–418

Bulk modulus of oil, definition of, 215

Cameras:

automatic focus control system for, 25–26

Nikon N6006 35-mm camera, 25–26

Capacitance:

of mechanical system, 223

of pressure system, 223

thermal, 223

Cascade compensation, methods of, 510–518

Cascaded elements, transfer function of, 82

Cauchy-Reimann conditions, 41

Cauchy’s theorem:

application to digital systems, 721

definition of, 350–352

principle of the argument, 350

Central Japan Railways Company, 11–14

Challenger, 8–9, 237–239

Characteristic equation, 83, 333–334

obtaining from classical methods, 334–335

obtaining from state variables, 335–340

Characteristic response, second-order system, 240–247

Chemical control systems, 1, 7, 32, 1020

equations for, 182–183

pH factor control of, 32

Circle criterion, see Generalized circle criterion

Circuit concept and analogy, 222–224

Classical approach, second-order system analysis, 240–247

Climate control system, 7

Closed-loop control system, definition of, 4–6

Closed-loop frequency response, relationship to time-domain, 405–408

Closed-loop resolvent matrix, definition of, 596

Closed-loop system matrix, definition of, 596

Closed-loop systems, transfer function, 82–95

CODAS-II program, description of, 462

Cofactors of matrices, definition of, 104

Column vector, 101–102

Command, control and communication system, 33

Command/control/communication:

airline reservation system, 33

antisubmarine warfare system, 33

control of, 33

ground traffic control system, 33

police command system, 33

satellite communication system, 33

strategic system, 33

Commercially available software:

ACET, 463

CODAS-II, 462

Ctrl-C, 461–462

description of, 456, 461–463

MATLAB, 461

Program CC, 462–463

Companion matrix, definition of, 110–111

Compensation:

Bode-diagram method of, 525–541

cascade-compensation techniques, 507–508, 510–518

definition of, 507

linear continuous system use of, 507–510

minor-loop feedback method of, 518–520

Nichols chart method of, 548–551

root locus method of, 549, 552–567

tradeoffs among methods of, 567–570

Complex variable, 39–43

analytic functions of, 39–42

definition of, 39

multivalued function of, 42–43

ordinary points of, 40

poles of, 42–43

singled-valued function of, 42–43

singularities of, 42

zeros of, 43

Complimentary sensitivity, definition of, 638

Computer programs:

ACET, 463

Bode diagram obtained using, 380–385

Codas II, 462

commercially available software, 456, 460–463

Ctrl-C, 461–462

margins, 375

MATLAB, 58–75, 118–121, 380–385, 437–442, 460–461

Nichols chart obtained using, 403–405

Program CC, 462–463

rlpoba, 429

rootangl, 429

root locus obtained using, 437–442

rootmag, 429

time response obtained using, 121–125, 393–398

wpmp, 402

Conditionally stable systems, 357–359

Constant magnitude loci, 400–402

Constant phase-angle loci, 400–402

Control-canonical form, 100

Controllability, definition of, 605–608

example of, 608

test for, 607

Control stroke, hydraulic system, 214

Control winding of ac servomotor, 206–207

Critical damping, definition of, 242

Cruise control system, 7

Ctrl-C program, description of, 461–462

Damped frequency oscillation, definition of, 241–247

Damping factor, 245

Damping ratio:

best damping ratio to use, 252–255

critical, 242

definition of, 242–245

nonlinear, 253–254

overdamped, 242–243

relation to the phase margin, 357

underdamped, 244–247

dc armature-controlled motor, 198–202

dc field-controlled servomotor, 203–206

dc generator, 197–198

dc Ward-Leonard system, 202–203

Dead-reckoning system, application of, 34

Decibel, definition of, 364

Delay time factor, Bode diagram of, 371–372

Depth control, submarine, 22, 28, 176

Design:

Bode-diagram method of, 528–541

cascade compensaton techniques, 510–518

linear continuous system, 507–591

minor-loop feedback method of, 518–520

Nichols chart method of, 548–551

root-locus method of, 552–556

Determinant, 104

Determinant of signal-flow graph, definition of, 88

Diagonal matrix, definition of, 102

Differentiation:

Bode diagram of, 366–367

Laplace transformation of, 54

Differentiation network, 79–81

Digital computer, data storage and retrieval for, 324–326

Disturbance:

signals, 94–95

torque, 231–232

Dominant poles, 555

Ecological control systems, 26, 177–178, 181–182, 497

modeling equations for, 177–178, 497

waste control system example of, 181–182

Economic considerations, 296, 482–483

Economic systems, control of, 1, 26, 31–32, 170

Eigenvalues, definition of, 338

Electro-mechanical devices:

armature-controlled dc motor, 198–202

dc generator, 197–198

field-controlled dc servomotor, 203–206

state-variable representation of, 201, 205–206, 209

transfer functions of, 195–213

two-phase ac servomotor, 206–213

Ward-Leonard system, 202–203

Elevator control system, 29, 31

English set of units, 194

conversion from International set of units, 194

Error constants, definition of, 279–280

Estimator design:

linear-state variable-feedback, 593–605, 617–630

pole placement, 611–617

Estimator gain matrix M, definition of, 617

Euler-Lagrange equation, 939

Feedback compensation, 507–510, 515–520, 522–525, 528–541, 548–657

Feedforward compensation, 164

Field-controlled dc motor, 203–206

automatic speed control, 5

Final-value theorem:

definition of Laplace transform, 55

Flight-control system, 14–16

Fluidic control systems, 478–479

Ford Motor Company, 8

FORTRAN programs:

Bode diagram obtained using, 386–398

root locus obtained using, 443–454

time-response obtained using, 122–124

Forward path:

definition of, 87

gain of, 87

Fourier integral, 48–50

definition of, 50

Fourier series:

complex form, 46–48

definition of, 43–44

trigonometric form of, 43–46

Fourier transform, definition of, 49–50

Frequency for maximum peaking, Nichols chart method for finding, 399

Frequency spectrum, 159

F-15 Eagle aircraft, 18–20

Gain margin, definition of, 357

multiple, 358–359

Gain-crossover frequency, definition of, 374

Gain-phase diagram, see Nichols chart

Gear ratio, 209–213

Gear trains, 209–213

illustrative problem of, 226–227

Generator constant, definition of, 197

Gimbal, gyroscope use of, 229

Grant’s rule, 421

Guidance systems, 1, 14–15

Gyroscope, 229

H^∞ control concepts, 636–651

examples illustrating, 642–645, 648–649

foundations of, 643–644

MIMO case, 641–643

SISO case, 644–649

theoretical concepts of, 637–641

Helicopter control system, 589–591

UH-60 Black Hawk, 17–18

Help-Mate robot, 10

High-speed trains, 10–14

Home heating system, 7, 27

Homogeneous solution, differential equations, 130

Human control systems, 6, 23–25, 30–31, 485–486, 492, 588–590

Human transfer function, 492–494, 500–501

Hydraulic devices, 213–219

motor and pump, 214–217

state-variable representation of, 216–217

transfer function of, 216, 218

valve-controlled motor, 217–219

Hydraulic-electrical analogies, 223

Hydraulic motor and pump, 214–217

state-variable representation, 216–217

transfer function of, 216, 218

Hydraulic valve-controlled motor, 217–219

transfer function of, 218

Hydrofoils, 1, 22–23

H.S. Denison, 578–579

pitch-control system for, 578–579

USS Pegasus (PHM-1), 22–23

IAE performance criterion, definition of, 291

Identity matrix, definition of, 102

Inductance:

of hydraulic systems, 223

of mechanical system, 223

Information theory, 38

Initial-value theorem:

definition of Laplace transform, 55

Input vector, definition of, 102

Instrument landing system, description of, 172–173

Integrating network, 78–80

Integration:

Bode diagram of, 365–366

Laplace transform of, 54–55

Interest accrual, control system for, 170–171

Internal combustion engine:

control of, 31

optimization of, 931

International set of units, 194

conversion to English set of units, 194

Inventory control systems, 7

Inverse Laplace transform, approach of, 56–58

Inverse of a square matrix, 106–107

ISE performance criterion, definition of, 291

ISTAE performance criterion, definition of, 291

ISTSE performance criterion, definition of, 291

ITAE performance criterion, 291, 294–295

definition of, 291

ITSE performance criterion, definition of, 291

Japan Railways Group, 10–14

Jitter, noise, 272, 296, 993

Kirchoff’s equations, 186–188, 223

Lag network, 78–81, 511–512

Bode-diagram compensatioin using, 510–511

compensation using, 528–530

Nichols chart compensation using, 548–551

root-locus compensation using, 557–567

tradeoffs of using, 567–570

Lag-lead network, 513–514

tradeoffs of using, 567–570

Laplace transform, 50–58

definition of, 51

differential equation solution, 54

exponential decay, 51–52

final-value theorem, 55

initial-value theorem, 55

inversion of, 56–58

inversion of using MATLAB, 71–75

properties of, 54–55

shifting theorem, 55

sinusoidal function, 52–53

tables of, 53, 683–684

unit ramp, 52

unit step, 51–52

useful examples of, 142–153

Lead network, 512, 515–517

Bode diagram compensation using, 530–541

circuit for, 80

linear-state variable feedback, 603–604

root locus compensation using, 552–555

tradeoffs of using, 567–570

Liberty Mutual Insurance Group, 24

Linear algebraic techniques, 649–651

Linear differential equation, 75–77, 130, 190

constant coefficient, 75–77, 190

homogeneous solution, 130

particular solution, 130

Linear-state variable feedback, 593–630

concept of, 593–605

controller and estimator design, 620–630

controller design using, 598–605

estimator design using, 617–620

general design procedure for, 593–598

regulator design using, 620–628

Linear system, 54–55, 507–508, 510–518, 525–541, 549–567

compensation of, 507–508, 510–518, 525–541, 549–567

Liquid-level control systems, 2–4, 488–489

Logarithm, definition of, 364

Logarithmic plot, 363–371

Log-magnitude versus phase plot, 363–371

Logspace MATLAB command, definition of, 381–382

Loop gain, definition of, 87

Lunar Excursion Module, equations for, 171–172

Lunar landing, 1, 171–172

M contours, definition of, 400–401

Machine-tool control, computer-controlled, 309–310, 322–323

Magnetic levitation, 10–14

Management control systems, 1

Man-machine control systems, 6, 23–25, 492–494, 500–501

Manual control systems, transfer function of, 237–239, 500–501

Map drive control system, 263–265

Mapping contours from s-plane to F(s)-plane, 344–349

Margins subroutine, Toolbox, 375

Marketing program, equations for, 180–181

Mason’s theorem:

application problems for, 90–93

definition of, 88

Mass-capacitance analogy, 223

Mass-inductance analogy, 223

MATLAB, 58–75

Bode diagram obtained using, 380–385

commands, 71–73

table of, 72–73

Control System Toolbox, 71, 73–74

data representation of, 68–71

Demonstration m-file, 59

description of, 58–75

fundamental concepts of, 66–68

Help, 59, 67

installation of, 61–64

Laplace transform inversion using, 71, 74–75

Modern Control System Theory and Design Toolbox, 58

Nichols chart obtained using, 402–405

Nonlinear Toolbox, 60

Nyquist diagram obtained using, 359–362

rise time curve obtained using, 289–290

root-locus diagram obtained from, 437–442

Simulink Toolbox, 60

Student Edition of MATLAB, 58, 61–62, 64

Symbolic Toolbox, 60

Synopsis File, 59

transformation from state-space to transfer function, 120–121

transformation from transfer function to state-space form, 119–120

transient response of systems using, 124–129

retrieving from anonymous FTP server, 58

tutorial, 59

Tutorial File, 59

Matrix:

addition/subtraction of matrices, 104–105

adjoint matrix, 104

algebra, 101–108

closed-loop resolvent, 596

cofactor of, 104

controller gain K, 594–595

diagonal matrix definition, 102

differentiation of a matrix, 107

estimator gain M, 617

identity matrix definition, 102

integration of a matrix, 108

inverse of a square matrix, 106–107

multiplication by a scalar, 105

multiplication of two matrices, 106

skew-symmetric matrix, 103

symmetric matrix, 103

transpose of a matrix, 103

zero matrix, 104

Matrix operations, rules of, 104–108

Maximization of K(σ) method, use of for root-locus method, 415–418

Maximum percent overshoot:

definition of, 247

root-locus determination of, 556–557

Maximum value of peaking, Nichols chart method for finding, 399–404

McDonneell Douglas Corporation, 14–16

Mechanical control systems, 189–95

rotational, 194–195

translational, 189–194

Mechanical devices:

state-variable representation of, 190–193, 195

tables of symbols, 190, 194

transfer functions of, 191

Mechanical-electrical analogies, 221–224

Metadyne, 202

Military control systems:

F-15 Eagle aircraft, 18–20

F-22 Raptor aircraft, 18–20

hydrofoils, 1, 22–23, 578–579

strategic missile submarine, 20–22

surface-effect ships, 22–23

Minimization nof K(σ) method, 415–418

Minimum-phase systems, definition of, 364

Missile systems:

acceleration-control steering, 262–263

launcher control system for, 3–5, 274–276

roll attitude control of, 501

roll-rate control of, 575–576

Modeling:

circuit concept and analogy, 221–224

transfer functions of control systems, 255–260

using principle of conservation, 221–222

Models of:

acquaculture control systems, 177–178

armature-controlled dc motor, 198–202

automobile leasing agency, 35

command, control, and communication system, 33

ecological control systems, 177–178, 497

economic systems, 26

field-controlled dc servomotor, 203–206

generator, 197–198

human control systems, 23–25, 30–31, 485–486, 492, 588–590

hydraulic motor and pump, 214–217

hydraulic valve-controlled motor, 217–219

interest accrual, 17–171

inventory control system, 7

mass-marketing campaign, 180–181

organization of an engineering corporation, 35

sociological systems, 179–180

thermal control systems, 219–221

Ward-Leonard system, 202–203

waste treatment, 181–182

Modern Control System Theory and Design Toolbox, 58

retrieving from anonymous FTP server, 58

table of commands used by, 74

Moment of inertia, determination of, 211–213

Motor constant, definition of, 208

Motor time constant, 208

Multivariable systems, definition of, 109

Myoelectric control signals, 24

NASA programs:

APOLLO 11, 171–172

Challenger, 8–9, 237–239

first untehered walk in, 237–239

International Space Station, 8–11

Lunar Excursion Module, 171–172

Shuttle Mission Simulator Motion-based trainer, 9, 12

Viking mission, 265–266

Navigation systems, accuracy of, 254, 296

Networks:

band-pass, 79–81

band-rejection, 79–81

differentiating, 79–81

integrating, 78–80

phase-lag, 510–512

phase-lag-lead, 513–514

phase-lead, 512–513

table of transfer functions for, 80–81

Newton’s law of motion, 191–192

Nichols chart, 398–405

compensation and design using, 548–551

MATLAB applied to obtain, 403–405

maximum value of peaking from, 402–404

Node, signal-flow graph, 86

Noise:

effect of bandwidth on, 532

effect of compensation on, 532, 567–569

Nonlinearities, 275–277, 296

backlash, 275–277, 296

Nonminimum-phase systems, definition of, 364–365

Nuclear control systems, 1

nuclear reactor control, 27–28

temperature-control sysem of, 577

Numerical methods, Runge-Kutta, 394

Nyquist’s stability criterion, 349–362

proof of, 685–688

Nyquist’s theorem:

diagram, 349–356

obtaining Nyquist diagram using MATLAB, 359–362

relationship to Bode diagram, 355, 357–359

Observer-canonical form, definition of, 100

Operational amplifiers, 94–99

illustrative example of, 98–101

table summarizing computing devices, 99

Ordinary points, definition of, 39–40

Output equation, definition of, 111

Output node, definition of, 86–87

Output vector, definition of, 109

Overdamped control system, definition of, 244

Overshoot:

curves of, 248–249

definition of, 247

Pacemaker, electronic, 315

Paper color control system, 232–234

Parabolic input, 280

Partial fraction expansion, Laplace transform inversion, 56-58

Particular solution, differential equation, 130

Path:

definition of, 87

gain of, 87

Peak time, 246

Performance indices, 291, 294–295

IAE, 291

ISE, 291

ISTAE, 291

ISTSE, 291

ITAE, 291, 294–295

ITSE, 291

Phase-crossover frequency, definition of, 374

Phase-lag network:

Bode-diagram compensation using, 510–512

characteristics of, 511

circuit for, 78–80

Nichols chart compensation using, 548–551

root-locus compensation using, 557–567

tradeoffs of using, 567–570

Phase-lag-lead network:

characteristics of, 513–514

circuit for, 78–80

tradeoffs of using, 567–570

Phase-lead network:

Bode-diagram compensation using, 530–532

characteristics of, 512–513

circuit for, 78–80

linear-state variable feedback using, 601–604

root-locus compensation using, 552–555

tradeoffs of using, 567–570

Phase margin:

definition of, 355

relation to damping ratio, 357

Phase-shift approximation, straight-line, 544–548

Phase-shift scale, 375–376

Phase-variable canonical form, 110–112

definition of, 111

PD compensators, 515–516, 520–521

PI compensators, 521–522

PID compensators, 520–522

Pole-placement design:

using Ackermann’s formula, 611–617

using linear-state-variable feedback, 593–605

Poles:

definition of, 42

of order n, 43

second-order, 241

simple, 42–43

Police command systems, control of, 33

Position constant:

definition of, 279

relationship to poles and zeros, 283–285

Positive feedback systems, root locus of, 434–437

Power consumption, considerations of, 295–296, 532

Principle of conservation, definition of, 221–222

Program CC, description of, 462–463

Programs:

Bode diagram obtained from, 380–385

CODAS II, 462

commercially available software, 456, 460–463

Ctrl-C, 461–462

margins, 375

MATLAB, 58–75, 118–126, 380–385, 437–440, 460–461

Nichols chart obtained from, 403–405

Program CC, 462–463

rlaxis, 428

rlpoba, 429

rootangl, 429

root locus obtained using, 437–442

rootmag, 429

time response obtained using, 121–125, 393–398

Prostheses, 23–25

Quadratic-phase lag network, Bode diagram of, 369–371

Quasilinear control systems, definition of, 206–207

Railroad control systems, 10–14

automatic control of, 14

high-speed trains, 10–14

Linear Express, 12

magnetic levitation used with, 10–13

Shinkansen, 13–14

Ramp input, 279–280

Rate feedback, linear system compensation using, 518–520

Reduction of multiloop systems:

block diagram, 84–85

signal-flow graph, 88–93

Regulator design, linear-state variable-feedback, 620–628

Regulex, 202

Resistance:

of hydraulic system, 223

of mechanical system, 223

of thermal system, 223

Rise time, definition of, 289

rlaxis subroutine, Toolbox, 429

rlpoba subroutine, Toolbox, 429

RoboKent, 34

Robotics:

automobile assembly using, 8, 266–267, 327–328

Ford Motor Company, 8

GMFanuc Robotics Corporation, 266–267, 327–328

Help-Mate, 8, 10

material transport using, 8, 10

NASA space shuttle using, 9

painting automobiles using, 266–267

RoboKent, 34

welding of automobiles using, 327–328

Robust control systems, 630–636

example illustrating, 632–636

Rocket flight, state and output equations for, 114–125

Root-locus method, 409–454, 549–567

angle of departure, 418–420

asymptotes for, 413–415

compensation and design using, 549–567

computer program for obtaining, 443–454

dipole, 559

dominant poles from, 555–556

examples of, 422–431, 549–567

Grant’s rule, 420–421

MATLAB applid to obtain, 437–443

maximization of K(σ) method, 415–417

negative feedback construction, 409–434

positive feedback construction, 434–437

Routh-Hurwitz method applied to, 418

transition method, 417–418

rootangl subroutine, Toolbox, 429

rootmag subroutine, Toolbox, 429

Rotorol, 202

Routh-Hurwitz stability criterion, 340–344, 418

application to root locus method, 418

Rudder control system, 29–30

Runge-Kutta, numerical integration using, 394

Satellite, equations for a spherical, 170

Satellite communications, control of, 33

Second-order control systems, 240–261

adaptive, 253–254

best damping ratio to use, 252–255

characteristics of, 240–247

modeling of, 255–260

nonlinear, 253–254

state-variable signal-flow graph, 248–252

step response of, 241–247

transient response of, 241–247

Sensitivity, 273–277, 637–649

complementary, 638

definition of, 274

Servomechanism, 5

Servomotor, 206–213

Settling time, deifnition of, 289

Shifting theorem, definition of, 55

Shinkansen train system, 13–14

Ship control systems, 1

Ship stabilization system, 323–324

Ship’s steering system, 29–30, 490

illustrative problem on, 304–305

Signal-flow graphs, 86–95

application problems using, 89–95

branches of, 86

definition of, 86–87

determinant of the graph for, 88

feedback loops for, 87

loop gain for, 87

Mason’s theorem to reduce, 88

nodes of, 86

path definition of, 87

path gain of, 87

reduction of, 88

relationship to state variables, 116–119

sink, definition of, 87

source, definition of, 86

Simulation diagrams, 98–101

Simulators, 310–311

MV-22A tilt rotor, Hughes Operational Flight Trainer of, 196

NASA Shuttle Mission Simulator Motion-based trainer, 8–9, 12

UH-60 Black Hawk Flight simulator, 17–19

Singularities, definition of, 42

Sink, defintiion of, 87

Size of equipment, considerations of, 295–296

Skew-symmetric matrix, definition of, 103

Sociological system model, equations for, 179–180

Source, definition of, 86

Space station, International, NASA, 8–11

Space vehicles:

attitude control of, 10–11

Challenger, 8–9, 237–239

International Space Station, 8–11

Lunar Excursion Module, 171–172

reentering earth’s atmosphere, 580–581

Viking spacecraft, 265–266

Specific heat of water, definition of, 220

Speed control systems, 5, 588

field-controlled dc motor with, 5

turbine, 588

Spring-mass-damper system, 189–195

Stability:

asymptotic, 236, 682–684

Bode method for determining, 362–398, 525–548

bounded input-bounded output, 332

comparison of various methods, 463–464

guidelines for use of methods, 463–464

Liapunov, 873, 879–896

linear continuous system, 331–591

local, 883

Nichols method for determining, 398–405

Nyquist method for determining, 349–362

Routh-Hurwitz method, 340–344, 418, 726–727

stabilization definition, 331–335

summary of linear system methods, 463–464

State equations, 110–112, 121–124, 186–189

computer soltion of, 121–124

derivation of, 110–112

electrical networks, 186–189

State space, definition of, 108

State of a system, definition of, 108

State transition equation:

definition of, 110

solution of, 135–137

State transition matrix, 129–135

derivation of, 129–130

examples of, 131–133

exponential series form for, 137–141

properties of, 130

State-variable concept:

advantages of using, 109

companion matrix, definition of, 110–111

concept of, 108–109

definition of, 108

phase-variable canonical form, 110–112

state of a system, 108

state space definition, 108

state vector definition, 108

State-variable diagram, 115–118

State-variable signal-flow graph, 116–118

State vector:

definition of, 102

norm of, 336

Static accuracy, 277–288

Steady-state error, 277–288

constants, 279–280

from Bode diagram, 534–536

Step function, unit, 51–52

Strategic missile submarines, USS Tennessee, SSBN-734, 20–22

Strategic systems, command/control/communication, 33

Submarines:

depth control system for, 22, 176, 480, 493

diving and control function for, 254

Subroutines from Modern Control System Theory and Design Toolbox:

margins, 375

rlaxis, 428

rlpoba, 429

rootangl, 429

rootmag, 429

wpmp, 402

Superposition, definition of, 801

Surface-effect ships, 22–23

Symmetric matrix, definition of, 103

Tables:

aceleration constant and error, 280

Bode-diagram program listings, 382–383, 385, 386–393

compensation methods comparison, 568–569

conversion factors in going from the International System to the English set of units, 194

ITAE form for zero ramp error, 295

ITAE form for zero step error, 295

Laplace transform, 53, 1023–1024

MATLAB commands and functions, 72–73

MATLAB program listings for:

Bode diagram obtained using, 382–383, 385

describing function, 836–837

Laplace transform inversion, 73–75

Nichols chart obtained using, 406

Nyquist diagram obtained using, 350, 362

root locus method obtained using, 439, 441

transformation from state-space to transfer function form, 121

transformation from transfer function to state-space form, 120

transient response of systems, 127

Modern Control System Theory and Design Toolbox, commands used by, 72–73

mechanical rotation symbols, 194

mechanical translation symbols, 190

network transfer functions, 80–81

operational amplifier computing devices, 99

position constant and error, 279

root-locus program listing, 450–453

steady-state constants summary, 281

time-response program listing, 124

transfer function of networks, 80–81

velocity constant and error, 280

Tank-level control system, 2–4, 32, 488–489

Taylor series expansion, 207

Television camera control system, 320–321

Temperature control system, 7, 27, 30

electric oven, 1–12

nuclear power plant, 577

xylene chemical process, 587

Thermal capacitance, 223

Thermal control systems, 7, 27, 30

transfer function of, 219–221

Thermal-electrical analogies, 224

Thermal resistance, 223

Tilt rotor aircraft, 16–17

Bell Boeing V-22 Osprey military tilt rotor, 16–17

Bell Boeing 609 commercial tilt rotor, 17

Time delay factor, 371–372, 431–434

Bode diagram of, 371–372

root locus of, 431–434

Time-domain response:

program for obtaining, 121–124, 393–398

relationship to frequency domain, 405–408

Time to the first peak:

definition of, 246

root-locus deermination of, 556

Time-invariant state equation, solution of, 135–137

Time response:

recurrence equation for, 121–124

recurrence equation sampling for, 122

Time-varying state equation, solution of, 111–112

Toolbox subroutines, Modern Control System Theory and Design, see Subroutines for Modern Control system Theory and Design Toolbox

Torpedo, control system for, 174–175

Torque constant, definition of, 200

Torque-speed curves, 207

Tracking, manual, 500–501

Traffic control system, ground, 33

Train control system, high speed, 10–14

Trainers, control system for, 310–311

aircraft, 5–33

NASA Shuttle Mission Simulator Motion-based trainer, 8–9, 12

UH-60 Black Hawk Flight Simulator, 17–19

Transfer-function concept:

armature-controlled dc motor, 198–202

block diagram transformations, 83–84

dc generator, 197–198

definition of, 77–78

field-controlled dc servomotor, 203–206

for common networks, 78–81

for systems, 82–86

hydraulic motor and pump, 214–217

hydraulic valve-controlled motor, 217–219

table of transfer functions, 80–81

thermal systems, 219–221

two-phase ac servomotor, 206–213

Ward-Leonard system, 202–203

Transformation between:

state-space to transfer function form, 120–121

transfer function to state-space form, 119–120

Transient response, 240–247, 288–290, 555–557

determination from root locus, 555–557

second-order systems, 240–247

Transition matrix, 129–135

derivation of, 129–130

examples of, 131–133

exponential series form for, 137–141

properties of, 130

state, 129–135

Transition from real axis method, root locus, 417–418

method use of, 424

Transitions Research Corporation, 10, 34

Transportation systems:

air, 14–20, 172–173, 500, 589–591

automobile, 35

hydrofoils, 1, 22–23, 578–579

rail, 10–14

space, 8–11, 171–172, 237–239, 271–272, 580–581

surface-effect ships, 22–23

underwater, 22, 176, 254, 176, 480, 493

Transpose of a matrix, definition of, 103

Turbine speed-control system, 588

Two-phase ac servomotor, 206–213

illustrative problem of, 224–226

nonlinear characteristics of, 206–207

state-variable representation of, 209

transfer function of, 208

with gear reducers, 209–213

Undamped natural frequency, definition of, 241

Underdamped control system, definition of, 245

Unit step function, 51–52

Van der Pol equation:

definition of, 171

Vector, state, 102

Velocity constant:

definition of, 279

determination from Bode diagram, 534–536

relationship to poles and zeros, 283–285

Velocity error, 279

Viking Mission, 265–266

Ward-Leonard system, 202–203

with armature-current feedback, 230

Warehousing, automatic, 314

Waste-treatment control system, equations for, 181–182

Weight considerations, 295–296

Wind-shear detection system, 14–15

wpmp subroutine, Toolbox, 402

Zero-error systems, definition of, 292–293

Zero-input stable, definition of, 332

Zero matrix, definition of, 104

Zeros, definition of, 43

Zero steady-state ramp error, definition of, 279

Zero steady-state step error, definition of, 279