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Dynamic Modeling and Control of Engineering Systems
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 (ISBN-13: 9780511287428)




Index



A-type elements , 4–7, 18, 31, 168, 198, 202, 219, 220, 222, 225

A-type variables. See Across variable

ac current , 172, 251

ac induction motor , 251

Acceleration

   rotational , 30

   translational , 16

Accumulator , 219

Across variable , 4–7, 31, 65, 170, 198, 213, 220, 222, 250, 254

Aliasing , 399

Amplifier

   operational , 179–186

   pneumatic , 239–243

Amplitude

   complex , 303

   Real , 303

Analytical solution , 81–111

Angle, shaft , 30

Antialiasing filter , 399

Asymptotic Bode diagrams , 309–311

Asymptotic frequency characteristics , 309–311

Asymptotic stability , 332

Automobile

   motion , 17–18

   steering , 330

   suspension system , 48

Backward-difference approximation , 391, 422

Bandwidth , 310

Bilinear transformation , 417

Biot number , 203

Block diagrams

   simulation , 143–147, 463

   system , 2

   transfer function , 286–293

Bode diagrams , 307–314

   asymptotic , 309–311

Break frequency , 310

Capacitance

   electrical , 170–171, 310

   fluid , 219–222

   pneumatic , 236

   thermal , 202

Capacitor , 4, 168, 170

   time-varying , 186

Capillary resistor , 223

Centrifugal pump , 253

Characteristic equation and roots , 83, 84, 93–98, 106–109

Charge. See Electrical capacitor

Classical solutions. See Analytical solution

Closed-loop control system , 356–357

Coefficient block , 143

Compatibility law , 23, 225

Compensation , 378–382

   feedback , 379–382

   feedforward , 379

   series , 379–382

Compensator

   lag , 380–382

   lag–lead , 381–382

   lead , 380–382

Complex number , 93

Complex plane , 274

Complex roots , 93–98

Complex variable

Conduction , 199–200

Continuity law , 225

Control laws

   on-off control , 366–367

   proportional (P) control , 367

   proportional–derivative (PD) control , 368

   proportional–integral (PI) control , 367

   proportional–integral–derivative (PID) control , 273, 368, 421

Controllers

   analog , 365–382

   digital , 421–423

Convection , 200–201

Convective heat transfer coefficient , 200

Corner frequency , 170–171, 310

Coulomb friction , 131, 154

Coupling coefficient , 249, 253

Critical damping , 96, 100

Current source , 169

D-type elements , 4, 7, 22, 33, 168, 173, 198, 219, 223

Damped natural frequency , 96, 415

Damper , 4

   rotational , 32, 39

   translational , 22

Damping ratio , 94–104, 415

dc motor , 251, 257

Decay ratio , 103

   logarithmic , 104

Decibel , 307

Delay time , 103, 369

Density

   mass , 222

   weight , 236

Differential equations

   linear , 54–71

   nonlinear , 34–44, 71–76

   solutions, analytical , 81–111

   solutions, numerical , 120–138

Digital control system , 410–424

Digital signal , 390

Digital simulation. See Simulation

Dirac’s delta function , 87, 398

Direct-transmission matrix , 65

Discrete-time system , 389–407

Discretized model of continuous system , 389–407

Distributed digital control system , 411

Disturbance , 361–364

   pulse transfer function , 420

   steady-state sensitivity , 361–364

   transfer function , 362

Divider , 144

Dominant roots , 106–109

Electric-field energy , 168, 171

Electrical capacitor. See Capacitor

Electrical circuits , 168–189

Electrical compensator. See Compensator

Electrical inductor. See Inductor

Electrical resistor. See Resistor

Electrical systems , 168–189

Energy

   converters , 249–254

     electromechanical , 250, 257

     fluid mechanical , 252

   dissipation , 4, 7

     elements , 7

electric field , 168, 171

   kinetic , 6, 18

   magnetic field , 4, 168, 172

   potential , 4, 19

   storage , 4–7

Equation(s)

   characteristic , 82–84, 93, 106

   differential , 54–76, 81–111

   input–output , 55–60, 68–71

   Laplace transformed , 276–277, 437

   state variable , 61–71

   s-transformed , 273–276

Error

   in numerical integration , 123–132

   steady-state , 357–361, 418–421

Error pulse transfer function , 418

Error transfer function , 358

Euler’s equation , 274, 428

Euler’s method , 121–123

   improved , 125–126

Expansion

   partial fraction , 403, 437

   Taylor series , 34–44

Exponential input function , 274–276

Feedback

   compensation , 378–382

   intentional or manmade , 329–331

   natural , 7, 146, 273

   negative , 329–331

   path , 146

Feedforward compensation. See Compensation

Field

   electric. See Electric field

   magnetic. See Magnetic filed

Filter

   antialiasing , 399

   Low-pass , 310

Final-value theorem , 358–364, 433

First law of thermodynamics , 202

First-order models , 84–92

Flow rate

   charge (electric) , 168–169

   heat , 198–201

   mass , 235

   volume , 220–228

   weight , 235

Fluid

   capacitance , 219–222

   capacitor , 220–222

   coupling , 33, 39, 236–237

   inertance , 4, 222, 237

   inertor , 222, 237

   pump , 253

   resistance , 4, 223, 237–238

   resistor , 223, 237–238

   sources , 224

Flux linkage , 171, 187

Force , 16

Forcing function

   impulse , 87

   ramp , 360

   sinusoidal

   step , 85, 359

Fourier series , 307, 427–431

Fourier transform , 427–431

Free-body diagram , 19

Free response , 82, 84, 93

Frequency analysis , 302–323

Frequency response , 302–323

Frequency, natural. See Natural frequency

Friction

   Coulomb , 131, 154

   nonlinear , 39, 131, 153

   viscous , 22, 32

Gain , 341, 467

Gain margin , 341

Gating function , 398

Gear

   ratio , 115

   train , 115

Guard filter. See Antialiasing filter

Huen’s method , 125

Higher-order models , 106–109

Holding device , 396–400

Homogeneous solution , 82, 84, 93, 100, 109

Hooke’s law , 19

Hurwitz determinants , 335

Hurwitz stability criterion , 334

Hydraulic orifice , 224, 227, 230

Hydraulic pump , 253

Hydraulic resistance. See Resistance

Hydraulic turbine , 253

Impulse function , 87

Impulse response , 90, 94

Incremental resistance , 175

Incremental spring constant , 20, 39

Incremental variables , 37–44

Inductance , 4, 168

Inductor , 168, 171–172

   time-varying , 187

Inertance. See Fluid inertance

Inertia

   rotational , 30

   translational. See Mass

Initial conditions , 82, 142, 144, 148, 276, 437

   at t =, 0− , 437

   at t =, 0+ , 82

Initial-value theorem , 433

input , 1, 55

   exponential , 274–276

   matrix , 65

   simulation , 142

   variables , 1, 55

Input–output models

   of continuous models , 55–60, 71–76

   of discrete-time systems , 390–394

Instability

   numerical computation , 133–138

   system. See Stability

Integration

   numerical , 120–138

   role of , 4, 18

   step-size , 129–132

Integrator , 144, 186

Inverse Laplace transform , 432

Inverse z transform , 402

Kinetic energy , 6, 18

Kirchhoff’s current law , 170

Kirchhoff’s voltage law , 170

Lag. See Time lag

Laminar flow , 224

Laplace transform , 276–277, 437

   basic properties , 433

   definition , 432

   equation , 199

   inverse , 432

   table of basic transforms , 435

Linearization , 34–44

   error , 43

Logarithmic decay ratio , 104

Loop method , 177

Loop variables , 177

Low-pass filter , 310

Lumped-parameter models. See Model

Lyapunov’s definition of stability , 332

Magnetic-field energy. See Energy

Mapping between the s and z planes , 412–418

Marginal stability , 94, 339

Mass , 16–19

Mathematical model. See Model

Matrix

   direct transmission , 65

   input , 65

   output , 65

   state , 65

Maximum overshoot , 103

Mechanical systems , 14–45

   rotational , 16–30

   translational , 30–34

Mixed systems , 249–261

Model , 2

   continuous , 4, 54–76

   discrete , 4, 390

   discretized , 4, 390

   distributed , 4

   Input–output , 55–60, 71–76

     of discrete-time systems , 390–396

   Linear , 4, 54–76

   Linearized , 34–44

   Lumped , 4

   Nonlinear , 4, 71–76

   Second-order , 92–105

   State

     of continuous systems , 61–68

     of discrete-time systems , 394–396

   Stationary , 251–252

   time-varying , 4

Motion

   rotational , 30–34

   translational , 16–30

Motor

   ac induction , 251

   dc , 251, 257

   electrical , 251–252, 257

   hydraulic , 252, 259

Multi-input, multi-output system , 60

Multiplier , 144

Natural frequency , 60, 94–100, 311

Newton’s laws , 16

Node method , 176

Node variables , 176

Nonlinear system. See Model

Normal operating point , 37

Numerical integration , 120–138

Nyquist frequency , 398

Nyquist stability criterion , 338–341

Octave , 311

On–off control. See Two-position control

Open-loop control system , 356

Operational amplifier , 179–186

Ordinary differential equations , 54–76

   analytical solution , 81–111

   numerical solution , 120–138

Orifice

   hydraulic , 224, 227, 230

   pneumatic , 237

Oscillations , 94, 101, 370

Output

   matrix , 65

   variables , 2, 55, 142

Overdamped system , 101

Overshoot , 103

Partial differential equations , 4, 15, 199

Partial fraction expansion method , 403, 437

Particular integral , 82

Passive systems , 329

Peak time , 102

Period of oscillations , 101

Periodic functions , 307, 427

Phase , 303, 307

Phase margin , 342

Pneumatic amplifier , 239–243

Pneumatic capacitance , 236

Pneumatic inertance , 237

Pneumatic orifice , 237

Pneumatic resistance , 237–238

Pneumatic systems , 235

Polar plots , 317–319

Poles , 344–347, 412–418

Porous plug resistor , 237

Power , 249–254

Pressure

   absolute , 220

   gauge , 220

   reference , 220

Proportional (P) control , 367

Proportional–derivative (PD) control , 368

Proportional–integral (PI) control , 367

Proportional–integral–derivative (PID) control , 273, 368, 421

   position form , 422

   velocity form , 422

Pulse function , 89

Pulse transfer function , 405–407

Pump

   centrifugal , 253

   hydraulic , 253

Quantization , 390

Rack and pinion , 115

Radiation thermal , 201

Ramp input , 360, 419

Reference

   frame of , 16

   nonaccelerating , 16

   pressure , 220

   velocity , 16

   voltage , 169

Resistance

   electrical , 169, 173

   hydraulic , 220, 223

   incremental , 175

   pneumatic , 237–238

   thermal , 202

     conductive , 203

     convective , 203

     radiative , 203

Resistor

   capillary , 223

   electrical , 169, 173, 186

   fluid , 223, 237–238

   nonlinear , 174

   time-varying , 186

Rise time , 103

Root-locus method , 344–347

Rotational system , 16–30

Round-off error. See Error, numerical integration

Routh stability criterion , 336–337

Runge–Kutta method , 126–129

s domain , 274–276, 413

s plane , 274–276, 413

   mapping to z plane , 413

Sampling device , 396–400

Sampling frequency. See Sampling time

Sampling time , 392, 398

Second-order models , 92–105

Self-tuning , 370

Sensitivity to disturbances , 361–364, 420

Series compensation , 379–382

Sevoactuator, electrohydraulic , 228–235

Settling time , 103

Shannon’s theorem , 398

Signal

   digital , 390

   periodical , 427

   sampled-data , 390

   sinusoidal , 275

Simplification (dominant roots) , 106–109

Simulation , 141–164

Simulation block diagrams , 143–147, 463

Single-input–single-output system , 55

Sinusoidal excitation , 275

Small-perturbation analysis , 37–44, 203, 240

Source

   current , 169

   flow , 224

   pressure , 224

   voltage , 169

Specific heat , 199, 202

Spring

   constant , 4

   real , 14

   rotational , 31

   stiffness , 19

   translational , 19–22

Stability

   asymptotic , 332

   of discrete-time systems , 415

   gain margin , 341

   Hurwitz criterion , 334

   Lyapunov’s definition , 332

   marginal , 94, 339

   necessary condition for , 334

   numerical computation , 133–138

   Nyquist criterion , 338–341

   phase margin , 342

   Routh criterion , 336–337

State , 61, 62

   matrix , 65

   model equations , 63, 71–76

   model of discrete-time systems , 394–396

   output equations , 64

   space , 61, 62

   trajectory , 62

   variables , 61

     auxiliary , 69

     selection , 65

   vector , 61, 62

Static position error coefficient , 359, 419

Static velocity error coefficient , 360, 420

Stationary system , 251–252

Steady sinusoidal excitation , 302–323

Steady–state control error , 357–361, 418–421

   in response to ramp input , 360–361, 419–421

   in response to step input , 359–360, 419

Steady-state disturbance sensitivity , 361–364, 420

Stefan–Boltzmann law , 201

Step function , 85

Step response , 86, 98

Stiff system , 133–138

Superposition , 89

System

   continuous , 4, 54–76

   discrete-time , 4

   dynamic , 1–4

   electrical , 168–189

   fluid , 219–244

   linear , 4

   lumped-parameter , 4

   mass–spring–damper , 25–26, 104–105, 145

   mechanical , 14–45

   mixed , 249–261

   model , 1–4, 54–76

   nonlinear , 4

   pneumatic , 235

   spring–damper , 23

   stable , 329–352

   stationary , 251–252

   thermal , 198–213

   type , 4, 359–361, 419–420

Table of Laplace and z transforms , 435

Taylor series , 34–44

Thermal capacitance , 203

Thermal conductivity , 199

Thermal resistance , 198, 202–204

Thermal systems , 198–213

Third-order models , 106–109

Through variable , 4–7, 22, 32, 65, 170, 172, 213, 222, 254

Time constant , 85

Time delay , 103, 156, 369

Time step size , 129–132, 142, 150, 390

   See also Sampling time

Torque , 30–34

Transducer

   electromechanical , 250, 257

   energy converting , 249–254

   fluid mechanical , 252

   mechanical translation to mechanical rotation , 249

   signal converting , 254

Transfer function , 273–299

   block diagrams , 286–293

   closed-loop , 289, 334

   frequency-response , 302–307

Transformer , 172

Transient response , 84–111, 364–365, 412–418

Translational systems , 16–30

Truncation error. See Error, numerical integration

T-type element , 4–7, 22, 32, 168, 219, 222

T-type variable. See Through variable

Tuning rules of Ziegler and Nichols , 368–370

Turbine , 253

Turbulent flow , 224

Two-position control , 366–367

Type of system , 4, 359–361, 419–420

Underdamped system , 99–100

Unit impulse function. See Impulse function

Unit impulse response. See Impulse response

Unit step function. See Step function

Unit step response. See Step response

Unstable system. See Stability

Valve , 228

Variable-displacement hydraulic motor , 259

Velocity

   rotational , 30

   translational , 16–19

Vibration absorber , 28

Viscous friction , 22, 32

Voltage source , 169

Volume chamber , 221

Weighting sequence , 406

Wind-up of a control error , 422

z domain , 400–407

z transform , 400–407

   inverse , 402

   one-sided , 400

   table of basic transforms , 435

   theorems , 402

Zero-order hold (ZOH) , 396–400

Zeros , 347

Ziegler–Nichols tuning rules , 368–370


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