SENSORS AND
ACTUATORS Control Systems
Instrumentation
CLARENCE W. de SILVA
( röC) CRC Press \ > ^ ' Taylor St Francis Group
Boca Raton London New York
CRC Press is an imprint of the Taylor & Francis Group, an informa business
Contents
1 Control, Instrumentation, and Design 1 1.1 Introduction 1 1.2 Control Engineering 2
1.2.1 Instrumentation and Design 4 1.2.2 Modeling and Design 5
1.3 Control System Architectures 6 1.3.1 Feedback Control with PID Action 7 1.3.2 Digital Control 8 1.3.3 Feed-Forward Control 10 1.3.4 Programmable Logic Controllers 11
1.3.4.1 PLC Hardware 13 1.3.5 Distributed Control 15
1.3.5.1 A Networked Application 15 1.3.6 Hierarchical Control 17
1.4 Organization of the Book 19 Problems 21
2 Component Interconnection and Signal Conditioning 27 2.1 Component Interconnection 28 2.2 Impedance Characteristics 28
2.2.1 Cascade Connection of Devices 29 2.2.2 Impedance Matching 33 2.2.3 Impedance Matching in Mechanical Systems 34
2.3 Amplifiers 37 2.3.1 Operational Amplifier 38
2.3.1.1 Use of Feedback in Op-Amps 41 2.3.2 Voltage, Current, and Power Amplifiers 42 2.3.3 Instrumentation Amplifiers 44
2.3.3.1 Differential Amplifier 44 2.3.3.2 Common Mode 46
2.3.4 Amplifier Performance Ratings 47 2.3.4.1 Common-Mode Rejection Ratio 49 2.3.4.2 AC-Coupled Amplifiers 51
2.3.5 Ground-Loop Noise 51 2.4 Analog Filters 52
2.4.1 Passive Filters and Active Filters 55 2.4.1.1 Number of Poles 56
2.4.2 Low-Pass Filters 56 2.4.2.1 Low-Pass Butterworth Filter 59
2.4.3 High-Pass Filters 61 2.4.4 Band-Pass Filters 63
2.4.4.1 Resonance-Type Band-Pass Filters 64 2.4.5 Band-Reject Filters 67
2.5 Modulators and Demodulators 69 2.5.1 Amplitude Modulation 73
2.5.1.1 Modulation Theorem 73 2.5.1.2 Side Frequencies and Side Bands 75
2.5.2 Application of Amplitude Modulation 75 2.5.2.1 Fault Detection and Diagnosis 76
2.5.3 Demodulation 77 2.6 Analog-Digital Conversion 78
2.6.1 Digital to Analog Conversion 81 2.6.1.1 Weighted Resistor DAC 81 2.6.1.2 LadderDAC 83 2.6.1.3 DAC Error Sources 85
2.6.2 Analog to Digital Conversion 86 2.6.2.1 Successive Approximation ADC 87 2.6.2.2 Dual-Slope ADC 88 2.6.2.3 Counter ADC 91 2.6.2.4 ADC Performance Characteristics 92
2.7 Sample-and-Hold Circuitry 94 2.8 Multiplexers 96
2.8.1 Analog Multiplexers 96 2.8.2 Digital Multiplexers 98
2.9 Digital Filters 99 2.9.1 Software Implementation and Hardware Implementation 99
2.10 Bridge Circuits 100 2.10.1 Wheatstone Bridge 101 2.10.2 Constant-Current Bridge 103 2.10.3 Hardware Linearization of Bridge Outputs 105 2.10.4 Bridge Amplifiers 105 2.10.5 Half-Bridge Circuits 105 2.10.6 Impedance Bridges 107
2.10.6.1 Owen Bridge 108 2.10.6.2 Wien-Bridge Oscillator 109
2.11 Linearizing Devices 110 2.11.1 Linearization by Software 112 2.11.2 Linearization by Hardware Logic 113 2.11.3 Analog Linearizing Circuitry 114 2.11.4 Offsetting Circuitry 115 2.11.5 Proportional-Output Circuitry 116 2.11.6 Curve-Shaping Circuitry 118
2.12 Miscellaneous Signal-Modification Circuitry 119 2.12.1 Phase Shifters 119 2.12.2 Voltage-to-Frequency Converters 121 2.12.3 Frequency-to-Voltage Converter 123 2.12.4 Voltage-to-Current Converter 124 2.12.5 Peak-Hold Circuits 125
2.13 Signal Analyzers and Display Devices 127 2.13.1 Signal Analyzers 128 2.13.2 Oscilloscopes 129
2.13.2.1 Triggering 129 2.13.2.2 Lissajous Patterns 130 2.13.2.3 Digital Oscilloscopes 132
Problems 133
3 Performance Specification and Analysis 145 3.1 Parameters for Performance Specification 145
3.1.1 Perfect Measurement Device 146 3.2 Time-Domain Specifications 146
3.2.1 RiseTime 146 3.2.2 DelayTime 147 3.2.3 Peak Time 147 3.2.4 SettlingTime 147 3.2.5 Percentage Overshoot 147 3.2.6 Steady-State Error 148 3.2.7 Simple Oscillator Model 148 3.2.8 Stability and Speed of Response 150
3.3 Frequency-Domain Specifications 151 3.3.1 Gain Margin and Phase Margin 153 3.3.2 Simple Oscillator Model 154
3.4 Linearity 155 3.4.1 Saturation 155 3.4.2 DeadZone 156 3.4.3 Hysteresis 156 3.4.4 The Jump Phenomenon 157 3.4.5 Limit Cycles 157 3.4.6 Frequency Creation 157
3.5 Instrument Ratings 158 3.5.1 Rating Parameters 159
3.6 Bandwidth Design 161 3.6.1 Bandwidth 161
3.6.1.1 Transmission Level of a Band-Pass Filter 162 3.6.1.2 Effective Noise Bandwidth 162 3.6.1.3 Half-Power (or 3dB) Bandwidth 163 3.6.1.4 Fourier Analysis Bandwidth 163 3.6.1.5 Useful Frequency Range 164 3.6.1.6 Instrument Bandwidth 164 3.6.1.7 Control Bandwidth 165
3.6.2 Static Gain 165 3.7 Aliasing Distortion due to Signal Sampling 170
3.7.1 Sampling Theorem 170 3.7.2 Antialiasing Filter 171 3.7.3 Another Illustration of Aliasing 174
3.8 Bandwidth Design of a Control System 177 3.8.1 Comment about Control Cycle Time 178
3.9 Instrument Error Analysis 179 3.9.1 Statistical Representation 179 3.9.2 Accuracy and Precision 180 3.9.3 Error Combination 181
3.9.3.1 Absolute Error 182 3.9.3.2 SRSS Error 182
3.10 Statistical Process Control 189 3.10.1 Control Limits or Action Lines 190 3.10.2 Steps of SPC 190
Problems 191
4 Analog Sensors and Transducers 207 4.1 Terminology 207
4.1.1 Motion Transducers 209 4.2 Potentiometer 211
4.2.1 Rotatory Potentiometers 212 4.2.1.1 Loading Nonlinearity 212
4.2.2 Performance Considerations 214 4.2.3 Optical Potentiometer 218
4.3 Variable-Inductance Transducers 220 4.3.1 Mutual-Induction Transducers 221 4.3.2 Linear-Variable Differential Transformer/Transducer 222
4.3.2.1 Phase Shift and Null Voltage 222 4.3.2.2 Signal Conditioning 226
4.3.3 Rotatory-Variable Differential Transformer/Transducer 230 4.3.4 Mutual-Induction Proximity Sensor 232 4.3.5 Resolver 233
4.3.5.1 Demodulation 234 4.3.5.2 Resolver with Rotor Output 234
4.3.6 Synchro Transformer 235 4.3.7 Self-Induction Transducers 237
4.4 Permanent-Magnet Transducers 238 4.4.1 DC Tachometer 238
4.4.1.1 Electronic Commutation 239 4.4.1.2 Modeling and Design Example 239 4.4.1.3 Loading Considerations 242
4.4.2 Permanent-Magnet AC Tachometer 242 4.4.3 AC Induction Tachometer 243 4.4.4 Eddy Current Transducers 244
4.5 Variable-Capacitance Transducers 246 4.5.1 Capacitive Rotation Sensor 246 4.5.2 Capacitive Displacement Sensor 247 4.5.3 Capacitive Angular Velocity Sensor 250 4.5.4 Capacitance Bridge Circuit 250 4.5.5 Differential (Push-Pull) Displacement Sensor 252
4.6 Piezoelectric Sensors 253 4.6.1 Sensitivity 254 4.6.2 Accelerometers 255 4.6.3 Piezoelectric Accelerometer 255 4.6.4 Charge Amplifier 257
4.7 Effort Sensors 260 4.7.1 Force Causality Issues 261
4.7.1.1 Force-Motion Causality 261 4.7.1.2 Physical Realizability 263
4.7.2 Force Control Problems 266 4.7.2.1 Force Feedback Control 266 4.7.2.2 Feedforward Force Control 266
4.7.3 Impedance Control 269 4.7.4 Force Sensor Location 272
4.8 Strain Gages 273 4.8.1 Equations for Strain-Gage Measurements 273
4.8.1.1 Bridge Sensitivity 276 4.8.1.2 The Bridge Constant 277 4.8.1.3 The Calibration Constant 279 4.8.1.4 Data Acquisition 282 4.8.1.5 Accuracy Considerations 282
4.8.2 Semiconductor Strain Gages 283 4.8.3 Automatic (Seif) Compensation for Temperature 287
4.9 Torque Sensors 289 4.9.1 Strain-Gage Torque Sensors 290 4.9.2 Design Considerations 292
4.9.2.1 Strain Capacity of the Gage 295 4.9.2.2 Strain-Gage Nonlinearity Limit 295 4.9.2.3 Sensitivity Requirement 296 4.9.2.4 Stiffness Requirement 296
4.9.3 Deflection Torque Sensors 301 4.9.3.1 Direct-Deflection Torque Sensor 301 4.9.3.2 Variable-Reluctance Torque Sensor 303
4.9.4 Reaction Torque Sensors 303 4.9.5 Motor Current Torque Sensors 305 4.9.6 Force Sensors 307
4.10 Tactile Sensing 307 4.10.1 Tactile Sensor Requirements 309 4.10.2 Construction and Operation of Tactile Sensors 310 4.10.3 Optical Tactile Sensors 312 4.10.4 Piezoresistive Tactile Sensors 314 4.10.5 Dexterity 315 4.10.6 A Strain-Gage Tactile Sensor 315 4.10.7 Other Types of Tactile Sensors 317 4.10.8 Passive Compliance 317
4.11 Gyroscopic Sensors 318 4.11.1 RateGyro 319 4.11.2 Coriolis Force Devices 320
4.12 Optical Sensors and Lasers 320 4.12.1 Fiber-Optic Position Sensor 321 4.12.2 Laser Interferometer 322 4.12.3 Fiber-Optic Gyroscope 323 4.12.4 Laser Doppler Interferometer 324
4.13 Ultrasonic Sensors 326 4.13.1 Magnetostrictive Displacement Sensors 327
4.14 Thermofluid Sensors 328 4.14.1 Pressure Sensors 328 4.14.2 Flow Sensors 329 4.14.3 Temperature Sensors 332
4.14.3.1 Thermocouple 332 4.14.3.2 Resistance Temperature Detector 333 4.14.3.3 Thermistor 333 4.14.3.4 Bi-Metal Strip Thermometer 334
4.15 Other Types of Sensors 334 Problems 335
5 Digital Transducers 357 5.1 Advantages of Digital Transducers 357 5.2 Shaft Encoders 359
5.2.1 Encoder Types 359 5.3 Incremental Optical Encoders 363
5.3.1 Direction of Rotation 364 5.3.2 Hardware Features 365 5.3.3 Displacement Measurement 366
5.3.3.1 Digital Resolution 367 5.3.3.2 Physical Resolution 368 5.3.3.3 Step-Up Gearing 369 5.3.3.4 Interpolation 371
5.3.4 Velocity Measurement 371 5.3.4.1 Velocity Resolution 372 5.3.4.2 Step-Up Gearing 374
5.3.5 Data Acquisition Hardware 375 5.4 Absolute Optical Encoders 377
5.4.1 GrayCoding 377 5.4.1.1 Code Conversion Logic 378
5.4.2 Resolution 379 5.4.3 Velocity Measurement 380 5.4.4 Advantages and Drawbacks 380
5.5 Encoder Error 381 5.5.1 Eccentricity Error 382
5.6 Miscellaneous Digital Transducers 385 5.6.1 Digital Resolvers 385 5.6.2 Digital Tachometers 387 5.6.3 Hall-Effect Sensors 388 5.6.4 Linear Encoders 389 5.6.5 Moire Fringe Displacement Sensors 390 5.6.6 Cable Extension Sensors 393 5.6.7 Binary Transducers 394
Problems 396
6 Stepper Motors 405 6.1 Principle of Operation 405
6.1.1 Permanent-Magnet (PM) Stepper Motor 406 6.1.2 Variable-Reluctance (VR) Stepper Motor 409 6.1.3 Polarity Reversal 409
6.2 Stepper Motor Classification 411 6.2.1 Single-Stack Stepper Motors 413 6.2.2 Toothed-Pole Construction 416 6.2.3 Another Toothed Construction 419 6.2.4 Microstepping 421 6.2.5 Multiple-Stack Stepper Motors 422
6.2.5.1 Equal-Pitch Multiple-Stack Stepper 423 6.2.5.2 Unequal-Pitch Multiple-Stack Stepper 424
6.2.6 Hybrid Stepper Motor 425 6.3 Driver and Controller 426
6.3.1 Driver Hardware 428 6.3.2 Motor Time Constant 430
6.4 Torque Motion Characteristics 432 6.4.1 Static Position Error 438
6.5 Damping of Stepper Motors 439 6.5.1 Mechanical Damping 440 6.5.2 Electronic Damping 443 6.5.3 Multiple Phase Energization 446
6.6 Stepping Motor Models 446 6.6.1 A Simplified Model 447 6.6.2 An Improved Model 448
6.6.2.1 Torque Equation for PM and HB Motors 449 6.6.2.2 Torque Equation for VR Motors 449
6.7 Control of Stepper Motors 450 6.7.1 Pulse Missing 450 6.7.2 Feedback Control 452 6.7.3 Torque Control through Switching 454 6.7.4 Model-Based Feedback Control 455
6.8 Stepper Motor Selection and Applications 456 6.8.1 Torque Characteristics and Terminology 456 6.8.2 Stepper Motor Selection 458
6.8.2.1 Positioning (x-y) Tables 459 6.8.3 Stepper Motor Applications 466
Problems 468
7 Continuous-Drive Actuators 487 7.1 DC Motors 488
7.1.1 Rotor and Stator 489 7.1.2 Commutation 491 7.1.3 Static Torque Characteristics 491 7.1.4 Brushless DC Motors 493
7.1.4.1 Constant-Speed Operation 495 7.1.4.2 Transient Operation 495
7.1.5 Torque Motors 497 7.2 DC Motor Equations 498
7.2.1 Steady-State Characteristics 499 7.2.1.1 Bearing Friction 500 7.2.1.2 Output Power 502 7.2.1.3 Combined Excitation of Motor Windings 503 7.2.1.4 Speed Regulation 504
7.2.2 Experimental Model 508 7.2.2.1 Electrical Damping Constant 508 7.2.2.2 Tinearized Experimental Model 508
7.3 Control of DC Motors 511 7.3.1 DC Servomotors 512 7.3.2 Armature Control 514
7.3.2.1 Motor Time Constants 515 7.3.2.2 Motor Parameter Measurement 516
7.3.3 Field Control 522 7.3.4 Feedback Control of DC Motors 523
7.3.4.1 Velocity Feedback Control 524
7.3.4.2 Position Plus Velocity Feedback Control 524 7.3.4.3 Position Feedback with Proportional, Integral,
and Derivative Control 525 7.3.5 Phase-Locked Control 526
7.4 Motor Driver 528 7.4.1 Interface Card 529 7.4.2 Drive Unit 529 7.4.3 Pulse-Width Modulation 530
7.5 DC Motor Selection 537 7.5.1 Motor Data and Specifications 537 7.5.2 Selection Considerations 538 7.5.3 Motor Sizing Procedure 541
7.5.3.1 Inertia Matching 541 7.5.3.2 Drive Amplifier Selection 542
7.6 Induction Motors 543 7.6.1 Rotating Magnetic Field 544 7.6.2 Induction Motor Characteristics 548 7.6.3 Torque-Speed Relationship 550
7.7 Induction Motor Control 553 7.7.1 Excitation Frequency Control 554 7.7.2 Voltage Control 556 7.7.3 Rotor Resistance Control 559 7.7.4 Pole-Changing Control 560 7.7.5 Field Feedback Control (Flux Vector Drive) 561 7.7.6 A Transfer-Function Model for an Induction Motor 561 7.7.7 Single-Phase AC Motors 566
7.8 Synchronous Motors 567 7.8.1 Control of a Synchronous Motor 568
7.9 Linear Actuators 569 7.9.1 Solenoid 569 7.9.2 Linear Motors 570
7.10 Hydraulic Actuators 571 7.10.1 Components of a Hydraulic Control System 572 7.10.2 Hydraulic Pumps and Motors 574 7.10.3 Hydraulic Valves 577
7.10.3.1 SpoolValve 578 7.10.3.2 Steady-State Valve Characteristics 581
7.10.4 Hydraulic Primary Actuators 582 7.10.5 Load Equation 584
7.11 Hydraulic Control Systems 585 7.11.1 Feedback Control 591 7.11.2 Constant-Flow Systems 596 7.11.3 Pump-Controlled Hydraulic Actuators 597 7.11.4 Hydraulic Accumulators 597 7.11.5 Pneumatic Control Systems 598 7.11.6 Flapper Valves 598 7.11.7 Hydraulic Circuits 601
7.12 Fluidics 602 7.12.1 Fluidic Components 603
7.12.1.1 Logic Components 603 7.12.1.2 Fluidic Motion Sensors 604 7.12.1.3 Fluidic Amplifiers 605
7.12.2 Fluidic Control Systems 606 7.12.2.1 Interfacing Considerations 606 7.12.2.2 Modular Laminated Construction 606
7.12.3 Applications of Fluidics 607 Problems 607
8 Mechanical Transmission Components 625 8.1 Mechanical Components 625 8.2 Transmission Components 627 8.3 Lead Screw and Nut 628 8.4 Harmonie Drives 632 8.5 Continuously Variable Transmission 637
8.5.1 Principle of Operation 637 8.5.2 Two-Slider CVT 639 8.5.3 A Three-Slider CVT 640
Problems 642
Bibliography and Further Reading 647
Answers to Numerical Problems 653
Index 655
