Linear Control System Analysis and Design

Table of Contents......Page 0
Linear Control System Analysis and Design with Matlab, Fifth Edition, Revised and Expanded......Page 1
Series Introduction......Page 5
Preface......Page 7
Contents......Page 11
1.1 INTRODUCTION......Page 19
Classical Examples......Page 20
Modern Examples......Page 23
1.3 DEFINITIONS......Page 30
1.4 HISTORICAL BACKGROUND [12]......Page 32
1.5 DIGITAL CONTROL DEVELOPMENT [16]......Page 36
1.6 MATHEMATICAL BACKGROUND......Page 38
1.7 THE ENGINEERING CONTROL PROBLEM......Page 40
1.8 COMPUTER LITERACY......Page 43
1.9 OUTLINE OF TEXT......Page 44
REFERENCES......Page 46
2.1 INTRODUCTION......Page 48
2.2 ELECTRIC CIRCUITS AND COMPONENTS [6]......Page 50
Series Resistor–Inductor Circuit......Page 51
Series Resistor–Inductor–Capacitor Circuit......Page 52
Multiloop Electric Circuits......Page 53
2.3 STATE CONCEPTS......Page 55
2.5 MECHANICAL TRANSLATION SYSTEMS [1,8,9]......Page 62
Simple Mechanical Translation System......Page 65
Multiple-Element Mechanical Translation System......Page 67
2.6 ANALOGOUS CIRCUITS......Page 69
2.7 MECHANICAL ROTATIONAL SYSTEMS......Page 70
Multiple-Element Mechanical Rotational System......Page 72
2.8 EFFECTIVE MOMENT OF INERTIA AND DAMPING OF A GEAR TRAIN......Page 73
2.9 THERMAL SYSTEMS [11]......Page 75
Simple Mercury Thermometer......Page 77
2.10 HYDRAULIC LINEAR ACTUATOR......Page 78
More Complete Analysis......Page 79
2.11 LIQUID-LEVEL SYSTEM [12,13]......Page 83
2.12 ROTATING POWER AMPLIFIERS [14,15]......Page 84
2.13 DC SERVOMOTOR......Page 86
2.14 AC SERVOMOTOR [16]......Page 88
2.15 LAGRANGE’S EQUATION......Page 90
REFERENCES......Page 94
3.1 INTRODUCTION......Page 96
3.2 STANDARD INPUTS TO CONTROL SYSTEMS......Page 97
3.3 STEADY-STATE RESPONSE: SINUSOIDAL INPUT......Page 98
3.4 STEADY-STATE RESPONSE: POLYNOMIAL INPUT......Page 100
Ramp-Function Input (Step Function of Velocity)......Page 101
3.5 TRANSIENT RESPONSE: CLASSICAL METHOD......Page 102
Damping Ratio z and Undamped Natural Frequency vn......Page 104
3.6 DEFINITION OF TIME CONSTANT......Page 106
3.7 EXAMPLE: SECOND-ORDER SYSTEM—MECHANICAL......Page 107
3.8 EXAMPLE: SECOND-ORDER SYSTEM—ELECTRICAL......Page 109
3.9 SECOND-ORDER TRANSIENTS [2]......Page 111
Response Characteristics......Page 114
3.10 TIME-RESPONSE SPECIFICATIONS [3]......Page 115
3.11 CAD ACCURACY CHECKS (CADAC)......Page 116
3.12 STATE-VARIABLE EQUATIONS [5–8]......Page 117
3.13 CHARACTERISTIC VALUES......Page 119
3.14 EVALUATING THE STATE TRANSITION MATRIX......Page 120
3.15 COMPLETE SOLUTION OF THE STATE EQUATION [10]......Page 123
3.16 SUMMARY......Page 124
REFERENCES......Page 125
4.1 INTRODUCTION......Page 126
4.3 DERIVATION OF LAPLACE TRANSFORMS OF SIMPLE FUNCTIONS......Page 127
Decaying Exponential e a t......Page 128
4.4 LAPLACE TRANSFORM THEOREMS......Page 129
4.6 APPLICATION OF THE LAPLACE TRANSFORM TO DIFFERENTIAL EQUATIONS......Page 132
4.7 INVERSE TRANSFORMATION......Page 134
4.8 HEAVISIDE PARTIAL-FRACTION EXPANSION THEOREMS......Page 135
Case 1: First-Order Real Poles......Page 136
Case 2: Multiple-Order Real Poles......Page 137
Case 3: Complex-Conjugate Poles......Page 139
4.9 MATLAB PARTIAL-FRACTION EXAMPLE......Page 143
The PARTFRAC Command......Page 144
4.10 PARTIAL-FRACTION SHORTCUTS......Page 145
4.11 GRAPHICAL INTERPRETATION OF PARTIAL-FRACTION COEFFICIENTS [7]......Page 147
4.12 FREQUENCY RESPONSE FROM THE POLE-ZERO DIAGRAM......Page 151
4.13 LOCATION OF POLES AND STABILITY......Page 154
4.14 LAPLACE TRANSFORM OF THE IMPULSE FUNCTION......Page 155
4.15 SECOND-ORDER SYSTEM WITH IMPULSE EXCITATION......Page 158
4.16 SOLUTION OF STATE EQUATION [9,10]......Page 159
4.17 EVALUATION OF THE TRANSFER-FUNCTION MATRIX......Page 161
4.18 MATLAB m-FILE FOR MIMO SYSTEMS......Page 163
4.19 SUMMARY......Page 165
REFERENCES......Page 166
5.1 INTRODUCTION......Page 167
Example 1: A Temperature Control System.......Page 168
Example 2: Command Guidance Interceptor System.......Page 169
Example 3: Aircraft Control System [1].......Page 171
5.3 DETERMINATION OF THE OVERALL TRANSFER FUNCTION......Page 172
Example: Overall Transfer Function......Page 175
5.4 STANDARD BLOCK DIAGRAM TERMINOLOGY [2]......Page 176
Definitions: Variables in the System......Page 177
Definitions: System Components......Page 178
5.5 POSITION CONTROL SYSTEM......Page 179
5.6 SIMULATION DIAGRAMS [3,4]......Page 183
5.7 SIGNAL FLOW GRAPHS [8,9]......Page 188
Flow-Graph Definitions......Page 189
Flow-Graph Algebra......Page 190
General Flow-Graph Analysis......Page 191
The Mason Gain Rule......Page 192
5.8 STATE TRANSITION SIGNAL FLOW GRAPH [10]......Page 194
5.9 PARALLEL STATE DIAGRAMS FROM TRANSFER FUNCTIONS......Page 198
5.10 DIAGONALIZING THE A MATRIX [11,12]......Page 201
Method 1: Matrix A in Companion Form......Page 203
Method 2: Adjoint Method......Page 204
Method 3: Simultaneous Equation Method......Page 207
Method 4: Reid’s Method [13]......Page 208
Method 5: Eigenvector Method......Page 210
Method 6: Using MATLAB......Page 212
5.11 USE OF STATE TRANSFORMATION FOR THE STATE EQUATION SOLUTION......Page 213
5.12 TRANSFORMING A MATRIX WITH COMPLEX EIGENVALUES......Page 214
5.13 TRANSFORMING AN A MATRIX INTO COMPANION FORM......Page 217
5.14 USING MATLAB TO OBTAIN THE COMPANION A MATRIX......Page 220
REFERENCES......Page 223
6.1 INTRODUCTION......Page 225
6.2 ROUTH’S STABILITY CRITERION [2–5]......Page 226
6.3 MATHEMATICAL AND PHYSICAL FORMS......Page 232
6.4 FEEDBACK SYSTEM TYPES......Page 234
6.5 ANALYSIS OF SYSTEM TYPES......Page 235
Case 1: m¼0 (Type 0 System)......Page 237
Case 2: m¼1 (Type 1 System)......Page 238
Case 3: m¼2 (Type 2 System)......Page 240
6.6 EXAMPLE: TYPE 2 SYSTEM......Page 241
6.7 STEADY-STATE ERROR COEFFICIENTS [9]......Page 243
Steady-State Step Error Coefficient......Page 244
Steady-State Ramp Error Coefficient......Page 245
Steady-State Parabolic Error Coefficient......Page 246
6.8 CAD ACCURACY CHECKS: CADAC......Page 247
Type 1 System......Page 248
Table of Steady-State Error Coefficients......Page 249
6.10 NONUNITY-FEEDBACK SYSTEM......Page 250
REFERENCES......Page 251
7.1 INTRODUCTION......Page 253
7.2 PLOTTING ROOTS OF A CHARACTERISTIC EQUATION......Page 254
7.3 QUALITATIVE ANALYSIS OF THE ROOT LOCUS......Page 258
7.4 PROCEDURE OUTLINE......Page 260
7.5 OPEN-LOOP TRANSFER FUNCTION......Page 262
7.6 POLES OF THE CONTROL RATIO C(s)/R(s)......Page 263
7.7 APPLICATION OF THE MAGNITUDE AND ANGLE CONDITIONS......Page 265
7.8 GEOMETRICAL PROPERTIES (CONSTRUCTION RULES)......Page 268
Rule 1: Number of Branches of the Locus......Page 269
Rule 2: Real-Axis Locus......Page 270
Rule 4: Asymptotes of Locus as s Approaches Infinity......Page 271
Rule 6: Breakaway Point on the Real Axis [4]......Page 272
Rule 7: Complex Pole (or Zero): Angle of Departure......Page 275
Rule 8: Imaginary-Axis Crossing Point......Page 276
Rule 10: Conservation of the Sum of the System Roots......Page 277
Rule 11: Determination of Roots on the Root Locus......Page 279
7.10 ROOT LOCUS EXAMPLE......Page 280
7.11 EXAMPLE OF SECTION 7.10: MATLAB ROOT LOCUS......Page 284
7.12 ROOT LOCUS EXAMPLE WITH AN RH PLANE ZERO......Page 288
7.13 PERFORMANCE CHARACTERISTICS......Page 289
General Introduction......Page 290
Plot of Characteristic Roots for 0< z < 1......Page 292
Variation of Roots with z......Page 293
Higher-Order Systems......Page 294
7.14 TRANSPORT LAG [7]......Page 295
7.15 SYNTHESIS......Page 296
7.16 SUMMARY OF ROOT-LOCUS CONSTRUCTION RULES FOR NEGATIVE FEEDBACK......Page 298
REFERENCES......Page 300
8.1 INTRODUCTION......Page 301
8.2 CORRELATION OF THE SINUSOIDAL AND TIME RESPONSE [3]......Page 302
8.3 FREQUENCY-RESPONSE CURVES......Page 303
8.4 BODE PLOTS (LOGARITHMIC PLOTS)......Page 305
8.5 GENERAL FREQUENCY-TRANSFER-FUNCTION RELATIONSHIPS......Page 307
ju Factors......Page 308
1QjuT Factors......Page 309
Quadratic Factors......Page 312
8.7 EXAMPLE OF DRAWING A BODE PLOT......Page 314
8.8 GENERATION OF MATLAB BODE PLOTS......Page 317
8.9 SYSTEM TYPE AND GAIN AS RELATED TO LOG MAGNITUDE CURVES......Page 318
Type 1 System......Page 319
Type 2 System......Page 320
8.11 EXPERIMENTAL DETERMINATION OF TRANSFER FUNCTION [5,9]......Page 321
8.12 DIRECT POLAR PLOTS......Page 322
Complex RC Network (Lag-Lead Compensator)......Page 323
Type 0 Feedback Control System......Page 324
Type 1 Feedback Control System......Page 326
Type 2 Feedback Control System......Page 328
8.13 SUMMARY: DIRECT POLAR PLOTS......Page 330
8.14 NYQUIST’S STABILITY CRITERION......Page 331
Mathematical Basis for Nyquist’s Stability Criterion......Page 332
Generalizing Nyquist’s Stability Criterion......Page 334
Obtaining a Plot of B(s)......Page 335
Effect of Poles at the Origin on the Rotation of B(s)......Page 336
8.15 EXAMPLES OF NYQUIST’S CRITERION USING DIRECT POLAR PLOT......Page 339
8.16 NYQUIST’S STABILITY CRITERION APPLIED TO SYSTEM HAVING DEAD TIME......Page 343
8.17 DEFINITIONS OF PHASE MARGIN AND GAIN MARGIN AND THEIR RELATION TO STABILITY [16]......Page 344
8.18 STABILITY CHARACTERISTICS OF THE LOG MAGNITUDE AND PHASE DIAGRAM......Page 347
8.19 STABILITY FROM THE NICHOLS PLOT (LOG MAGNITUDE—ANGLE DIAGRAM)......Page 348
8.20 SUMMARY......Page 351
REFERENCES......Page 352
9.1 INTRODUCTION......Page 354
9.2 DIRECT POLAR PLOT......Page 355
9.3 DETERMINATION OF Mm AND um FOR A SIMPLE SECOND-ORDER SYSTEM......Page 356
9.4 CORRELATION OF SINUSOIDAL AND TIME RESPONSES [3]......Page 360
Equation of a Circle......Page 361
M(u) Contours......Page 362
a(u) Contours......Page 365
Tangents to the M Circles......Page 367
9.6 CONSTANT 1/M AND a CONTOURS (UNITY FEEDBACK) IN THE INVERSE POLAR PLANE......Page 368
9.7 GAIN ADJUSTMENT OF A UNITY-FEEDBACK SYSTEM FOR A DESIRED Mm: DIRECT POLAR PLOT......Page 370
9.8 CONSTANT M AND a CURVES ON THE LOG MAGNITUDE—ANGLE DIAGRAM (NICHOLS CHART) [4]......Page 373
Bode Plot......Page 376
Nyquist Plot......Page 377
9.10 ADJUSTMENT OF GAIN BY USE OF THE LOG MAGNITUDE–ANGLE DIAGRAM (NICHOLS CHART)......Page 378
9.11 CORRELATION OF POLE-ZERO DIAGRAM WITH FREQUENCY AND TIME RESPONSES......Page 381
9.12 SUMMARY......Page 383
REFERENCES......Page 385
10.1 INTRODUCTION TO DESIGN......Page 386
10.2 TRANSIENT RESPONSE: DOMINANT COMPLEX POLES [1]......Page 389
10.3 ADDITIONAL SIGNIFICANT POLES [4]......Page 394
First Design......Page 397
Second Design......Page 398
10.5 RESHAPING THE ROOT LOCUS......Page 399
10.7 IDEAL INTEGRAL CASCADE COMPENSATION (PI CONTROLLER)......Page 400
10.8 CASCADE LAG COMPENSATION DESIGN USING PASSIVE ELEMENTS......Page 401
10.9 IDEAL DERIVATIVE CASCADE COMPENSATION (PD CONTROLLER)......Page 406
10.10 LEAD COMPENSATION DESIGN USING PASSIVE ELEMENTS......Page 408
Design Example—Lead Compensation Applied to a Type 1 System......Page 409
10.11 GENERAL LEAD-COMPENSATOR DESIGN......Page 413
10.12 LAG-LEAD CASCADE COMPENSATION DESIGN......Page 415
Design Example—Lag-Lead Compensation Applied to a Type 1 System......Page 416
10.13 COMPARISON OF CASCADE COMPENSATORS......Page 417
10.14 PID CONTROLLER......Page 420
10.15 INTRODUCTION TO FEEDBACK COMPENSATION......Page 422
10.16 FEEDBACK COMPENSATION: DESIGN PROCEDURES......Page 424
10.17 SIMPLIFIED RATE FEEDBACK COMPENSATION: A DESIGN APPROACH......Page 425
10.18 DESIGN OF RATE FEEDBACK......Page 427
10.19 DESIGN: FEEDBACK OF SECOND DERIVATIVE OF OUTPUT......Page 432
10.20 RESULTS OF FEEDBACK COMPENSATION DESIGN......Page 434
10.21 RATE FEEDBACK: PLANTS WITH DOMINANT COMPLEX POLES......Page 435
10.22 SUMMARY......Page 436
REFERENCES......Page 437
11.1 INTRODUCTION TO FEEDBACK COMPENSATION DESIGN......Page 438
11.2 SELECTION OF A CASCADE COMPENSATOR......Page 440
11.3 CASCADE LAG COMPENSATOR......Page 444
11.4 DESIGN EXAMPLE: CASCADE LAG COMPENSATION......Page 447
11.5 CASCADE LEAD COMPENSATOR......Page 451
11.6 DESIGN EXAMPLE: CASCADE LEAD COMPENSATION......Page 454
11.7 CASCADE LAG-LEAD COMPENSATOR......Page 458
11.8 DESIGN EXAMPLE: CASCADE LAG-LEAD COMPENSATION......Page 460
11.9 FEEDBACK COMPENSATION DESIGN USING LOG PLOTS [1]......Page 461
11.10 DESIGN EXAMPLE: FEEDBACK COMPENSATION (LOG PLOTS)......Page 465
11.11 APPLICATION GUIDELINES: BASIC MINOR-LOOP FEEDBACK COMPENSATORS......Page 472
11.12 SUMMARY......Page 473
REFERENCES......Page 474
12.1 INTRODUCTION [1]......Page 475
12.2 MODELING A DESIRED TRACKING CONTROL RATIO......Page 476
12.3 GUILLEMIN-TRUXAL DESIGN PROCEDURE [4]......Page 481
12.4 INTRODUCTION TO DISTURBANCE REJECTION [6,7]......Page 483
12.5 A SECOND-ORDER DISTURBANCE-REJECTION MODEL......Page 484
Frequency Domain......Page 485
12.6 DISTURBANCE-REJECTION DESIGN PRINCIPLES FOR SISO SYSTEMS [7]......Page 486
Trial Solution......Page 489
12.7 DISTURBANCE-REJECTION DESIGN EXAMPLE......Page 492
12.8 DISTURBANCE-REJECTION MODELS......Page 495
REFERENCES......Page 499
13.1 INTRODUCTION......Page 501
13.2 CONTROLLABILITY AND OBSERVABILITY [5–9]......Page 502
Example: MATLAB Controllability and Observability......Page 509
13.3 STATE FEEDBACK FOR SISO SYSTEMS......Page 511
13.4 STATE-FEEDBACK DESIGN FOR SISO SYSTEMS USING THE CONTROL CANONICAL (PHASE-VARIABLE) FORM......Page 514
13.5 STATE-VARIABLE FEEDBACK [10] (PHYSICAL VARIABLES)......Page 517
13.6 GENERAL PROPERTIES OF STATE FEEDBACK (USING PHASE VARIABLES)......Page 521
Step Input rðtÞ ¼ R0u 1ðtÞ RðsÞ ¼ R0=s......Page 524
Ramp Input rðtÞ ¼ R1u 2ðtÞ ¼ R1tu 1ðtÞ RðsÞ ¼ R1=s2......Page 525
Parabolic Input rðtÞ ¼ R2u 3ðtÞ ¼ ðR2t2=2Þu 1ðtÞ RðsÞ ¼ R2=s3......Page 526
13.8 USE OF STEADY-STATE ERROR COEFFICIENTS......Page 527
13.9 STATE-VARIABLE FEEDBACK: ALL-POLE PLANT......Page 531
13.10 PLANTS WITH COMPLEX POLES......Page 534
13.11 COMPENSATOR CONTAINING A ZERO......Page 536
13.12 STATE-VARIABLE FEEDBACK: POLE-ZERO PLANT......Page 537
13.13 OBSERVERS [12–17]......Page 546
13.14 CONTROL SYSTEMS CONTAINING OBSERVERS......Page 548
13.15 SUMMARY......Page 550
REFERENCES......Page 551
14.2 SENSITIVITY......Page 553
Case 1: Open-Loop System of Fig. 14.1a......Page 554
Case 2: Closed-Loop Unity-Feedback System of Fig. 14.1b......Page 555
Case 4: Closed-Loop Nonunity-Feedback System of Fig. 14.1b [Feedback Function HðsÞ Variable and GðsÞ Fixed]......Page 556
14.3 SENSITIVITY ANALYSIS [3,4]......Page 558
14.4 SENSITIVITY ANALYSIS [3,4] EXAMPLES......Page 561
14.5 PARAMETER SENSITIVITY EXAMPLES......Page 567
14.6 INACCESSIBLE STATES [5]......Page 568
14.7 STATE-SPACE TRAJECTORIES [6]......Page 572
14.8 LINEARIZATION (JACOBIAN MATRIX) [6,7]......Page 575
REFERENCES......Page 579
15.1 INTRODUCTION [1–5]......Page 581
15.2 SAMPLING......Page 582
15.3 IDEAL SAMPLING......Page 585
15.5 DIFFERENTIATION PROCESS [1]......Page 590
15.5.1 First Derivative Approximation......Page 591
15.5.3 r th Derivative Approximation......Page 592
15.6 SYNTHESIS IN THE z DOMAIN (DIRECT METHOD)......Page 593
15.6.2 System Stability [5]......Page 595
15.6.3 System Analysis......Page 597
15.7 THE INVERSE Z TRANSFORM......Page 599
15.8 ZERO-ORDER HOLD......Page 600
15.9 LIMITATIONS......Page 602
15.10 STEADY-STATE ERROR ANALYSIS FOR STABLE SYSTEMS......Page 603
15.10.1 Steady-State Error-Coefficients......Page 605
15.10.2 Evaluation of Steady-State Error Coefficients......Page 606
15.10.3 Use of Steady-State Error Coefficients......Page 607
15.11 ROOT-LOCUS ANALYSIS FOR SAMPLED-DATA CONTROL SYSTEMS......Page 610
15.11.2 Root-Locus Construction Rules for Negative Feedback......Page 611
15.11.3 Root-Locus Design Examples......Page 614
15.12 SUMMARY......Page 620
REFERENCES......Page 621
16.1 INTRODUCTION [1,2]......Page 622
16.2 COMPLEMENTARY SPECTRA [3]......Page 623
16.3 TUSTIN TRANSFORMATION: s TO z PLANE TRANSFORMATION [1]......Page 624
16.3.1 Tustin Transformation Properties......Page 625
16.3.2 Tustin Mapping Properties......Page 627
16.4 z-DOMAIN TO THE w- AND w0-DOMAIN TRANSFORMATIONS [1]......Page 631
16.5 DIGITIZATION (DIG) TECHNIQUE......Page 632
16.6 DIGITIZATION (DIG) DESIGN TECHNIQUE......Page 633
16.7 THE PSUEDO-CONTINUOUS-TIME (PCT) CONTROL SYSTEM......Page 635
16.7.1 Introduction to Psuedo-Continuous-Time System DIG Technique [1]......Page 636
16.7.2 MATLAB Design for Sec. 16.7.1......Page 638
16.7.3 Simple PCT Example......Page 641
Case 1: PCT Open-Loop Control System......Page 642
16.7.4 Sampled-Data Control System Example......Page 643
Case 3: The DIR Approach Using the Exact Z Transformation......Page 644
Case 4: The Tustin Control-Ratio Transfer Function......Page 645
16.7.6 PCT Design Summary......Page 647
16.9 DIRECT (DIR) COMPENSATOR......Page 649
16.10 PCT LEAD CASCADE COMPENSATION......Page 650
DIG (PCT) Design......Page 653
DIR Design (Exact z Domain Design): T¼0.1 s......Page 655
16.11 PCT LAG COMPENSATION......Page 656
16.11.1 MATLAB Design for Sec. 16.11......Page 659
16.12 PCT LAG-LEAD COMPENSATION......Page 661
16.12.1 MATLAB Design for Sec. 16.12......Page 665
16.13.1 General Analysis......Page 668
16.13.2 DIG Technique for Feedback Control......Page 672
16.14.1 PCT DIG Technique......Page 677
16.15.1 PCT DIG Example......Page 681
16.16 CONTROLLER IMPLEMENTATION [1]......Page 683
16.17 SUMMARY......Page 685
REFERENCES......Page 686
Appendix A: Table of Laplace Transform Pairs......Page 688
B.2 MATRIX......Page 692
B.5 ADDITION AND SUBTRACTION OF MATRICES......Page 693
B.6 MULTIPLICATION OF MATRICES......Page 694
B.8 UNIT OR IDENTITY MATRIX......Page 695
B.11 ADDITIONAL MATRIX OPERATIONS AND PROPERTIES......Page 696
B.12 GENERALIZED DETERMINANT......Page 698
B.13 HERMITE NORMAL FORM......Page 700
B.14 MATRIX INVERSION BY ROW OPERATIONS......Page 701
B.15 EVALUATION OF THE CHARACTERISTIC POLYNOMIAL......Page 702
REFERENCES......Page 703
C.1 INTRODUCTION......Page 705
C.2 BASICS......Page 706
C.2.2 Matrix Transpose......Page 707
C.2.3 Range of Values......Page 708
C.3 DEFINING SYSTEMS......Page 711
C.3.2 State Space Model......Page 712
C.4.1 Root Locus......Page 714
C.4.2 Frequency Response......Page 715
C.5 SIMULATION......Page 716
C.6 IMPLEMENTATION OF RESULTS......Page 719
D.1 INTRODUCTION......Page 722
D.2 OVERVIEW OF TOTAL-PC......Page 723
D.3 QFT CAD PACKAGE......Page 726
REFERENCES......Page 728
Problems......Page 729
Answers to Selected Problems......Page 804