Linear Control System Analysis and Design with Matlab

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
Answers to Selected Problems......Page 19
Table of Contents......Page 0
1.1 INTRODUCTION......Page 38
Classical Examples......Page 39
Modern Examples......Page 42
1.3 DEFINITIONS......Page 49
1.4 HISTORICAL BACKGROUND [12]......Page 51
1.5 DIGITAL CONTROL DEVELOPMENT [16]......Page 55
1.6 MATHEMATICAL BACKGROUND......Page 57
1.7 THE ENGINEERING CONTROL PROBLEM......Page 59
1.8 COMPUTER LITERACY......Page 62
1.9 OUTLINE OF TEXT......Page 63
REFERENCES......Page 65
2.1 INTRODUCTION......Page 67
2.2 ELECTRIC CIRCUITS AND COMPONENTS [6]......Page 69
Series Resistor–Inductor Circuit......Page 70
Series Resistor–Inductor–Capacitor Circuit......Page 71
Multiloop Electric Circuits......Page 72
2.3 STATE CONCEPTS......Page 74
2.5 MECHANICAL TRANSLATION SYSTEMS [1,8,9]......Page 81
Simple Mechanical Translation System......Page 84
Multiple-Element Mechanical Translation System......Page 86
2.6 ANALOGOUS CIRCUITS......Page 88
2.7 MECHANICAL ROTATIONAL SYSTEMS......Page 89
Multiple-Element Mechanical Rotational System......Page 91
2.8 EFFECTIVE MOMENT OF INERTIA AND DAMPING OF A GEAR TRAIN......Page 92
2.9 THERMAL SYSTEMS [11]......Page 94
Simple Mercury Thermometer......Page 96
2.10 HYDRAULIC LINEAR ACTUATOR......Page 97
More Complete Analysis......Page 98
2.11 LIQUID-LEVEL SYSTEM [12,13]......Page 102
2.12 ROTATING POWER AMPLIFIERS [14,15]......Page 103
2.13 DC SERVOMOTOR......Page 105
2.14 AC SERVOMOTOR [16]......Page 107
2.15 LAGRANGE’S EQUATION......Page 109
REFERENCES......Page 113
3.1 INTRODUCTION......Page 115
3.2 STANDARD INPUTS TO CONTROL SYSTEMS......Page 116
3.3 STEADY-STATE RESPONSE: SINUSOIDAL INPUT......Page 117
3.4 STEADY-STATE RESPONSE: POLYNOMIAL INPUT......Page 119
Ramp-Function Input (Step Function of Velocity)......Page 120
3.5 TRANSIENT RESPONSE: CLASSICAL METHOD......Page 121
Damping Ratio z and Undamped Natural Frequency vn......Page 123
3.6 DEFINITION OF TIME CONSTANT......Page 125
3.7 EXAMPLE: SECOND-ORDER SYSTEM—MECHANICAL......Page 126
3.8 EXAMPLE: SECOND-ORDER SYSTEM—ELECTRICAL......Page 128
3.9 SECOND-ORDER TRANSIENTS [2]......Page 130
Response Characteristics......Page 133
3.10 TIME-RESPONSE SPECIFICATIONS [3]......Page 134
3.11 CAD ACCURACY CHECKS (CADAC)......Page 135
3.12 STATE-VARIABLE EQUATIONS [5–8]......Page 136
3.13 CHARACTERISTIC VALUES......Page 138
3.14 EVALUATING THE STATE TRANSITION MATRIX......Page 139
3.15 COMPLETE SOLUTION OF THE STATE EQUATION [10]......Page 142
3.16 SUMMARY......Page 143
REFERENCES......Page 144
4.1 INTRODUCTION......Page 145
4.3 DERIVATION OF LAPLACE TRANSFORMS OF SIMPLE FUNCTIONS......Page 146
Decaying Exponential e a t......Page 147
4.4 LAPLACE TRANSFORM THEOREMS......Page 148
4.6 APPLICATION OF THE LAPLACE TRANSFORM TO DIFFERENTIAL EQUATIONS......Page 151
4.7 INVERSE TRANSFORMATION......Page 153
4.8 HEAVISIDE PARTIAL-FRACTION EXPANSION THEOREMS......Page 154
Case 1: First-Order Real Poles......Page 155
Case 2: Multiple-Order Real Poles......Page 156
Case 3: Complex-Conjugate Poles......Page 158
4.9 MATLAB PARTIAL-FRACTION EXAMPLE......Page 162
The PARTFRAC Command......Page 163
4.10 PARTIAL-FRACTION SHORTCUTS......Page 164
4.11 GRAPHICAL INTERPRETATION OF PARTIAL-FRACTION COEFFICIENTS [7]......Page 166
4.12 FREQUENCY RESPONSE FROM THE POLE-ZERO DIAGRAM......Page 170
4.13 LOCATION OF POLES AND STABILITY......Page 173
4.14 LAPLACE TRANSFORM OF THE IMPULSE FUNCTION......Page 174
4.15 SECOND-ORDER SYSTEM WITH IMPULSE EXCITATION......Page 177
4.16 SOLUTION OF STATE EQUATION [9,10]......Page 178
4.17 EVALUATION OF THE TRANSFER-FUNCTION MATRIX......Page 180
4.18 MATLAB m-FILE FOR MIMO SYSTEMS......Page 182
4.19 SUMMARY......Page 184
REFERENCES......Page 185
5.1 INTRODUCTION......Page 186
Example 1: A Temperature Control System.......Page 187
Example 2: Command Guidance Interceptor System.......Page 188
Example 3: Aircraft Control System [1].......Page 190
5.3 DETERMINATION OF THE OVERALL TRANSFER FUNCTION......Page 191
Example: Overall Transfer Function......Page 194
5.4 STANDARD BLOCK DIAGRAM TERMINOLOGY [2]......Page 195
Definitions: Variables in the System......Page 196
Definitions: System Components......Page 197
5.5 POSITION CONTROL SYSTEM......Page 198
5.6 SIMULATION DIAGRAMS [3,4]......Page 202
5.7 SIGNAL FLOW GRAPHS [8,9]......Page 207
Flow-Graph Definitions......Page 208
Flow-Graph Algebra......Page 209
General Flow-Graph Analysis......Page 210
The Mason Gain Rule......Page 211
5.8 STATE TRANSITION SIGNAL FLOW GRAPH [10]......Page 213
5.9 PARALLEL STATE DIAGRAMS FROM TRANSFER FUNCTIONS......Page 217
5.10 DIAGONALIZING THE A MATRIX [11,12]......Page 220
Method 1: Matrix A in Companion Form......Page 222
Method 2: Adjoint Method......Page 223
Method 3: Simultaneous Equation Method......Page 226
Method 4: Reid’s Method [13]......Page 227
Method 5: Eigenvector Method......Page 229
Method 6: Using MATLAB......Page 231
5.11 USE OF STATE TRANSFORMATION FOR THE STATE EQUATION SOLUTION......Page 232
5.12 TRANSFORMING A MATRIX WITH COMPLEX EIGENVALUES......Page 233
5.13 TRANSFORMING AN A MATRIX INTO COMPANION FORM......Page 236
5.14 USING MATLAB TO OBTAIN THE COMPANION A MATRIX......Page 239
REFERENCES......Page 242
6.1 INTRODUCTION......Page 244
6.2 ROUTH’S STABILITY CRITERION [2–5]......Page 245
6.3 MATHEMATICAL AND PHYSICAL FORMS......Page 251
6.4 FEEDBACK SYSTEM TYPES......Page 253
6.5 ANALYSIS OF SYSTEM TYPES......Page 254
Case 1: m¼0 (Type 0 System)......Page 256
Case 2: m¼1 (Type 1 System)......Page 257
Case 3: m¼2 (Type 2 System)......Page 259
6.6 EXAMPLE: TYPE 2 SYSTEM......Page 260
6.7 STEADY-STATE ERROR COEFFICIENTS [9]......Page 262
Steady-State Step Error Coefficient......Page 263
Steady-State Ramp Error Coefficient......Page 264
Steady-State Parabolic Error Coefficient......Page 265
6.8 CAD ACCURACY CHECKS: CADAC......Page 266
Type 1 System......Page 267
Table of Steady-State Error Coefficients......Page 268
6.10 NONUNITY-FEEDBACK SYSTEM......Page 269
REFERENCES......Page 270
7.1 INTRODUCTION......Page 272
7.2 PLOTTING ROOTS OF A CHARACTERISTIC EQUATION......Page 273
7.3 QUALITATIVE ANALYSIS OF THE ROOT LOCUS......Page 277
7.4 PROCEDURE OUTLINE......Page 279
7.5 OPEN-LOOP TRANSFER FUNCTION......Page 281
7.6 POLES OF THE CONTROL RATIO C(s)/R(s)......Page 282
7.7 APPLICATION OF THE MAGNITUDE AND ANGLE CONDITIONS......Page 284
7.8 GEOMETRICAL PROPERTIES (CONSTRUCTION RULES)......Page 287
Rule 1: Number of Branches of the Locus......Page 288
Rule 2: Real-Axis Locus......Page 289
Rule 4: Asymptotes of Locus as s Approaches Infinity......Page 290
Rule 6: Breakaway Point on the Real Axis [4]......Page 291
Rule 7: Complex Pole (or Zero): Angle of Departure......Page 294
Rule 8: Imaginary-Axis Crossing Point......Page 295
Rule 10: Conservation of the Sum of the System Roots......Page 296
Rule 11: Determination of Roots on the Root Locus......Page 298
7.10 ROOT LOCUS EXAMPLE......Page 299
7.11 EXAMPLE OF SECTION 7.10: MATLAB ROOT LOCUS......Page 303
7.12 ROOT LOCUS EXAMPLE WITH AN RH PLANE ZERO......Page 307
7.13 PERFORMANCE CHARACTERISTICS......Page 308
General Introduction......Page 309
Plot of Characteristic Roots for 0< z < 1......Page 311
Variation of Roots with z......Page 312
Higher-Order Systems......Page 313
7.14 TRANSPORT LAG [7]......Page 314
7.15 SYNTHESIS......Page 315
7.16 SUMMARY OF ROOT-LOCUS CONSTRUCTION RULES FOR NEGATIVE FEEDBACK......Page 317
REFERENCES......Page 319
8.1 INTRODUCTION......Page 320
8.2 CORRELATION OF THE SINUSOIDAL AND TIME RESPONSE [3]......Page 321
8.3 FREQUENCY-RESPONSE CURVES......Page 322
8.4 BODE PLOTS (LOGARITHMIC PLOTS)......Page 324
8.5 GENERAL FREQUENCY-TRANSFER-FUNCTION RELATIONSHIPS......Page 326
ju Factors......Page 327
1QjuT Factors......Page 328
Quadratic Factors......Page 331
8.7 EXAMPLE OF DRAWING A BODE PLOT......Page 333
8.8 GENERATION OF MATLAB BODE PLOTS......Page 336
8.9 SYSTEM TYPE AND GAIN AS RELATED TO LOG MAGNITUDE CURVES......Page 337
Type 1 System......Page 338
Type 2 System......Page 339
8.11 EXPERIMENTAL DETERMINATION OF TRANSFER FUNCTION [5,9]......Page 340
8.12 DIRECT POLAR PLOTS......Page 341
Complex RC Network (Lag-Lead Compensator)......Page 342
Type 0 Feedback Control System......Page 343
Type 1 Feedback Control System......Page 345
Type 2 Feedback Control System......Page 347
8.13 SUMMARY: DIRECT POLAR PLOTS......Page 349
8.14 NYQUIST’S STABILITY CRITERION......Page 350
Mathematical Basis for Nyquist’s Stability Criterion......Page 351
Generalizing Nyquist’s Stability Criterion......Page 353
Obtaining a Plot of B(s)......Page 354
Effect of Poles at the Origin on the Rotation of B(s)......Page 355
8.15 EXAMPLES OF NYQUIST’S CRITERION USING DIRECT POLAR PLOT......Page 358
8.16 NYQUIST’S STABILITY CRITERION APPLIED TO SYSTEM HAVING DEAD TIME......Page 362
8.17 DEFINITIONS OF PHASE MARGIN AND GAIN MARGIN AND THEIR RELATION TO STABILITY [16]......Page 363
8.18 STABILITY CHARACTERISTICS OF THE LOG MAGNITUDE AND PHASE DIAGRAM......Page 366
8.19 STABILITY FROM THE NICHOLS PLOT (LOG MAGNITUDE—ANGLE DIAGRAM)......Page 367
8.20 SUMMARY......Page 370
REFERENCES......Page 371
9.1 INTRODUCTION......Page 373
9.2 DIRECT POLAR PLOT......Page 374
9.3 DETERMINATION OF Mm AND um FOR A SIMPLE SECOND-ORDER SYSTEM......Page 375
9.4 CORRELATION OF SINUSOIDAL AND TIME RESPONSES [3]......Page 379
Equation of a Circle......Page 380
M(u) Contours......Page 381
a(u) Contours......Page 384
Tangents to the M Circles......Page 386
9.6 CONSTANT 1/M AND a CONTOURS (UNITY FEEDBACK) IN THE INVERSE POLAR PLANE......Page 387
9.7 GAIN ADJUSTMENT OF A UNITY-FEEDBACK SYSTEM FOR A DESIRED Mm: DIRECT POLAR PLOT......Page 389
9.8 CONSTANT M AND a CURVES ON THE LOG MAGNITUDE—ANGLE DIAGRAM (NICHOLS CHART) [4]......Page 392
Bode Plot......Page 395
Nyquist Plot......Page 396
9.10 ADJUSTMENT OF GAIN BY USE OF THE LOG MAGNITUDE–ANGLE DIAGRAM (NICHOLS CHART)......Page 397
9.11 CORRELATION OF POLE-ZERO DIAGRAM WITH FREQUENCY AND TIME RESPONSES......Page 400
9.12 SUMMARY......Page 402
REFERENCES......Page 404
10.1 INTRODUCTION TO DESIGN......Page 405
10.2 TRANSIENT RESPONSE: DOMINANT COMPLEX POLES [1]......Page 408
10.3 ADDITIONAL SIGNIFICANT POLES [4]......Page 413
First Design......Page 416
Second Design......Page 417
10.5 RESHAPING THE ROOT LOCUS......Page 418
10.7 IDEAL INTEGRAL CASCADE COMPENSATION (PI CONTROLLER)......Page 419
10.8 CASCADE LAG COMPENSATION DESIGN USING PASSIVE ELEMENTS......Page 420
10.9 IDEAL DERIVATIVE CASCADE COMPENSATION (PD CONTROLLER)......Page 425
10.10 LEAD COMPENSATION DESIGN USING PASSIVE ELEMENTS......Page 427
Design Example—Lead Compensation Applied to a Type 1 System......Page 428
10.11 GENERAL LEAD-COMPENSATOR DESIGN......Page 432
10.12 LAG-LEAD CASCADE COMPENSATION DESIGN......Page 434
Design Example—Lag-Lead Compensation Applied to a Type 1 System......Page 435
10.13 COMPARISON OF CASCADE COMPENSATORS......Page 436
10.14 PID CONTROLLER......Page 439
10.15 INTRODUCTION TO FEEDBACK COMPENSATION......Page 441
10.16 FEEDBACK COMPENSATION: DESIGN PROCEDURES......Page 443
10.17 SIMPLIFIED RATE FEEDBACK COMPENSATION: A DESIGN APPROACH......Page 444
10.18 DESIGN OF RATE FEEDBACK......Page 446
10.19 DESIGN: FEEDBACK OF SECOND DERIVATIVE OF OUTPUT......Page 451
10.20 RESULTS OF FEEDBACK COMPENSATION DESIGN......Page 453
10.21 RATE FEEDBACK: PLANTS WITH DOMINANT COMPLEX POLES......Page 454
10.22 SUMMARY......Page 455
REFERENCES......Page 456
11.1 INTRODUCTION TO FEEDBACK COMPENSATION DESIGN......Page 457
11.2 SELECTION OF A CASCADE COMPENSATOR......Page 459
11.3 CASCADE LAG COMPENSATOR......Page 463
11.4 DESIGN EXAMPLE: CASCADE LAG COMPENSATION......Page 466
11.5 CASCADE LEAD COMPENSATOR......Page 470
11.6 DESIGN EXAMPLE: CASCADE LEAD COMPENSATION......Page 473
11.7 CASCADE LAG-LEAD COMPENSATOR......Page 477
11.8 DESIGN EXAMPLE: CASCADE LAG-LEAD COMPENSATION......Page 479
11.9 FEEDBACK COMPENSATION DESIGN USING LOG PLOTS [1]......Page 480
11.10 DESIGN EXAMPLE: FEEDBACK COMPENSATION (LOG PLOTS)......Page 484
11.11 APPLICATION GUIDELINES: BASIC MINOR-LOOP FEEDBACK COMPENSATORS......Page 491
11.12 SUMMARY......Page 492
REFERENCES......Page 493
12.1 INTRODUCTION [1]......Page 494
12.2 MODELING A DESIRED TRACKING CONTROL RATIO......Page 495
12.3 GUILLEMIN-TRUXAL DESIGN PROCEDURE [4]......Page 500
12.4 INTRODUCTION TO DISTURBANCE REJECTION [6,7]......Page 502
12.5 A SECOND-ORDER DISTURBANCE-REJECTION MODEL......Page 503
Frequency Domain......Page 504
12.6 DISTURBANCE-REJECTION DESIGN PRINCIPLES FOR SISO SYSTEMS [7]......Page 505
Trial Solution......Page 508
12.7 DISTURBANCE-REJECTION DESIGN EXAMPLE......Page 511
12.8 DISTURBANCE-REJECTION MODELS......Page 514
REFERENCES......Page 518
13.1 INTRODUCTION......Page 520
13.2 CONTROLLABILITY AND OBSERVABILITY [5–9]......Page 521
Example: MATLAB Controllability and Observability......Page 528
13.3 STATE FEEDBACK FOR SISO SYSTEMS......Page 530
13.4 STATE-FEEDBACK DESIGN FOR SISO SYSTEMS USING THE CONTROL CANONICAL (PHASE-VARIABLE) FORM......Page 533
13.5 STATE-VARIABLE FEEDBACK [10] (PHYSICAL VARIABLES)......Page 536
13.6 GENERAL PROPERTIES OF STATE FEEDBACK (USING PHASE VARIABLES)......Page 540
Step Input rðtÞ ¼ R0u 1ðtÞ RðsÞ ¼ R0=s......Page 543
Ramp Input rðtÞ ¼ R1u 2ðtÞ ¼ R1tu 1ðtÞ RðsÞ ¼ R1=s2......Page 544
Parabolic Input rðtÞ ¼ R2u 3ðtÞ ¼ ðR2t2=2Þu 1ðtÞ RðsÞ ¼ R2=s3......Page 545
13.8 USE OF STEADY-STATE ERROR COEFFICIENTS......Page 546
13.9 STATE-VARIABLE FEEDBACK: ALL-POLE PLANT......Page 550
13.10 PLANTS WITH COMPLEX POLES......Page 553
13.11 COMPENSATOR CONTAINING A ZERO......Page 555
13.12 STATE-VARIABLE FEEDBACK: POLE-ZERO PLANT......Page 556
13.13 OBSERVERS [12–17]......Page 565
13.14 CONTROL SYSTEMS CONTAINING OBSERVERS......Page 567
13.15 SUMMARY......Page 569
REFERENCES......Page 570
14.2 SENSITIVITY......Page 572
Case 1: Open-Loop System of Fig. 14.1a......Page 573
Case 2: Closed-Loop Unity-Feedback System of Fig. 14.1b......Page 574
Case 4: Closed-Loop Nonunity-Feedback System of Fig. 14.1b [Feedback Function HðsÞ Variable and GðsÞ Fixed]......Page 575
14.3 SENSITIVITY ANALYSIS [3,4]......Page 577
14.4 SENSITIVITY ANALYSIS [3,4] EXAMPLES......Page 580
14.5 PARAMETER SENSITIVITY EXAMPLES......Page 586
14.6 INACCESSIBLE STATES [5]......Page 587
14.7 STATE-SPACE TRAJECTORIES [6]......Page 591
14.8 LINEARIZATION (JACOBIAN MATRIX) [6,7]......Page 594
REFERENCES......Page 598
15.1 INTRODUCTION [1–5]......Page 600
15.2 SAMPLING......Page 601
15.3 IDEAL SAMPLING......Page 604
15.5 DIFFERENTIATION PROCESS [1]......Page 609
15.5.1 First Derivative Approximation......Page 610
15.5.3 r th Derivative Approximation......Page 611
15.6 SYNTHESIS IN THE z DOMAIN (DIRECT METHOD)......Page 612
15.6.2 System Stability [5]......Page 614
15.6.3 System Analysis......Page 616
15.7 THE INVERSE Z TRANSFORM......Page 618
15.8 ZERO-ORDER HOLD......Page 619
15.9 LIMITATIONS......Page 621
15.10 STEADY-STATE ERROR ANALYSIS FOR STABLE SYSTEMS......Page 622
15.10.1 Steady-State Error-Coefficients......Page 624
15.10.2 Evaluation of Steady-State Error Coefficients......Page 625
15.10.3 Use of Steady-State Error Coefficients......Page 626
15.11 ROOT-LOCUS ANALYSIS FOR SAMPLED-DATA CONTROL SYSTEMS......Page 629
15.11.2 Root-Locus Construction Rules for Negative Feedback......Page 630
15.11.3 Root-Locus Design Examples......Page 633
15.12 SUMMARY......Page 639
REFERENCES......Page 640
16.1 INTRODUCTION [1,2]......Page 641
16.2 COMPLEMENTARY SPECTRA [3]......Page 642
16.3 TUSTIN TRANSFORMATION: s TO z PLANE TRANSFORMATION [1]......Page 643
16.3.1 Tustin Transformation Properties......Page 644
16.3.2 Tustin Mapping Properties......Page 646
16.4 z-DOMAIN TO THE w- AND w0-DOMAIN TRANSFORMATIONS [1]......Page 650
16.5 DIGITIZATION (DIG) TECHNIQUE......Page 651
16.6 DIGITIZATION (DIG) DESIGN TECHNIQUE......Page 652
16.7 THE PSUEDO-CONTINUOUS-TIME (PCT) CONTROL SYSTEM......Page 654
16.7.1 Introduction to Psuedo-Continuous-Time System DIG Technique [1]......Page 655
16.7.2 MATLAB Design for Sec. 16.7.1......Page 657
16.7.3 Simple PCT Example......Page 660
Case 1: PCT Open-Loop Control System......Page 661
16.7.4 Sampled-Data Control System Example......Page 662
Case 3: The DIR Approach Using the Exact Z Transformation......Page 663
Case 4: The Tustin Control-Ratio Transfer Function......Page 664
16.7.6 PCT Design Summary......Page 666
16.9 DIRECT (DIR) COMPENSATOR......Page 668
16.10 PCT LEAD CASCADE COMPENSATION......Page 669
DIG (PCT) Design......Page 672
DIR Design (Exact z Domain Design): T¼0.1 s......Page 674
16.11 PCT LAG COMPENSATION......Page 675
16.11.1 MATLAB Design for Sec. 16.11......Page 678
16.12 PCT LAG-LEAD COMPENSATION......Page 680
16.12.1 MATLAB Design for Sec. 16.12......Page 684
16.13.1 General Analysis......Page 687
16.13.2 DIG Technique for Feedback Control......Page 691
16.14.1 PCT DIG Technique......Page 696
16.15.1 PCT DIG Example......Page 700
16.16 CONTROLLER IMPLEMENTATION [1]......Page 702
16.17 SUMMARY......Page 704
REFERENCES......Page 705
Problems......Page 707
Appendix A: Table of Laplace Transform Pairs......Page 782
B.2 MATRIX......Page 786
B.5 ADDITION AND SUBTRACTION OF MATRICES......Page 787
B.6 MULTIPLICATION OF MATRICES......Page 788
B.8 UNIT OR IDENTITY MATRIX......Page 789
B.11 ADDITIONAL MATRIX OPERATIONS AND PROPERTIES......Page 790
B.12 GENERALIZED DETERMINANT......Page 792
B.13 HERMITE NORMAL FORM......Page 794
B.14 MATRIX INVERSION BY ROW OPERATIONS......Page 795
B.15 EVALUATION OF THE CHARACTERISTIC POLYNOMIAL......Page 796
REFERENCES......Page 797
C.1 INTRODUCTION......Page 799
C.2 BASICS......Page 800
C.2.2 Matrix Transpose......Page 801
C.2.3 Range of Values......Page 802
C.3 DEFINING SYSTEMS......Page 805
C.3.2 State Space Model......Page 806
C.4.1 Root Locus......Page 808
C.4.2 Frequency Response......Page 809
C.5 SIMULATION......Page 810
C.6 IMPLEMENTATION OF RESULTS......Page 813
D.1 INTRODUCTION......Page 816
D.2 OVERVIEW OF TOTAL-PC......Page 817
D.3 QFT CAD PACKAGE......Page 820
REFERENCES......Page 822