Linear control system analysis and design : conventional and modern

목차 (Table of Contents)

• CONTENTS
• Preface = xv
• 1. Introduction = 1
• 1.1 Introduction = 1
• 1.2 Introduction to Control Systems = 1
• 1.3 Definitions = 7
• 1.4 Historical Background = 9
• 1.5 Digital Control Development = 13
• 1.6 Mathematical Background = 15
• 1.7 General Nature of the Engineering Control Problem = 17
• 1.8 Outline of Text = 18
• 2. Writing System Equations = 21
• 2.1 Introduction = 21
• 2.2 Electric Circuits and Components = 23
• 2.3 Basic Linear Algebra = 27
• 2.4 State Concepts = 30
• 2.5 Transfer Function and Block Diagram = 36
• 2.6 Mechanical Translation Systems = 37
• 2.7 Analogue Circuits = 43
• 2.8 Mechanical Rotational Systems = 44
• 2.9 Thermal Systems = 49
• 2.10 Hydraulic Linear Actuator = 53
• 2.11 Positive-Displacement Rotation Hydraulic Transmission = 58
• 2.12 Liquid-Level System = 60
• 2.13 Rotating Power Amplifiers = 62
• 2.14 DC Servomotor = 63
• 2.15 AC Servomotor = 67
• 2.16 Lagrange's Equation = 68
• 2.17 Summary = 72
• 3. Solution of Different Equations = 73
• 3.1 Introduction = 73
• 3.2 Input to Control Systems = 74
• 3.3 Steady-State Response : Sinusoidal Input = 75
• 3.4 Steady-State Response : Polynomial Input = 77
• 3.5 Transient Response : Classical Method = 79
• 3.6 Definition of Time Constant = 83
• 3.7 Example : Second-Order System-Mechanical = 83
• 3.8 Example : Second-Order System-Electrical = 85
• 3.9 Second-Order Transients = 87
• 3.10 Time-Response Specifications = 90
• 3.11 State-Variable Equations = 91
• 3.12 Characteristic Values = 93
• 3.13 Evaluating the State Transition Matrix = 94
• 3.14 Complete Solution of the State Equation = 97
• 3.15 Discrete State Equation = 98
• 3.16 Summary = 100
• 4. Laplace Transform = 101
• 4.1 Introduction = 101
• 4.2 Definition of the Laplace Transform = 102
• 4.3 Derivation of Laplace Transforms of Simple Functions = 102
• 4.4 Laplace Transform Theorems = 104
• 4.5 Application of the Laplace Transform to Differential Equations = 106
• 4.6 Inverse Transformation = 108
• 4.7 Heaviside Partial-Fraction Expansion Theorems = 109
• 4.8 Partial-Fraction Shortcuts = 116
• 4.9 Graphical Interpretation of Partial-Fraction Coefficients = 117
• 4.10 Frequency Response from the Pole-Zero Diagram = 121
• 4.11 Location of Poles and Stability = 124
• 4.12 Laplace Transform of the Impulse Function = 125
• 4.13 Second Order System with Impulse Excitation = 127
• 4.14 Additional Matrix Operations and Properties = 128
• 4.15 Solution of State Equation = 134
• 4.16 Evaluation of the Transfer-Function Matrix = 136
• 4.17 Summary = 137
• 5. System Representation = 139
• 5.1 Introduction = 139
• 5.2 Block Diagrams = 140
• 5.3 Determination of the Overall Transfer Function = 144
• 5.4 Standard Block-Diagram Terminology = 146
• 5.5 Position-Control System = 149
• 5.6 Simulation Diagrams = 153
• 5.7 Signal Flow Graphs = 158
• 5.8 State Transition Signal Flow Graph = 163
• 5.9 Parallel State Diagrams from Transfer Functions = 167
• 5.10 Diagonalizing the A Matrix = 169
• 5.11 Use of State Transformation for the State Equation Solution = 177
• 5.12 Transforming a Matrix with Complex Eigenvalues = 178
• 5.13 Transforming an A Matrix into Companion Form = 180
• 5.14 Summary = 183
• 6. Control-System Characteristics = 185
• 6.1 Introduction = 185
• 6.2 Routh's Stability Criterion = 185
• 6.3 Mathematical and Physical Forms = 191
• 6.4 Types of Feedback Systems = 192
• 6.5 Analysis of System Types = 194
• 6.6 Example : Type 2 System = 200
• 6.7 Steady-State Error Coefficients = 201
• 6.8 Use of Steady-State Error Coefficients = 205
• 6.9 Nonunity-Feedback System = 207
• 6.10 Summary = 208
• 7. Root Locus = 209
• 7.1 Introduction = 209
• 7.2 Plotting Roots of a Characteristic Equation = 210
• 7.3 Qualitative Analysis of the Root Locus = 214
• 7.4 Procedure Outline = 217
• 7.5 Open-Loop Transfer Function = 218
• 7.6 Poles of the Control Ratio C(s)／R(s) = 218
• 7.7 Application of the Magnitude and Angle Condition = 220
• 7.8 Geometrical Properties(Construction Rules) = 225
• 7.9 Examples = 235
• 7.10 Frequency Response = 240
• 7.11 Performance Characteristics = 241
• 7.12 Transprot Lag = 246
• 7.13 Synthesis = 247
• 7.14 Summary of Root-Locus Construction Rules for Negative Feedback = 249
• 7.15 Summary = 250
• 8. Frequency Response = 252
• 8.1 Introduction = 252
• 8.2 Correlation of the Sinusoidal and Time Response = 253
• 8.3 Frequency-Response Curves = 254
• 8.4 Bode Plots(Logarithmic Plots) = 255
• 8.5 General Frequency-Transfer-Function Relationships = 257
• 8.6 Drawing the Bode Plots = 258
• 8.7 Example of Drawing the Bode Plot = 264
• 8.8 System Type and Gain as Related to Log Magnitude Curves = 268
• 8.9 Experimental Determination of Transfer Functions = 271
• 8.10 Direct Polar Plots = 271
• 8.11 Summary : Direct Polar Plots = 278
• 8.12 Inverse Polar Plots = 279
• 8.13 Nyquist's Stability Criterion = 283
• 8.14 Examples of Nyquist's Criterion Using Direct Polar Plot = 290
• 8.15 Nyquist's Stability Criterion Applied to Systems Having Dead Time = 294
• 8.16 Nyquist's Stability Criterion Applied to the Inverse Polar Plots = 295
• 8.17 Examples of Nyquist's Criterion Using the Inverse Polar Plots = 297
• 8.18 Definitions of Phase Margin and Gain Margin and Their Relation to Stability = 299
• 8.19 Stability Characteristics of the Log Magnitude and Phase Diagram = 302
• 8.20 Stability from the Nichols Plot(Log Magnitude-Angle Diagram) = 303
• 8.21 Summary = 305
• 9. Closed-Loop Tracking Performance Based on the Frequency Response = 307
• 9.1 Introduction = 307
• 9.2 Direct Polar Plot = 308
• 9.3 Determination of $$M_m$$ and $$ω_m$$ for a Simple Second-Order System = 309
• 9.4 Correlation of Sinusoidal and Time Responses = 313
• 9.5 Constant M(ω) and α(ω) Contours of C(jω)／R(jω) on the Complex Plane(Direct Polt) = 314
• 9.6 Contours in the Inverse Polar Plane = 324
• 9.7 Gain Adjustment for a Desired $$M_m$$ of a Unity-Feedback System : Direct Polar Plot = 327
• 9.8 Gain Adjustment for a Desired $$M_m$$ of a Unity-Feedback System : Inverse Polar Plot = 330
• 9.9 Constant M and α Curves on the Log Magnitude-Angle Diagram(Nichols Chart) = 332
• 9.10 Adjustment of Gain by Use of the Log Magnitude-Angle Diagram = 334
• 9.11 Correlation of the Pole-Zero Diagram with Frequency and Time Responses = 338
• 9.12 Summary = 341
• 10. Root-Locus Compensation = 343
• 10.1 Introduction = 343
• 10.2 Transient Response : Dominant Complex Poles = 346
• 10.3 Additional Significant Poles = 351
• 10.4 Root-Locus Design Considerations = 354
• 10.5 Reshaping the Root-Locus = 356
• 10.6 Ideal Integral Cascade Compensation(PI Controller) = 357
• 10.7 Cascade Lag Compensation Using Passive Elements = 358
• 10.8 Ideal Derivative Cascade Compensations(PD Controller) = 363
• 10.9 Lead Compensation Using Passive Elements = 365
• 10.10 General Lead-Compensator Design = 370
• 10.11 Lag-Lead Cascade Compensation = 371
• 10.12 Comparison of Cascade Compensators = 375
• 10.13 PID Controller = 377
• 10.14 Introduction to Feedback Compensation = 378
• 10.15 Feedback Compensation : Design Procedures = 380
• 10.16 Simplified Rate Feedback Compensation = 381
• 10.17 Rate Feedback = 383
• 10.18 Feedback of Second Derivative of Output = 387
• 10.19 Results of Feedback Compensation = 390
• 10.20 Rate Feedback : Plants with Dominant Complex Poles = 390
• 10.21 Summary = 391
• 11 Cascade and Feedback Compensation : Frequency-Response Plots = 393
• 11.1 Introduction = 393
• 11.2 Selection of a Cascade Compensator = 395
• 11.3 Cascade Lag Compensator = 398
• 11.4 Example : Cascade Lag Compensation = 401
• 11.5 Lead Compensator = 405
• 11.6 Example : Cascade Lead Compensation = 407
• 11.7 Lag-Lead Compensator = 412
• 11.8 Example : Cascade Lag-Lead Compensation = 414
• 11.9 Feedback Compensation Using Log Plots = 417
• 11.10 Example : Feedback Compensation(Log Plots) = 419
• 11.11 Application Guidelines : Basic Minor-Loop Feedback Compensators = 425
• 11.12 Summary = 426
• 12 Control-Ratio Modeling = 428
• 12.1 Introduction = 428
• 12.2 Modeling a Desired Tracking Control Ratio = 429
• 12.3 Guillemin-Truxal Design Procedure = 433
• 12.4 Introduction to Disturbance Rejection = 435
• 12.5 A Second-Order Disturbance-Rejection Model = 436
• 12.6 Disturbance-Rejection Design Principles for SISO Systems = 439
• 12.7 Disturbance-Rejection Design Example = 443
• 12.8 Disturbance-Rejection Models = 446
• 12.9 Summary = 450
• 13 Closed-Loop Pole-Zero Assignment(State-Variable Feedback) = 452
• 13.1 Introduction = 452
• 13.2 State-Variable Feedback = 453
• 13.3 General Properties of State Feedback(Using Phase Variables) = 456
• 13.4 State-Variable Feedback : Steady-State Error Analysis = 459
• 13.5 Use of Steady-State Error Coefficients = 462
• 13.6 Definition of Zero-Error Systems = 466
• 13.7 Controllability and Observability = 467
• 13.8 State-Variable Feedback : All Pole Plant = 473
• 13.9 Plant Complex Poles = 476
• 13.10 State-Variable Feedback : Pole-Zero Plant = 478
• 13.11 Summary = 486
• 14 Parameter Sensitivity and Inaccessible States = 488
• 14.1 Introduction = 488
• 14.2 Sensitivity = 488
• 14.3 Sensitivity Analysis = 492
• 14.4 Parameter Sensitivity Examples = 499
• 14.5 Inaccessible States = 499
• 14.6 Summary = 504
• 15 Liapunov's Second Method = 505
• 15.1 Introduction = 505
• 15.2 State-Space Trajectories = 506
• 15.3 Linearization(Jacobian Matrix) = 517
• 15.4 Quadratic Forms = 521
• 15.5 Stability = 527
• 15.6 Second Method of Liapunov = 529
• 15.7 Application of the Liapunov Method to Linear Systems = 534
• 15.8 Estimation of Transient Settling Time = 538
• 15.9 Summary = 540
• 16 Introduction to Optimal Control = 542
• 16.1 Introduction = 542
• 16.2 Development of the Solution-Time Criterion = 544
• 16.3 Control-Area Criterion = 546
• 16.4 Additional Performance Indexes = 547
• 16.5 Zero Steady-State Step-Error Systems = 549
• 16.6 Modern Control Performance Index = 552
• 16.7 Algebraic Riccati Equation = 556
• 16.8 Examples = 561
• 16.9 Bode Diagram Analysis of Optimal State-Variable-Feedback Systems = 563
• 16.10 Root-Square-Locus Analysis of Optimal State-Variable-Feedback Systems = 569
• 16.11 Determination of HFG Conditions = 572
• 16.12 Summary = 575
• 17 Optimal Design by Use of Quadratic Performance Index = 577
• 17.1 Introduction = 577
• 17.2 Basic System = 577
• 17.3 Quadratic Performance Index = 578
• 17.4 Steady-State Error Requirements = 580
• 17.5 Exact Correlation(Conventional vs. Modern) = 587
• 17.6 Correlation of Higher-Order Systems with All-Pole Plants = 590
• 17.7 Higher-Order System Correlation(Pole-Zero Plant) = 597
• 17.8 Analysis of Correlations Results = 604
• 17.9 A General Design Procedure = 605
• 17.10 Effect of Control Weighting = 606
• 17.11 Alternate Design Method = 608
• 17.12 Plant with Variable Parameters = 612
• 17.13 Summary = 617
• 18 Structural Properties of Linear Multivariable Control Systems = 619
• 18.1 Introduction = 619
• 18.2 State Feedback for SISO Systems = 620
• 18.3 Observers = 621
• 18.4 Control Systems Containing Observers = 624
• 18.5 State-Feedback Design for SISO Systems Using the Control Canonical Form = 626
• 18.6 Generalized Control Canonical From(GCCF) for MIMO Systems = 628
• 18.7 Pole Placement by State Feedback : MIMO Systems = 634
• 18.8 Effect of Eigenstructure of Time Response = 636
• 18.9 Entire Eigenstructure Assignment = 638
• 18.10 Eigenstructure Assignment for Observers = 640
• 18.11 Summary = 641
• 19 Synthesis of Linear Multivariable Regulators, Observers, and Trackers Using Entire Eigenstructure Assignment = 643
• 19.1 Introduction = 643
• 19.2 Examples of Entire Eigenstructure Assignment for Regulators = 644
• 19.3 Uncontrollable Systems = 649
• 19.4 Tracking Systems = 651
• 19.5 Tracking System Design Example = 653
• 19.6 Example of Observer Synthesis = 656
• 19.7 Summary = 657
• 20 Design of Tracking Systems Using Output Feedback = 660
• 20.1 Introduction = 660
• 20.2 Output Feedback Tracking System = 661
• 20.3 Block Diagonalization = 663
• 20.4 Analysis of Closed-Loop System Performance = 665
• 20.5 Design Procedure for Regular Plants = 667
• 20.6 Regular System Design Example = 669
• 20.7 Irregular Plant Characteristics = 671
• 20.8 Irregular System Performance = 674
• 20.9 Design of the Measurement Matrix M = 675
• 20.10 Irregular System Design Example = 677
• 20.11 Tracker Simulation = 680
• 20.12 Summary = 684
• 21 Quantitative : Feedback Theory(QFT) Technique = 686
• 21.1 Introduction = 686
• 21.2 Frequency Response with Parameter Variations = 688
• 21.3 Introduction to the QFT Method(Single-Loop System) = 690
• 21.4 Minimum-Phase System Performance Specifications = 692
• 21.5 Multiple-Input Multiple-Output(MIMO) Uncertain Plants = 695
• 21.6 Introduction to MIMO Compensation = 696
• 21.7 MIMO Compensation = 698
• 21.8 Justification of the MISO Equivalent Method = 699
• 21.9 Effective MISO Loops of the MIMO System = 701
• 21.10 Plant Templates of P(s), JP(j$$ω_i$$) = 703
• 21.11 U-Contour = 704
• 21.12 Tracking Bounds Lm $$B_R$$(jω) of the NC = 706
• 21.13 Disturbance Bounds $$B_D$$(j$$ω_i$$) : Case 1 [d₂(t) ＝ $$D_0$$$$u_{-1}$$(t), d₁(t) ＝ 0] = 713
• 21.14 Disturbance Bounds $$B_D$$(j$$ω_i$$) : Case 2 [d₁(t) ＝ $$D_0$$$$u_{-1}$$(t), d₂(t) ＝ 0] = 715
• 21.15 The Composite Boundary $$B_D$$(j$$ω_i$$) = 717
• 21.16 Shaping of $$L_o$$(jω) = 719
• 21.17 Guidelines for Shaping $$L_o$$(jω) = 724
• 21.18 Design of the Refilter F(s) = 725
• 21.19 Basic Design Procedure for a MISO System = 727
• 21.20 Design Example = 729
• 21.21 Unstable Plant Template Generation = 738
• 21.22 Summary = 740
• 22 Digital Control Systems = 743
• 22.1 Introduction = 743
• 22.2 Sampling = 744
• 22.3 z-Transform Theorems = 749
• 22.4 Synthesis in the z Domain(DIR Method) = 751
• 22.5 The Inverse z Transform = 753
• 22.6 Zero-Order Hold = 753
• 22.7 Digital-Computer Compensation = 755
• 22.8 s- to z-(or w-) Plane Transformation Methods = 757
• 22.9 Pseudo-Continuous-Time(PCT) Control System(DIG Method) = 762
• 22.10 Analysis of a Basic(Uncompensated) System = 764
• 22.11 Summary = 769
• Appendixes = 771
• A Table of Laplace Transform Pairs = 771
• B Interactive Computer-Aided-Design(CAD) Programs for Digital and Continuous Control- System Analysis and Synthesis = 775
• Problems = 783
• Answers to Selected Problems = 862
• Index = 877