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E-grāmata: Classical Feedback Control with Nonlinear Multi-Loop Systems: With MATLAB(R) and Simulink(R), Third Edition

(California Institute of Technology, Pasadena, USA), (California Institute of Technology, Pasadena, USA)
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Classical Feedback Control with Nonlinear Multi-Loop Systems: With MATLAB(R) and Simulink(R), Third EditionPalielināt

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Classical Feedback Control with Nonlinear Multi-Loop Systems describes the design of high-performance feedback control systems, emphasizing the frequency-domain approach widely used in practical engineering. It presents design methods for high-order nonlinear single- and multi-loop controllers with efficient analog and digital implementations. Bode integrals are employed to estimate the available system performance and to determine the ideal frequency responses that maximize the disturbance rejection and feedback bandwidth. Nonlinear dynamic compensators provide global stability and improve transient responses. This book serves as a unique text for an advanced course in control system engineering, and as a valuable reference for practicing engineers competing in today’s industrial environment.

Preface xiii
To Instructors xv
Authors xix
1 Feedback and Sensitivity 1(34)
1.1 Feedback Control System
1(2)
1.2 Feedback: Positive and Negative
3(1)
1.3 Large Feedback
4(2)
1.4 Loop Gain and Phase Frequency Responses
6(6)
1.4.1 Gain and Phase Responses
6(3)
1.4.2 Nyquist Diagram
9(2)
1.4.3 Nichols Chart
11(1)
1.5 Disturbance Rejection
12(1)
1.6 Example of System Analysis
13(4)
1.7 Effect of Feedback on the Actuator Nondynamic Nonlinearity
17(2)
1.8 Sensitivity
19(2)
1.9 Effect of Finite Plant Parameter Variations
21(1)
1.10 Automatic Signal Level Control
21(1)
1.11 Lead and PID Compensators
22(1)
1.12 Conclusion and a Look Ahead
23(1)
Problems
23(10)
Answers to Selected Problems
33(2)
2 Feedforward, Multi-Loop, and MIMO Systems 35(22)
2.1 Command Feedforward
35(3)
2.2 Prefilter and the Feedback Path Equivalent
38(1)
2.3 Error Feedforward
39(1)
2.4 Black's Feedforward
39(2)
2.5 Multi-Loop Feedback Systems
41(1)
2.6 Local, Common, and Nested Loops
42(1)
2.7 Crossed Loops and Main/Vernier Loops
43(2)
2.8 Block Diagram Manipulations and Transfer Function Calculations
45(3)
2.9 MIMO Feedback Systems
48(3)
Problems
51(6)
3 Frequency Response Methods 57(48)
3.1 Conversion of Time Domain Requirements to Frequency Domain
57(6)
3.1.1 Approximate Relations
57(4)
3.1.2 Filters
61(2)
3.2 Closed-Loop Transient Response
63(3)
3.3 Root Locus
66(1)
3.4 Nyquist Stability Criterion
67(3)
3.5 Robustness and Stability Margins
70(5)
3.6 Nyquist Criterion for Unstable Plants
75(2)
3.7 Successive Loop Closure Stability Criterion (Bode-Nyquist)
77(1)
3.8 Nyquist Diagrams for Loop Transfer Functions with Poles at the Origin
78(3)
3.9 Bode Phase-Gain Relation
81(4)
3.9.1 Minimum Phase Systems
81(1)
3.9.2 Phase-Gain Relation
82(3)
3.10 Phase Calculations
85(3)
3.11 From the Nyquist Diagram to the Bode Diagram
88(2)
3.12 More on Non-Minimum Phase Lag
90(1)
3.13 Ladder Networks and Parallel Connections of m.p. Links
91(2)
3.14 Other Bode Definite Integrals
93(4)
3.14.1 Integral of the Feedback
93(1)
3.14.2 Integral of the Imaginary Part
94(1)
3.14.3 Gain Integral over Finite Bandwidth
95(1)
3.14.4 Integral of the Resistance
95(2)
Problems
97(5)
Answers to Selected Problems
102(3)
4 Shaping the Loop Frequency Response 105(42)
4.1 Optimality of the Compensator Design
105(2)
4.2 Feedback Maximization
107(17)
4.2.1 Structural Design
107(1)
4.2.2 Bode Step
108(3)
4.2.3 Example of a System Having a Loop Response with a Bode Step
111(8)
4.2.4 Reshaping the Feedback Response
119(1)
4.2.5 Bode Cutoff
120(1)
4.2.6 Band-Pass Systems
121(1)
4.2.7 Nyquist-Stable Systems
122(2)
4.3 Feedback Bandwidth Limitations
124(11)
4.3.1 Feedback Bandwidth
124(1)
4.3.2 Sensor Noise at the System Output
125(2)
4.3.3 Sensor Noise at the Actuator Input
127(1)
4.3.4 Non-Minimum Phase Shift
128(1)
4.3.5 Plant Tolerances
129(2)
4.3.6 Lightly Damped Flexible Plants: Collocated and Non-Collocated Control
131(3)
4.3.7 Unstable Plants
134(1)
4.4 Coupling in MIMO Systems
135(2)
4.5 Shaping Parallel Channel Responses
137(4)
Problems
141(3)
Answers to Selected Problems
144(3)
5 Compensator Design 147(46)
5.1 Loop Shaping Accuracy
147(1)
5.2 Asymptotic Bode Diagram
148(3)
5.3 Approximation of Constant Slope Gain Response
151(1)
5.4 Lead and Lag Links
152(3)
5.5 Complex Poles
155(1)
5.6 Cascaded Links
156(4)
5.7 Parallel Connection of Links
160(1)
5.8 Simulation of a PID Controller
161(3)
5.9 Analog and Digital Controllers
164(1)
5.10 Digital Compensator Design
165(14)
5.10.1 Discrete Trapezoidal Integrator
165(2)
5.10.2 Laplace and Tustin Transforms
167(3)
5.10.3 Design Sequence
170(1)
5.10.4 Block Diagrams, Equations, and Computer Code
170(2)
5.10.5 Compensator Design Example
172(3)
5.10.6 Aliasing and Noise
175(2)
5.10.7 Transfer Function for the Fundamental
177(2)
Problems
179(5)
Answers to Selected Problems
184(9)
6 Analog Controller Implementation 193(42)
6.1 Active RC Circuits
193(11)
6.1.1 Operational Amplifier
193(2)
6.1.2 Integrator and Differentiator
195(1)
6.1.3 Noninverting Configuration
196(1)
6.1.4 Op-Amp Dynamic Range, Noise, and Packaging
197(1)
6.1.5 Transfer Functions with Multiple Poles and Zeros
198(2)
6.1.6 Active RC Filters
200(2)
6.1.7 Nonlinear Links
202(2)
6.2 Design and Iterations in the Element Value Domain
204(5)
6.2.1 Cauer and Foster RC Two-Poles
204(3)
6.2.2 RC-Impedance Chart
207(2)
6.3 Analog Compensator, Analog or Digitally Controlled
209(1)
6.4 Switched-Capacitor Filters
210(2)
6.4.1 Switched-Capacitor Circuits
210(1)
6.4.2 Example of Compensator Design
210(2)
6.5 Miscellaneous Hardware Issues
212(4)
6.5.1 Ground
212(1)
6.5.2 Signal Transmission
213(2)
6.5.3 Stability and Testing Issues
215(1)
6.6 PID Tunable Controller
216(4)
6.6.1 PID Compensator
216(2)
6.6.2 TID Compensator
218(2)
6.7 Tunable Compensator with One Variable Parameter
220(4)
6.7.1 Linear Fractional Transfer Function
220(1)
6.7.2 Symmetrical Regulator
221(2)
6.7.3 Hardware Implementation
223(1)
6.8 Loop Response Measurements
224(4)
Problems
228(4)
Answers to Selected Problems
232(3)
7 Linear Links and System Simulation 235(42)
7.1 Mathematical Analogies
235(6)
7.1.1 Electromechanical Analogies
235(3)
7.1.2 Electrical Analogy to Heat Transfer
238(1)
7.1.3 Hydraulic Systems
239(2)
7.2 Junctions of Unilateral Links
241(3)
7.2.1 Structural Design
241(1)
7.2.2 Junction Variables
241(2)
7.2.3 Loading Diagram
243(1)
7.3 Effect of the Plant and Actuator Impedances on the Plant Transfer Function Uncertainty
244(1)
7.4 Effect of Feedback on the Impedance (Mobility)
245(4)
7.4.1 Large Feedback with Velocity and Force Sensors
245(1)
7.4.2 Blackman's Formula
246(1)
7.4.3 Parallel Feedback
247(1)
7.4.4 Series Feedback
248(1)
7.4.5 Compound Feedback
248(1)
7.5 Effect of Load Impedance on Feedback
249(1)
7.6 Flowchart for Chain Connection of Bidirectional Two-Ports
250(8)
7.6.1 Chain Connection of Two-Ports
250(3)
7.6.2 DC Motors
253(1)
7.6.3 Motor Output Mobility
254(1)
7.6.4 Piezoelements
255(1)
7.6.5 Drivers, Transformers, and Gears
255(2)
7.6.6 Coulomb Friction
257(1)
7.7 Examples of System Modeling
258(3)
7.8 Flexible Structures
261(4)
7.8.1 Impedance (Mobility) of a Lossless System
261(1)
7.8.2 Lossless Distributed Structures
262(1)
7.8.3 Collocated Control
263(1)
7.8.4 Non-Collocated Control
264(1)
7.9 Sensor Noise
265(3)
7.9.1 Motion Sensors
265(2)
7.9.1.1 Position and Angle Sensors
265(1)
7.9.1.2 Rate Sensors
266(1)
7.9.1.3 Accelerometers
266(1)
7.9.1.4 Noise Responses
266(1)
7.9.2 Effect of Feedback on the Signal-to-Noise Ratio
267(1)
7.10 Mathematical Analogies to the Feedback System
268(1)
7.10.1 Feedback-to-Parallel-Channel Analogy
268(1)
7.10.2 Feedback-to-Two-Pole-Connection Analogy
269(1)
7.11 Linear Time-Variable Systems
269(2)
Problems
271(4)
Answers to Selected Problems
275(2)
8 Introduction to Alternative Methods of Controller Design 277(14)
8.1 QFT
277(3)
8.2 Root Locus and Pole Placement Methods
280(1)
8.3 State-Space Methods and Full-State Feedback
281(5)
8.3.1 Comments on Example 8.3
284(2)
8.4 LQR and LQG
286(1)
8.5 Hinfinity, µ-Synthesis, and Linear Matrix Inequalities
287(4)
9 Adaptive Systems 291(10)
9.1 Benefits of Adaptation to the Plant Parameter Variations
291(2)
9.2 Static and Dynamic Adaptation
293(1)
9.3 Plant Transfer Function Identification
294(1)
9.4 Flexible and N.P. Plants
294(1)
9.5 Disturbance and Noise Rejection
295(2)
9.6 Pilot Signals and Dithering Systems
297(2)
9.7 Adaptive Filters
299(2)
10 Provision of Global Stability 301(26)
10.1 Nonlinearities of the Actuator, Feedback Path, and Plant
301(2)
10.2 Types of Self-Oscillation
303(1)
10.3 Stability Analysis of Nonlinear Systems
304(2)
10.3.1 Local Linearization
304(1)
10.3.2 Global Stability
305(1)
10.4 Absolute Stability
306(1)
10.5 Popov Criterion
307(4)
10.5.1 Analogy to Passive Two-Poles' Connection
307(3)
10.5.2 Different Forms of the Popov Criterion
310(1)
10.6 Applications of Popov Criterion
311(1)
10.6.1 Low-Pass System with Maximum Feedback
311(1)
10.6.2 Band-Pass System with Maximum Feedback
311(1)
10.7 Absolutely Stable Systems with Nonlinear Dynamic Compensation
312(11)
10.7.1 Nonlinear Dynamic Compensator
312(1)
10.7.2 Reduction to Equivalent System
313(1)
10.7.3 Design Examples
314(9)
Problems
323(2)
Answers to Selected Problems
325(2)
11 Describing Functions 327(36)
11.1 Harmonic Balance
327(2)
11.1.1 Harmonic Balance Analysis
327(1)
11.1.2 Harmonic Balance Accuracy
328(1)
11.2 Describing Function
329(2)
11.3 Describing Functions for Symmetrical Piece-Linear Characteristics
331(4)
11.3.1 Exact Expressions
331(3)
11.3.2 Approximate Formulas
334(1)
11.4 Hysteresis
335(3)
11.5 Nonlinear Links Yielding Phase Advance for Large-Amplitude Signals
338(2)
11.6 Two Nonlinear Links in the Feedback Loop
340(1)
11.7 NDC with a Single Nonlinear Nondynamic Link
341(3)
11.8 NDC with Parallel Channels
344(2)
11.9 NDC Made with Local Feedback
346(3)
11.10 Negative Hysteresis and Clegg Integrator
349(2)
11.11 Nonlinear Interaction between the Local and the Common Feedback Loops
351(1)
11.12 NDC in Multi-Loop Systems
352(1)
11.13 Harmonics and Intermodulation
353(3)
11.13.1 Harmonics
353(2)
11.13.2 Intermodulation
355(1)
11.14 Verification of Global Stability
356(2)
Problems
358(3)
Answers to Selected Problems
361(2)
12 Process Instability 363(12)
12.1 Process Instability
363(1)
12.2 Absolute Stability of the Output Process
364(2)
12.3 Jump Resonance
366(4)
12.4 Subharmonics
370(2)
12.4.1 Odd Subharmonics
370(1)
12.4.2 Second Subharmonic
371(1)
12.5 Nonlinear Dynamic Compensation
372(1)
Problems
372(3)
13 Multiwindow Controllers 375(20)
13.1 Composite Nonlinear Controllers
375(2)
13.2 Multiwindow Control
377(2)
13.3 Switching from a Hot Controller to a Cold Controller
379(2)
13.4 Wind-Up and Anti-Wind-Up Controllers
381(3)
13.5 Selection Order
384(1)
13.6 Acquisition and Tracking
385(2)
13.7 Time-Optimal Control
387(1)
13.8 Examples
388(4)
Problems
392(3)
14 Nonlinear Multi-Loop Systems with Uncertainty 395(10)
14.1 Systems with High-Frequency Plant Uncertainty
395(2)
14.2 Stability and Multi-Frequency Oscillations in Band-Pass Systems
397(1)
14.3 Bode Single-Loop System
398(1)
14.4 Multi-Input Multi-Output Systems
399(1)
14.5 Nonlinear Multi-Loop Feedback
399(3)
14.6 Design of the Internal Loops
402(1)
14.7 Input Signal Reconstruction
402(3)
Appendix 1: Feedback Control, Elementary Treatment 405(14)
Appendix 2: Frequency Responses 419(14)
Appendix 3: Causal Systems, Passive Systems and Positive Real Functions, and Collocated Control 433(2)
Appendix 4: Derivation of Bode Integrals 435(8)
Appendix 5: Program for Phase Calculation 443(4)
Appendix 6: Generic Single-Loop Feedback System 447(4)
Appendix 7: Effect of Feedback on Mobility 451(2)
Appendix 8: Regulation 453(4)
Appendix 9: Balanced Bridge Feedback 457(2)
Appendix 10: Phase-Gain Relation for Describing Functions 459(2)
Appendix 11: Discussions 461(14)
Appendix 12: Design Sequence 475(2)
Appendix 13: Examples 477(46)
Appendix 14: Bode Step Toolbox 523(24)
Appendix 15: Nonlinear Multi-Loop Feedback Control (Patent Application) 547(10)
Bibliography 557(4)
Notation 561(4)
Index 565
Boris J. Lurie worked for many years in the telecommunication and aerospace industries, and taught at Russian, Israeli, and American universities. He was a senior staff member of the Jet Propulsion Laboratory, California Institute of Technology.

Paul J. Enright currently works in the field of quantitative finance in Chicago. As a member of the technical staff at the Jet Propulsion Laboratory, California Institute of Technology, he designed attitude control systems for interplanetary spacecraft and conducted research in nonlinear control.
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