Nonlinear Control Systems

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CRC Press, Feb 4, 2003 - Technology & Engineering - 408 pages
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This text emphasizes classical methods and presents essential analytical tools and strategies for the construction and development of improved design methods in nonlinear control. It offers engineering procedures for the frequency domain, as well as solved examples for clear understanding of control applications in the industrial, electrical, process, manufacturing, and automotive industries. The authors discuss Properties of nonlinear systems, stability, linearization methods, operating modes and dynamic analysis methods, phase trajectories in dynamic analysis of nonlinear systems, and harmonic linearization in dynamic analysis of nonlinear control systems operating in stabilization mode.
 

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Contents

Properties of Nonlinear Systems
1
12 Basic Mathematical and Structural Models of Nonlinear Systems
4
13 Basic Specific Properties of Nonlinear Systems
13
14 Stability and Equilibrium States
23
15 Basic Properties of Nonlinear Functions
25
16 Typical Nonlinear Elements
29
162 Nonlinear Elements with SingleValued Discontinuous Characteristics
32
163 Nonlinear Elements with DoubleValued Characteristics
34
52 Methods of Defining Phase Trajectories
206
521 Estimation of Stability and Performance by Means of Phase Trajectories
214
53 Examples of Application of Various Methods to Obtain Phase Trajectories
218
54 Conclusion
224
Harmonic Linearization in Dynamic Analysis of Nonlinear Control Systems Operating in Stabilization Mode
227
611 Analysis of Symmetrical SelfOscillations
229
612 Analytical Stability Criterion of SelfOscillations
237
613 Determination of Symmetrical SelfOscillations
242

164 Nonlinear Elements with MultiValued Characteristics
36
17 Atypical NonStandard Nonlinear Elements
41
18 Basic Nonlinearity Classes
44
19 Conclusion
46
Stability
49
21 Equilibrium States and Concepts of Stability
51
211 Stability of a Nonlinear System Based on Stability of the Linearized System
53
22 Lyapunov Stability
56
221 Definitions of Stability
57
222 Lyapunov Direct Method
64
23 Absolute Stability
100
24 Absolute Stability of Equilibrium States of an Unforced System Popov Criterion
108
241 Geometrical Interpretation of Popov Criterion
110
242 Absolute Stability with Unstable Linear Part
115
25 Examples of Determining Absolute Stability by Using Popov Plot
119
26 Absolute Stability of an Unforced System with TimeVarying Nonlinear Characteristic
124
27 Absolute Stability of Forced Nonlinear Systems
133
271 Absolute Stability of Forced Nonlinear Systems with an Unstable Linear Part
135
28 Conclusion
138
Linearization Methods
141
31 Graphical Linearization Methods
142
32 Algebraic Linearization
144
33 Analytical Linearization Method Linearization in the Vicinity of the Operating Point
146
34 Evaluation of Linearization Coefficients by LeastSquares Method
152
35 Harmonic Linearization
155
36 Describing Function
159
37 Statistical Linearization
168
38 Combined DualInput Describing Functions
174
39 Conclusion
179
Operating Modes and Dynamic Analysis Methods
181
411 SelfOscillations
182
412 Forced Oscillations
184
42 Methods of Dynamic Analysis of Nonlinear Systems
188
Phase Trajectories in Dynamic Analysis of Nonlinear Systems
191
51 Phase Plane
193
512 Phase Trajectories of Nonlinear Systems
201
614 Asymmetrical SelfOscillationsSystems with Asymmetrical Nonlinear Static Characteristic
244
615 Asymmetrical SelfOscillationsSystems with Symmetrical Nonlinear Characteristic
251
616 Reliability of the Describing Function Method
258
62 Forced Oscillations of Nonlinear Systems
260
622 Asymmetrical Forced Oscillations
269
623 Resonance Jump
272
63 Conclusion
281
Harmonic Linearization in Dynamic Analysis of Nonlinear Control Systems in Tracking Mode of Operation
283
72 Dynamic Analysis of Nonlinear Control Systems in Tracking Mode of Operation with Forced Oscillations
294
Performance Estimation of Nonlinear Control System Transient Responses
305
81 Determining Symmetrical Transient Responses Near Periodic Solutions
306
82 Performance Diagrams of Nonlinear System Transient Responses
317
Describing Function Method in Fuzzy Control Systems
325
91 Basics of Fuzzy Logic
326
912 Fuzzy Sets Fundamentals
327
913 Crisp and Fuzzy Sets and Their Membership Functions
328
914 Fuzzy Set Parameter Presentation
331
915 Basic Operation on Fuzzy Sets in Control Systems
333
916 Language Variable Operators
337
917 General Language Variable Operators
338
918 Fuzzy Relations
339
919 Fuzzy Relational Equations
342
9110 Use of Language Variables and Language Expressions
343
9111 Fuzzification
344
9112 Language Description of the System by Means of IF THEN Rules
345
9113 Language Description of the System with Fuzzy Decision Making
348
9114 Defuzzification or Fuzzy Set Adjustment Calculating Crisp Output Values
350
92 Describing Function of SISO Fuzzy Element
352
93 Stability Analysis of a Fuzzy Control System
355
94 Influence of Fuzzy Regulator on Resonance Jump
361
Harmonic Linearization
365
Popov Diagrams
375
Bibliography
379
Index
389
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