complex behavior of switching power supply

laobo

Contents
Preface
1 Introduction
1.1 Overview of Power Electronics Circuits
1.1.1 Switching Power Converters
1.1.2 Voltage-Mode Control
1.1.3 Current-Mode Control
1.1.4 Complexity of Operation
1.2 Overview of Modeling Strategies for Switching Converters
1.2.1 From Nonlinear Models to Linear Models
1.2.2 Back to Nonlinear Models
1.3 Overview of Nonlinear Dynamical Systems
1.3.1 Qualitative Behavior of Dynamical Systems
1.3.2 Bifurcation
1.3.3 Deterministic Chaos
1.3.4 Quantifying Chaos
1.3.5 Routes to Chaos
1.4 Complex Behavior in Power Electronics
2 Computer and Laboratory Techniques for StudyingNonlinear
Behavior in Switching Power Converters
2.1 The Use and Misuse of Computer Simulations
2.1.1 Improper Choice of Models
2.1.2 Insufficient Resolution
2.2 Accuracy of Models: Does It Matter?
2.3 Mode of Investigation
2.4 Capturing Complex Behavior on Computers
2.4.1 Time-Evolution Behavior under Fixed Parameters
2.4.2 Bifurcation Behavior under Varying Parameters
2.5 Test for Chaos: The Lyapunov Exponent
2.5.1 Computing Lyapunov Exponents from Iterative Maps
2.5.2 Computing Lyapunov Exponents from Time Series
2.6 Laboratory Investigation
2.6.1 Capturing Waveforms, Phase Portraits and Frequency Spectra
2.6.2 Capturing Poincar′e Sections on Oscilloscopes
2.6.3 Plotting Bifurcation Diagrams on Oscilloscopes
2.6.4 Alternative Methods of Plotting Bifurcation Diagrams
in the Laboratory
2.7 Roles of Laboratory Experiments and Computer Simulations
3 Modeling of Switching Power Converters for Nonlinear
Dynamical Analysis
3.1 A Glimpse at Discrete-Time Modeling
3.1.1 Ad Hoc Derivation of the Discrete-Time Iterative Map
for the Boost Converter
3.1.2 Steady-State Solution
3.1.3 Approximation by Series Expansion
3.2 General Procedure for Derivation of Discrete-Time Iterative
Maps for the Basic Switching Converters
3.2.1 Continuous Conduction Mode
3.2.2 Discontinuous Conduction Mode
3.3 Approximation of Iterative Maps by Series Expansions
3.4 Approximate Iterative Maps for the Boost and Buck
Converters
3.4.1 Continuous Conduction Mode
3.4.2 Discontinuous Conduction Mode
3.5 The Method of Averaging
3.5.1 General Procedure
3.5.2 Averaged Models for the Boost and Buck Converters
3.5.3 Steady-State Solutions
3.5.4 Averaged Circuit Models
3.6 Control Law to Complete the Model
3.7 Determination of the Boundary of Operating Modes
3.8 Border Collision: A Trivial Case
3.9 Pros and Cons of the Models
4 Analysis of Period-Doubling Bifurcation in Switching
Converters Operating in Discontinuous Conduction Mode
4.1 Review of the Derivation of Iterative Maps
4.2 The Closed-Loop System and Control Equation
4.3 Period-Doubling Bifurcation
4.4 Computer Simulations
4.5 Experimentation
4.5.1 Circuit Operation
4.5.2 Experimental Observations
4.6 Recapitulation of Basic Phenomenology
5 Bifurcation Behavior in Switching Power Converters: Smooth
versus Non-Smooth Bifurcations
5.1 A Quick Glimpse at Complexity
5.1.1 Buck Converter Operating in Continuous Conduction
Mode under Simple Voltage Feedback Control
5.1.2 Bifurcation Behavior from Simulations and
Measurements
5.1.3 A Zoo of Complex Behaviors
5.1.4 “Skipped” Cycles and Border Collision
5.2 Current-Mode Controlled Switching Converters
5.2.1 Overview of Operation
5.2.2 Derivation of the Describing Iterative Map
5.3 Initial Simulation Study of the Boost Converter under
Current-Mode Control
5.4 Bifurcation Behavior of the Open-Loop Current-Mode
Controlled Boost Converter
5.4.1 Analysis via the Iterative Map
5.4.2 Bifurcation Diagrams Based on the Iterative Map
5.4.3 Bifurcation Diagrams Based on Circuit Simulations
5.4.4 Experimental Verification
5.5 Theoretical Analysis of Period-Doubling Bifurcation and
Border Collision
5.5.1 Analysis of Period-Doubling
5.5.2 Analysis of Border Collision
5.6 Bifurcation Behavior of the Closed-Loop Current-Mode
Controlled Boost Converter
5.7 Border Collision: Is It Important?
6 Nonlinear Dynamics of the ′ Cuk Converter
6.1 Review of the ′
Cuk Converter and Its Operation
6.2 Bifurcation Behavior for Fixed-Frequency Operation
6.2.1 Fixed-Frequency Current-Mode Control
6.2.2 Analysis of Bifurcation Behavior
6.2.3 Verification by Computer Simulations
6.2.4 Interim Conclusion on the Basic Phenomenology
6.3 Bifurcation Behavior for Free-Running Operation
6.3.1 Autonomous System Modeling
6.3.2 Dimensionless Equations
6.3.3 Stability of Equilibrium Point and Hopf Bifurcation
6.3.4 Local Trajectories from Describing Equation
6.3.5 Computer Simulations
6.4 Recapitulation
7 Bifurcation Behavior of Parallel-Connected Buck Converters
via Discrete-Time Models
7.1 Parallel-Connected Switching Converters
7.1.1 The Basic Issue of Current Sharing
7.1.2 The Master-Slave Scheme for Current Sharing
7.2 State Equations for Two Parallel Buck Converters
7.3 Initial Simulation Study
7.4 Experimentation
7.5 Analysis of Period-Doubling Bifurcation
7.5.1 Derivation of the Discrete-Time Map
7.5.2 Derivation of the Jacobian
7.5.3 Characteristic Multipliers and Period-Doubling
Bifurcation
7.6 Analysis of Border Collision
7.7 A Remark on Modeling: Can It Be Simpler?
8 Slow-Scale Bifurcation Behavior of Parallel-Connected Boost
Converters via Averaged Models
8.1 The System of Parallel-Connected Boost Converters
8.2 Initial Experimentation
8.3 Averaged Model for Two Parallel Boost Converters
8.3.1 Derivation of State Equations
8.3.2 Dimensionless Equations
8.3.3 Equilibrium Point Calculation
8.4 Stability of Equilibrium Point and Hopf Bifurcation
8.5 Local Trajectories from the Averaged Equations
8.6 Computer Simulation Study
8.7 Usefulness of Averaged Models
9 Fast-Scale Bifurcation Analysis of Power-Factor-Correction
Boost Converters
9.1 Bifurcation Analysis of Boost Converters under Current-Mode
Control with Ramp Compensation
9.1.1 Review of Basic Operation
9.1.2 Review of Period-Doubling Bifurcation
9.1.3 Ramp Compensation from a Bifurcation Control
Viewpoint
9.2 Application to Power-Factor-Correction Boost Converter
9.2.1 Bifurcation Analysis
9.2.2 Fast-Scale Instability by Computer Simulations
9.3 A Note on Fast-Scale and Slow-Scale Instabilities
10 Intermittent Chaotic Operation in Switching Power
Converters
10.1 Simplified Model of Spurious Signal Intrusion
10.2 Quick Glimpse at “Intermittent” Chaos
10.3 Time-Bifurcation Diagrams – A Closer Look
10.3.1 Sinusoidal Intruding Source
10.3.2 Rectangular Pulse Intruding Source
10.4 Experimental Observations
10.5 Parameters Affecting the Occurrence of “Intermittent” Chaos
10.6 Summary of the Basic Phenomenon

luoxianliang

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fireworker

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wqd4488

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weii

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