Control Design Techniques in Power Electronics Devices

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1 Hebertt Sira-Ramfrez and Ramön Silva-Ortigoza Control Design Techniques in Power Electronics Devices With 202 Figures < } Spri inger g<

2 Contents 1 Introduction 1 Part I Modelling 2 Modelling of DC-to-DC Power Converters Introduction The Bück Converter Model of the Converter Normalization Equilibrium Point and Static Transfer Function A Bück Converter Prototype The Boost Converter Model of the Converter Normalization Equilibrium Point and Static Transfer Function Alternative Model of the Boost Converter A Boost Converter Prototype The Buck-Boost Converter Model of the Converter Normalization Equilibrium Point and Static Transfer Function A Buck-Boost Converter Prototype The Non-inverting Buck-Boost Converter Model of the Converter Normalization Equilibrium Point and Static Transfer Function The Cük Converter Model of the Converter Normalization Equilibrium Point and Static Transfer Function 37

3 XII Contents 2.7 The Sepie Converter Model of the Converter Normalization Equilibrium Point and Static Transfer Function The Zeta Converter Model of the Converter Normalization Equilibrium Point and Static Transfer Function The Quadratic Bück Converter Model of the Converter Normalized Model Equilibrium Point Static Transfer Function The Boost-Boost Converter Model of the Boost-Boost Converter Average Normalized Model Equilibrium Point and Static Transfer Function Alternative Model of the Boost-Boost Converter A Boost-Boost Converter Experimental Prototype The Double Buck-Boost Converter Model of the Double Buck-Boost Converter Average Normalized Model Equilibrium Point and Static Transfer Function Power Converter Models with Non-ideal Components A General Mathematical Model for Power Electronics Devices Some Illustrative Examples of the General Model 56 Part II Controller Design Methods 3 Sliding Mode Control Introduction Variable Structure Systems Control of Single Switch Regulated Systems Sliding Surfaces Notation Equivalent Control and the Ideal Sliding Dynamics Accessibility of the Sliding Surface Invariance Conditions for Matched Perturbations Control of the Boost Converter Direct Control Indirect Control Simulations Experimental Implementation Control of the Buck-Boost Converter 78

4 Contents XIII Direct Control Indirect Control Simulations Control of the Cük Converter Direct Control Indirect Control Simulations Control of the Zeta Converter Direct Control Indirect Control Simulations Control of the Quadratic Bück Converter Direct Control Indirect Control Simulations Multi-variable Gase Sliding Surfaces Equivalent Control and Ideal Sliding Dynamics Invariance with Respect to Matched Pertiirbations Accessibility of the Sliding Surface Control of the Boost-Boost Converter Direct Control Indirect Control Simulations Experimental Sliding Mode Control Implementation Control of the Double Buck-Boost Converter Direct Control Indirect Control Simulations A Modulation ^-Modulators Average Feedbacks and - A -Modulation A Hardware Realization of a 17 - A-Modulator Approximate Linearization in the Control of Power Electronics Devices Introduction Linear Feedback Control Pole Placement by Füll State Feedback Pole Placement Based on Observer Design Reduced Order Observers Flatness Generalized Proportional Integral Controllers Passivity Based Control A Hamiltonian Systems Viewpoint 139

5 XIV Contents 4.3 The Bück Converter Generalities about the Average Normalized Model Controller Design by Pole Placement Proportional-Derivative Control via State Feedback Trajectory Tracking Fliess' Generalized Canonical Forms State Feedback Control via Observer Design GPI Controller Design Passivity Based Control The Hamiltonian Systems Viewpoint Implementation of the Linear Passivity Based Control for the Bück Converter The Boost Converter Generalities about the Average Normalized Model Control via State Feedback Proportional-Derivative State Feedback Control Trajectory Tracking Fliess' Generalized Canonical Form State Feedback Control via Observer Design GPI Controller Design Passivity Based Control The Hamiltonian Systems Viewpoint The Buck-Boost Converter Generalities about the Model State Feedback Controller Design Dynamic Proportional-Derivative State Feedback Control Trajectory Tracking Fliess' Generalized Canonical Forms Control via Observer Design GPI Controller Design Passivity Based Control The Hamiltonian Systems Viewpoint Experimental Passivity based Control of the Buck-Boost Converter The Cük Converter Generalities about the Model The Hamiltonian System Approach The Zeta Converter Generalities about the Model The Hamiltonian System Approach The Quadratic Bück Converter Generalities about the Model State Feedback Controller Design The Hamiltonian System Approach 227

6 Contents XV 4.9 The Boost-Boost Converter Generalities about the Model The Hamiltonian System Approach Nonlinear Methods in the Control of Power Electronics Devices Introduction Feedback Linearization Isidori's Canonical Form Input-Output Feedback Linearization State Feedback Linearization The Boost Converter The Buck-Boost Converter The Cük Converter The Sepie Converter The Zeta Converter The Quadratic Bück Converter Passivity Based Control The Boost Converter The Buck-Boost Converter The Cük Converter The Sepie Converter The Zeta Converter The Quadratic Bück Converter Exact Error Dynamics Passive Output Feedback Control A General Result The Boost Converter Experimental Implementation The Buck-Boost Converter The Cük Converter The Sepie Converter The Zeta Converter The Quadratic Bück Converter The Boost-Boost Converter The Double Buck-Boost Converter Error Dynamics Passive Output Feedback The Boost Converter Experimental Results Control via Fliess' Generalized Canonical Form The Boost Converter The Buck-Boost Converter The Quadratic Bück Converter Nonlinear Observers for Power Converters Füll Order Observers The Boost Converter 333

7 XVI Contents The Buck-Boost Converter Reduced Order Observers The Boost Converter The Buck-Boost Converter GPI Sliding Mode Control The Bück Converter The Boost Converter The Buck-Boost Converter 355 Part III Applications 6 DC-to-AC Power Conversion Introduction Nominal Trajectories in DC-to-AC Power Conversion The Bück Converter Two-Sided E - A Modulation The Boost Converter The Buck-Boost Converter An Approximate Linearization Approach The Boost Converter The Buck-Boost Converter A Flatness Based Approach The Double Bridge Bück Converter The Boost Converter The Buck-Boost Converter A Sliding Mode Control Approach The Boost Converter A Feasible Indirect Inpvit Current Tracking Approach Exact Tracking Error Dynamics Passive Output Feedback Control The Double Bridge Bück Converter The Boost Converter The Buck-Boost Converter AC Rectiflers Introduction Boost Unit Power Factor Rectifier Model of the Monophasic Boost Rectifier The Control Objectives Steady State Considerations Exact Open Loop Tracking Error Dynamics and Controller Design Simulations 389

8 Contents XVII The Use of the Differential Flatness Property in the Passive Controller Design Simulations Three Phase Boost Rectifier The Tliree Phase Boost Rectifier Average Model A Statte Passivity Based Controller Trajectory Planning Switched Implementation of the Average Design Simulations A Unit Power Factor Rectifier-DC Motor System The Combined Rectifier-DC Motor Model The Exact Tracking Error Dynamics Passive Output Feedback Controller Trajectory Generation Simulations A Three Phase Rectifier-DC Motor System The Combined Three Phase Rectifier DC Motor Model The Exact Tracking Error Dynamics Passive Output Feedback Controller Trajectory Generation Simulations 412 References 415 Index 421

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