Model Predictive Control for Multi-Phase Buck .WITH 7-VOLT AMPLITUDE ... PWM Pulse Width Modulation

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  • Universidad Politcnica de Madrid

    Escuela Tcnica Superior de Ingenieros Industriales

    Departamento de Automtica, Ingeniera Electrnica e Informtica Industrial

    Mster Universitario en Electrnica Industrial

    Model Predictive Control for Multi-Phase Buck Converter with Variable Output Voltage

    Autor: Giuseppe Catalanotto

    Tutor: Jess A. Oliver, scar Garca

    Abril 2012

    Trabajo Fin de Mster

  • Contents 3

    Model Predictive Control for Multi-Phase Buck Converter with Variable Output Voltage

    Contents

    Contents ........................................................................................................ 3

    List of Figures .............................................................................................. 5

    List of Tables ................................................................................................ 6

    List of abbreviations ..................................................................................... 7

    Acknowledgments ........................................................................................ 9

    Resumen ..................................................................................................... 10

    Abstract ....................................................................................................... 13

    Introduction ................................................................................................ 15

    Chapter: 1 Modeling a MP Buck Converter .............................................. 19

    I. Choice of the converter ..................................................................................................... 19

    I. The Switched model ........................................................................................................... 22

    II. Large Signal Model ............................................................................................................. 23

    III. Discrete time model ............................................................................................................ 26

    IV. The Multi - Frequency Model ............................................................................................ 27

    Chapter: 2 Proposed Control Approach .................................................... 31

    I. Introduction to Model Predictive Control ..................................................................... 31

    II. Integral action ..................................................................................................................... 34

    III. State reference tracking ....................................................................................................... 37

    IV. Delay compensator .............................................................................................................. 41

    Chapter: 3 Control Architecture ................................................................ 45

    I. Regulator Design ................................................................................................................ 45

    II. Control Architecture .......................................................................................................... 48

    III. New Digital multi-phase PWM ......................................................................................... 50

    IV. ADC resolution and data precision .................................................................................. 52

    Chapter: 4 Simulation and Experimental Results ..................................... 55

  • 4 Contents

    Model Predictive Control for Multi-Phase Buck Converter with Variable Output Voltage

    I. Simulation Results .............................................................................................................. 55

    II. Validation ............................................................................................................................. 56

    Conclusions ................................................................................................ 63

    References .................................................................................................. 64

  • List of Figures and Tables 5

    Model Predictive Control for Multi-Phase Buck Converter with Variable Output Voltage

    List of Figures

    FIGURE 1: COMPARISON BETWEEN ANALOG AND DIGITAL REGULATORS COST ........................... 15

    FIGURE 2: SCHEME OF A RF TRANSMITTER .......................................................................... 16

    FIGURE 3: LOSSES IN RF AMPLIFIERS WITH CONSTANT SUPPLY VOLTAGE .................................. 17

    FIGURE 4: TYPICAL FREQUENCY RESPONSE AND BANDWIDTH OF A CONVERTER .......................... 19

    FIGURE 5: PICTURE OF THE FOUR-PHASE CONVERTER ............................................................ 21

    FIGURE 6: SWITCHED MODEL USED FOR VALIDATION ............................................................ 22

    FIGURE 7: CCM BUCK POSSIBLE CONFIGURATION ................................................................ 23

    FIGURE 8: BUCK EQUIVALENT MODEL ................................................................................ 24

    FIGURE 9: SWITCHED MODEL VS. AVERAGED MODEL ........................................................... 25

    FIGURE 10: DISCRETE-TIME MODEL VALIDATION ................................................................. 27

    FIGURE 11: LIMITS OF THE AVERAGED MODEL ..................................................................... 28

    FIGURE 12 FUNCTIONING OF MPC .................................................................................... 31

    FIGURE 13: STRICTLY-PROPER INTEGRAL ACTION.................................................................. 34

    FIGURE 14: NON-STRICTLY PROPER INTEGRAL ACTION .......................................................... 35

    FIGURE 15: ANTI WIND-UP INTEGRAL ACTION ..................................................................... 37

    FIGURE 16: MPC SCHEME ............................................................................................... 38

    FIGURE 17: OVERALL CONTROL SCHEME WITH INTEGRAL ACTION ........................................... 39

    FIGURE 18: OVERALL CONTROL SCHEME WITHOUT INTEGRAL ACTION ...................................... 40

    FIGURE 19: EFFECT OF THE DELAY COMPENSATOR ................................................................ 41

    FIGURE 20: KALMAN PREDICTOR ...................................................................................... 42

    FIGURE 21: EXAMPLE OF CROSSOVER ................................................................................ 46

    FIGURE 22: EXAMPLE OF MUTATION ................................................................................. 46

    FIGURE 23: CHOSEN REFERENCE FOR WEIGHTS OPTIMIZATION ............................................... 48

    FIGURE 24: PROPOSED CONTROL SCHEME .......................................................................... 49

    FIGURE 25: FPGA CONTROL ARCHITECTURE....................................................................... 50

  • 6 List of Figures and Tables

    Model Predictive Control for Multi-Phase Buck Converter with Variable Output Voltage

    FIGURE 26: TIMING DIAGRAM SHOWING THE FUNCTIONING OF THE NEW MPM ....................... 51

    FIGURE 27: MULTI-PHASE CONVERTER ............................................................................... 51

    FIGURE 28: COMPARISON BETWEEN THE PROPOSED APPROACH AND CONVENTIONAL REGULATOR ............................................................................................................................ 55

    FIGURE 29: CLOSED LOOP AND OPEN LOOP GAIN OF THE DESIGN OF A CONVENTIONAL REGULATOR ............................................................................................................ 56

    FIGURE 30: PROPOSED MPC CONTROLLER TRACKING A 50 KHZ SIGNAL .................................. 57

    FIGURE 31: PROPOSED MPC CONTROLLER TRACKING A 50 KHZ SIGNAL .................................. 57

    FIGURE 32: CONVENTIONAL REGULATOR TRACKING 100 KHZ REFERENCE SIGNAL ...................... 58

    FIGURE 33: PROPOSED MPC CONTROLLER TRACKING A 100 KHZ SIGNAL ................................ 58

    FIGURE 34: PROPOSED MPC CONTROLLER TRACKING A 200 KHZ SIGNAL ................................ 59

    FIGURE 35: COMPARISON WITH A CONVENTIONAL REGULATOR TRACKING A SIGNAL AT 400 KHZ IN ALL THE OUTPUT VOLTAGE RANGE .............................................................................. 59

    FIGURE 36: COMPARISON WITH A CONVENTIONAL REGULATOR TRACKING A SIGNAL AT 400 KH WITH 7-VOLT AMPLITUDE ......................................................................................... 60

    FIGURE 37: ROBUSTNESS UNDER 20% VARIATION OF THE LOAD ............................................. 60

    List of Tables

    TABLE 1: CHARACTERISTIC OF THE CONVERTER .................................................................... 20

    TABLE 2: CHARACTERISTIC OF THE CONVERTER .................................................................... 21

  • List of abbreviations 7

    Model Predictive Control for Multi-Phase Buck Converter with Variable Output Voltage

    List of abbreviations

    ADC Analog Digital Converter

    CCM Continuous Conduction Mode

    CPU Central Processing Unit

    DCM Discontinuous Conduction Mode

    DMM Digital Multiphase Modulator

    DSP Digital Signal Processor

    DVS Dynamic Voltage Scaling