Tesi etd-10022025-104519
Link copiato negli appunti
Tipo di tesi
Corso Ordinario Secondo Livello
Autore
PACINI, DIEGO
URN
etd-10022025-104519
Titolo
Modeling of PWM Buck Converters for Analog Control Design and Stability Analysis
Struttura
Classe Scienze Sperimentali
Corso di studi
INGEGNERIA - INGEGNERIA
Relatori
Tutor Prof. FORESTIERI, ENRICO
Relatore Prof. BRUSCHI, PAOLO
Relatore Prof. BRUSCHI, PAOLO
Parole chiave
- Buck
- PWM
- Small-Signal Models
- Voltage Mode Control
- Current Mode Comtrol
- Sampling
Data inizio appello
12/12/2025;
Disponibilità
completa
Riassunto analitico
This thesis develops a unified theoretical and methodological framework for the modeling, analysis, and control design of PWM buck converters operating under both voltage-mode and current-mode control. The work aims to derive analytical models that accurately capture converter dynamics, establish a systematic approach to feedback design, and clarify the mechanisms governing stability and performance in both continuous-time and sampled-data domains.
Starting from the fundamental principles of inductor volt–second balance and capacitor charge balance, the study derives a steady-state model based on the small-ripple approximation. Averaged modeling techniques, including state-space and circuit averaging, are presented and shown to be equivalent, forming the basis for linearized control-oriented representations of the converter and enabling accurate low-frequency analysis.
The analysis of voltage-mode control integrates the converter’s averaged model with the feedback network to derive key transfer functions and compensation strategies. The design of multi-pole, multi-zero compensators ensures the desired crossover frequency, phase margin, and transient response. The study then extends the framework to current-mode control, introducing an inner current loop that enhances dynamic response and simplifies compensation. Analytical derivations highlight the role of current feedback in reducing system order and improving stability, while identifying the compensation ramp slope as a critical parameter for preventing subharmonic oscillations.
A cascade control methodology is established, following a sequential design approach that ensures appropriate time-scale separation between inner and outer loops. The work further refines the averaged model by incorporating the effects of sampling through a sampled-data formulation. This extension explains the onset of discrete-time phenomena, such as subharmonic oscillations, and provides conditions for maintaining stable operation. A modified averaged model with an additional modulator pole bridges the gap between continuous and discrete representations, offering improved accuracy without losing analytical tractability.
Overall, the thesis demonstrates that averaged and sampled-data models are complementary analytical tools. Their integration yields a comprehensive understanding of converter dynamics across all relevant frequencies. The proposed framework unifies classical and modern control perspectives, providing rigorous design guidelines that enhance stability, robustness, and performance in both analog and digitally implemented switching converters.
Starting from the fundamental principles of inductor volt–second balance and capacitor charge balance, the study derives a steady-state model based on the small-ripple approximation. Averaged modeling techniques, including state-space and circuit averaging, are presented and shown to be equivalent, forming the basis for linearized control-oriented representations of the converter and enabling accurate low-frequency analysis.
The analysis of voltage-mode control integrates the converter’s averaged model with the feedback network to derive key transfer functions and compensation strategies. The design of multi-pole, multi-zero compensators ensures the desired crossover frequency, phase margin, and transient response. The study then extends the framework to current-mode control, introducing an inner current loop that enhances dynamic response and simplifies compensation. Analytical derivations highlight the role of current feedback in reducing system order and improving stability, while identifying the compensation ramp slope as a critical parameter for preventing subharmonic oscillations.
A cascade control methodology is established, following a sequential design approach that ensures appropriate time-scale separation between inner and outer loops. The work further refines the averaged model by incorporating the effects of sampling through a sampled-data formulation. This extension explains the onset of discrete-time phenomena, such as subharmonic oscillations, and provides conditions for maintaining stable operation. A modified averaged model with an additional modulator pole bridges the gap between continuous and discrete representations, offering improved accuracy without losing analytical tractability.
Overall, the thesis demonstrates that averaged and sampled-data models are complementary analytical tools. Their integration yields a comprehensive understanding of converter dynamics across all relevant frequencies. The proposed framework unifies classical and modern control perspectives, providing rigorous design guidelines that enhance stability, robustness, and performance in both analog and digitally implemented switching converters.
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