Ανάλυση - ερμηνεία της φυσικής συμπεριφοράς και εύρωστος έλεγχος διακοπτικών μετατροπέων ισχύος

Abstract

The subject of this thesis is the analysis and interpretation of the physical behavior and the robust control of switch mode dc-dc power converters. Switch mode dc-dc converters are known to exhibit a strongly non-linear behavior that is expressed by the emergence of subharmonic and chaotic oscillations. In this thesis, the core of this behavior is tracked down to the Pulse Width Modulation (PWM) technique that is used for all fixed frequency dc-dc converters. For the mathematical description of the above phenomena, a non-linear difference equation, with respect to the duty cycle d, is derived. The difference equation allows the calculation of the different periodic steady states as well as the determination of each solution's local stability. This method is developed for any converter topology and any control strategy and is applied to the Buck dc-dc and the Boost dc-dc converter, under Proportional and Proportional-Integral control. The application of this analysis reveals the complicated dynamics of dc-dc converters and shows that only a ripple- free error voltage can secure their stable operation. Based on this principle, two new control methods are applied to the Buck dc-dc converter. The first, the Internal Model Control, has its origin in the robust control techniques used in chemical procedures. Its main advantage when applied to the Buck dc-dc converter is the production of a ripple-free error voltage, without the interference of any filtering that would cause undesired delays to the system's dynamics. The controller is designed by application of the H∞, norm on the system's sensitivity function and alternatively, on the complementary sensitivity function as well. The second method presents a discrete-time approach, by introducing sample and hold circuits both at the input and the output of the error amplifier. By this, the duty cycle is determined at the beginning of each switching period. Thus, the system is mathematically described by means of the pulse transfer function in the z domain. The controller is realized as an analog circuit and is designed by applying the FL norm on the system's complementary sensitivity function.