MATLAB: A Systems Tool for Design of Fuzzy LMI Controller in DC-DC Converters

Abstract

DC-DC switching converters are devices usually used to adapt primary energy sources to the load requirements (Erickson & Macksimovic, 2001). These devices produce a regulated output voltage despite changes in the feed voltage or in the load current. There are three basic topologies of dc-dc converters, namely the buck, the boost and the buck-boost converter. The buck converter is used to reduce output voltage, while the boost converter increase the output voltage. In the buck-boost converter, the output voltage can be maintained either higher or lower than the source but in the opposite polarity. These basic converters consist of two reactive elements; namely, an inductor and a capacitor, besides a transistor and a diode to perform the commutation, the size of reactive elements are chosen to guarantee a low level of ripple and hence an averaged dynamical model behavior is a good approximation of the switched behavior. In order to maintain a regulated output and to have a damped enough response some control loops are added to command the converter. The signal which drives the transistor used to be a squared, constant-period and high frequency signal. The design of the control loops is commonly based on linearized dynamic models around equilibrium point of the converter (Erickson & Macksimovic, 2001). Nevertheless, commonly the averaged dynamical models of these plants are nonlinear and their linearization is non minimum phase. Therefore, using linear controllers can only ensures stability and dynamic performances around equilibrium point, and hence, instabilities or bad performances may appear when large signal perturbations occur. This fact has prompted several authors to apply nonlinear control methods to regulate switching converters. Some of the first researches on nonlinear controller design for dc-dc converters can be found in the studies of (Sanders & Verghese, 1992) and (Kawasaki et al., 1995). These authors propose non-linear strategies based on Lyapunov functions, which allows the converter to ensure stability over a wide range of operating conditions. More recent studies are those of (Leyva et al., 2006) and (He & Luo, 2006) which derive robust non-linear controller for large-signal stability in dc-dc converters and present efficient implementations. Furthermore, robust control approaches have been applied in dc-dc converters which take into account nonlinearities and uncertainties (Olalla et al., 2009; 2010). Another promising nonlinear technique for controlling power converters is the model-based fuzzy control technique. The model-based fuzzy approaches begin by constructing the MATLAB: A Systems Tool for Design of Fuzzy LMI Controller in DC-DC Converters 13