Derivation of a second-order switching surface in the boundary control of buck converters

A second-order switching surface in the boundary control of buck converters is derived in this letter. The formulated switching surface can make the overall converter exhibit better steady-state and transient behaviors than the one with a first-order switching surface. The switching surface is derived by estimating the state trajectory movement after a switching action, resulting in a high state trajectory velocity along the switching surface. This phenomenon accelerates the trajectory moving toward the target operating point. The proposed control scheme has been successfully applied to a 120-W buck converter. The large-signal performance and a comparison with the first-order switching surface have been studied.