Effective Mathematical Modeling for Design of Feedback Control System in ZETA Converter

Abstract

This study presents a mathematical modeling approach to design a feedback control system in a ZETA converter to facilitate pole-zero cancellation. The state-space averaging method was employed to derive the transfer functions, and the number of terms in these functions was reduced by imposing conditions on the circuit parameters that are consistent with the circuit design methodology and do not adversely affect circuit operation. Moreover, the transfer functions are systematically organized based on assumptions regarding the relationship between parasitic resistance and damping coefficient. This organization elucidates the relationship between resonance frequencies, damping coefficients, zero frequencies, and circuit parameters within the transfer functions.

Additionally, because of the resonance elements, the ZETA converter imposes severe constraints on the stability margin in control system design. As the current-mode control (CMC) can suppress the effects of resonance elements, the one-round transfer function of the feedback control system with CMC applied to the ZETA converter is modeled. The modeling mathematically evaluates the CMC control systems with feedback of each current for the two inductor currents in the ZETA converter. The results indicate that the control system with feedback of the inductor current near the output part can more effectively suppress resonance elements.