Modeling, Design and Control of Non-isolated Single-Input Multi-Output Zeta–Buck–Boost Converter

In this article, we focus on the analytical modeling of nonisolated single-input multiple-output (SIMO) dc-dc converters governed by linear differential algebraic equations (DAEs). The modeling challenge in nonisolated SIMO converters arises due to the switching among multiple DAEs governing the circuit. Averaged models of such converters, described by an ordinary differential equation, are derived using the notion of quasi-Weierstrass transformation. Using this technique, we derive the averaged model for a nonisolated Zeta-Buck-Boost (ZBB) converter. It is observed that the dynamics of the state variable corresponding to the algebraic constraint is uncontrollable and eliminating this state leads to a fourth-order completely controllable averaged model. This model is used to design a linear state-feedback controller for line regulation. In the case of bipolar SIMO converters, ZBB being an example, regulation of the two outputs can be achieved using any one of the two output integral states. Although the state-feedback controller successfully rejects the disturbance asymptotically, it is found that the deviations from the set point in the transient phase can be large. To see if smaller deviations can be achieved by appending the linear controller with a nonlinear term, we explore a nonlinear controller based on the Lyapunov redesign technique. Smaller deviations with complete disturbance rejection are possible if the disturbance is matched. When it is unmatched, small deviations are achieved at the expense of steady-state errors, whose estimate is explicitly found. The proposed model and control scheme are verified through a laboratory built hardware prototype.