Analytical multi-parametric stability boundaries of DC-DC buck converters under V¹ control concept

Two main methods for controlling switching converters exist in the literature. The direct one is the voltage mode control, which suffers from some disadvantages such as slow response to load variations and an input voltage-dependent total loop gain. The current mode control can overcome these problems but at the expense of extra cost and more complex control design. V¹ concept is a new promising control technique for designing voltage mode control of buck-type converters with an optimal response similar to current mode control. In this paper, the dynamics and the stability of buck converters under V¹ control are studied. In particular, subharmonic oscillation limits in the parameter space are addressed. First, a closed-loop state-space model is derived and then used to formulate an analytical matrix-form expression for predicting the stability limit of the system. Using this expression, multi-parametric stability boundaries are obtained. It is shown that the equivalent series inductance of the output capacitor can narrow the stability region. It is also demonstrated that the integral action in the feedback loop of a V¹-controlled buck converter has a negligible effect on the subharmonic oscillation boundary. The theoretical analysis is validated through numerical simulation of the circuit-level switched model of the system.