Bifurcation and chaos behaviors of Lyapunov function controlled PWM boost converter

Abstract

In this paper, we have derived the mathematical model of the Lyapunov function-based boost converter, which is essentially a voltage and current double-loop controller, and studied the stability of the closed-loop modulation system. The analysis shows that the Lyapunov function controlled boost converter is not globally asymptotically stable when the switching frequency is limited. We also used a Monodromy matrix to analyze the nonlinear dynamic behavior of the system. It is found that with the decrease of the reference current, the Monodromy matrix eigen multiplier gradually jumps from inside to the outside on the unit circle, and correspondingly, the converter will move from the period-one steady state to period-doubling state, and then period-doubling state to the chaotic state. Simulation and experimental results show that the theoretical analysis is correct.

Keywords

• Lyapunov function
• Boost converter
• Bifurcation
• Chaos