A stable energy-based control strategy for DC-DC boost converter circuits

This paper has proposed a new switching scheme for controlling DC-DC boost converter circuits and presented the stability analysis by using the method of multiple Lyapunov functions. The DC-DC boost converter is modeled to operate in three modes of operations. The switching among these three modes depends on capacitor output voltage and inductor peak current. The inductor peak current is calculated from the basic principle of energy balance. Whatever energy is lost by the capacitor to the load, the same amount of energy has to be gained by the inductor. The minimum load resistance is also calculated to determine the maximum energy transfer to the load. The stability of this scheme is analyzed in the phase plane and the stability of the limit cycle is established by using multiple Lyapunov functions. In particular, it is shown that state trajectories in the phase plane reach a stable limit cycle and remain there. Different Lyapunov functions are defined for different modes that are shown to be positive and decreasing whenever the corresponding mode is active. The simulation results demonstrate the performance of the proposed scheme under various load conditions and sudden input and load disturbances. Stability of the limit cycle is established analytically and illustrated through the simulation results.