In many papers, the averaged model of power switching converters is used to design the control system due to its simple manipulation, which can be approximated by linear transfer functions. Therefore, the power converter commutation causes a state variable ripple that is not considered on the averaged model. The component frequency of the state variables is composed by a power spectrum with a unique peak at the DC level (average variable), a unique peak at the switching frequency (ripple component) and a finite number of peaks in each sub-harmonic (instabilities). The Filippov method is used for instability predictions due to fast dynamics, this method predicts the parameters range that avoids the first bifurcation of the fast dynamics. In this paper a stable space of parameters (Kp, Ti) for a PI controller is presented, it estimated with the Filippov method, for a buck converter with voltage regulation. Finally, the presented results are validated using both Matlab and Psim simulations.
Multi-phase converter; controller design; method of Filippov; instability; bifurcations; piecewise linear systems.