Nonlinear Phenomena in Pulse Width Modulated Feedback Controlled Systems

Nonlinear phenomena in two phases piecewise LTI systems are analyzed. Dealing with closed loop pulse width modulated second order systems with a linear state feedback control, impacts are defined as the intersections of the control voltage with the periodic carrier signal. Using this definition, a new discrete time nonlinear mapping, the impact map, is defined and compared with the stroboscopic map which is usually adopted to model piecewise LTI systems. Also, it is shown how the impact map allows one to obtain analytical conditions for the periodic orbits and the flip bifurcations. Moreover, independently of the system operating conditions, a sort of grazing bifurcation is illustrated to occur when the control signal is tangent to the carrier signal. The results presented have an interesting application in current and voltage controlled dc/dc converters.