Stability analysis of two-cell Buck converter driven DC motor with a discrete-time closed loop

In this paper we deal with the dynamical behavior modeling, design and simulation of a two-cell DC-DC Buck converter driven DC motor. The angular velocity of the motor is controlled with a feedback loop through a Digital Pulse Width Modulation (DPWM). The stress of the switches of the converter are also balanced between the cells. Discrete time approach is used to obtain accurate information on the stability and to detect possible subharmonic oscillations quasi-periodic behavior and chaotic regimes. Under certain operating conditions, the switching model can be approximated by a three dimensional piecewise constant vector field and the corresponding the discrete time model is nonlinear map. We present a number of analytical, numerical and graphical tools that may be useful to study the dynamical behavior and stability of the fixed point of the map. Stability conditions are derived in terms of parameters. These results are confirmed by two-dimensional bifurcation diagrams.