Stabilization of periodic orbits of the buck converter by time‐delayed feedback

Time-delay autosynchronization (TDAS) can be used to stabilize unstable periodic orbits in dynamical systems. The technique involves continuous feedback of signals delayed by the orbit's period so that the feedback signal vanishes on the target orbit and hence the later is a solution of the original dynamical system. Furthermore, this control method only requires the knowledge of the period of the unstable orbit. The feedback gain needed to achieve stabilization varies with the bifurcation parameter(s) of the system, resulting in a domain of control, the computation of which requires, in general, detailed information about the target orbit(s). In this paper we compute the domain of control of the unstable periodic orbits of the PWM controlled buck converter for a couple of TDAS schemes. For both schemes we get an analytical expression for the closed curve whose index determines the stability, and this index is then numerically computed. We run several simulations of the controlled systems and discuss the results. The main result is that TDAS greatly increases the range of values of the input voltage where the PWM control yields a periodic orbit with a small rippling.