Modeling, Control, and Implementation of DC–DC Converters for Variable Frequency Operation

In this paper, novel small-signal averaged models for dc-dc converters operating at variable switching frequency are derived. This is achieved by separately considering the on-time and the off-time of the switching period. The derivation is shown in detail for a synchronous buck converter and the model for a boost converter is also presented. The model for the buck converter is then used for the design of two digital feedback controllers, which exploit the additional insight in the converter dynamics. First, a digital multiloop PID controller is implemented, where the design is based on loop-shaping of the proposed frequency-domain transfer functions. And second, the design and the implementation of a digital LQG state-feedback controller, based on the proposed time-domain state-space model, is presented for the same converter topology. Experimental results are given for the digital multiloop PID controller integrated on an application-specified integrated circuit in a 0.13 μm CMOS technology, as well as for the state-feedback controller implemented on an FPGA. Tight output voltage regulation and an excellent dynamic performance is achieved, as the dynamics of the converter under variable frequency operation are considered during the design of both implementations.