Discrete-Time Poles and Dynamics of Discontinuous Mode Boost and Buck Converters Under Various Control Schemes
Provides a unified analytical framework for power electronics engineers to understand and design control schemes for DC-DC converters in discontinuous mode.
The paper analyzes the discrete-time dynamics of boost and buck converters in discontinuous conduction mode under seven control schemes, deriving a single-pole model that accurately predicts behavior. The model matches exact switching simulations and prior results, revealing that compensating ramp does not affect pole location in current-mode boost converters.
Nonlinear systems, such as switching DC-DC boost or buck converters, have rich dynamics. A simple one-dimensional discrete-time model is used to analyze the boost or buck converter in discontinuous conduction mode. Seven different control schemes (open-loop power stage, voltage mode control, current mode control, constant power load, constant current load, constant-on-time control, and boundary conduction mode) are analyzed systematically. The linearized dynamics is obtained simply by taking partial derivatives with respect to dynamic variables. In the discrete-time model, there is only a single pole and no zero. The single closed-loop pole is a linear combination of three terms: the open-loop pole, a term due to the control scheme, and a term due to the non-resistive load. Even with a single pole, the phase response of the discrete-time model can go beyond -90 degrees as in the two-pole average models. In the boost converter with a resistive load under current mode control, adding the compensating ramp has no effect on the pole location. Increasing the ramp slope decreases the DC gain of control-to-output transfer function and increases the audio-susceptibility. Similar analysis is applied to the buck converter with a non-resistive load or variable switching frequency. The derived dynamics agrees closely with the exact switching model and the past research results.