Sensibility study of the control loops of voltage and current mode controlled DC-DC converters by means of robust parametric control theory

Robust parametric control theory is a powerful tool for the research of the robustness of linear control systems against simultaneous changes in the parameters that define the plant and controller transfer functions. The purpose of this paper is to show how those techniques can be applied to the sensibility study of voltage mode and current node controlled DC-DC converters with respect to simultaneous variations (or tolerances) of all the parameters of the power stage: line voltage, load and passive elements of the power stage (I, C, R_c…). After obtaining the small-signal linear model of the voltage or current mode controlled power stage, it is possible to represent the power stage transfer function as a linear interval plant, and to predict, once a regulator has been designed, the worst case bandwidth and stability margins of the converter control loop with all values of the power stage components varying simultaneously inside known and closed intervals, i.e., with any combination of those values. In fact, envelopes of the open and closed loop dynamic performance of the system can be obtained, in form of Bode and Nyquist plots envelopes. In this work, the robust parametric study of a buck converter under voltage and current mode (current injected control or CIC) control is shown, with the theoretical Bode and Nyquist envelopes obtained with MATLAB^TM software