Exact Mathematical Analysis of DC-DC Converters Employing Type 3 Controllers

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Abstract
A new method for analysing the stability of dc-dc converters in closed-loop operation is developed. A generalized discrete model is proposed consisting of two nonlinear vector equations: the state equation and the nondynamic constraint. After model linearization, the classical technique of using characteristic multipliers can be applied. Several problems were solved regarding: the nondynamic constraint derivation; the steady-state operation point calculation; verifying that the parameters defining the steady-state operation point are located in the linear region and are not in the proximity of a saturated vicinity; partial derivatives determination and Jacobian calculation. The above concepts have been easily implemented in Matlab, allowing: determination of the parameter value for which instability occurs; to demonstrate that instability is installed with a Neimark-Sacker bifurcation; to prove that the proposed exact method predicts a much larger stable region, 327% higher compared to that predicted by the traditional approach. The theoretical considerations were accurately validated by computer simulation.

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