Nonlinear Dynamics and Interactions in Power Electronic Systems


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Virginia Tech


The nonlinear dynamics of PWM DC-DC switching regulators operating in the continuous conduction mode are investigated. A quick review of the existing analysis techniques and their limitations is first presented. A discrete nonlinear time-domain model is derived for open-loop DC-DC converters. This model is then extended for closed-loop regulator systems implementing any type of compensation scheme.

The equilibrium solutions of the closed-loop system are calculated and their stability is determined. The methods developed are used to study the dynamic behavior of a DC-DC buck regulator implementing different types of compensation design: proportional, integral, proportional-integral, and proportional-integral-derivative feedback control.

A detailed bifurcation analysis of the dynamic solutions as a design or a control parameter is changed is presented. A period-doubling route to chaos is shown to exist in voltage-mode regulators, depending on the values of the parameters of the compensator and the input voltage. An investigation of the behavior of the converter in the instability regions has been carried out to shed light on its bifurcations.

The interactions of input filters with DC-DC switching-mode regulators are investigated as well. It is shown that the small-signal averaged model widely used in the design of DC-DC regulators does not provide a complete understanding of the stability of the filter-regulator system. It can only provide the local borders of small-signal stable operation. The large-signal time-domain nonlinear averaged model is used to further understand the interaction on the slow scale using nonlinear analysis techniques. No fast scale interactions, however, can be predicted using this model. A complete nonlinear switching model is thus used to investigate the interaction of the filter and the regulator on all scales: fast and slow.



nonlinear dynamics, power electronics