Chaotic dynamics of a zero average dynamics controlled DC–DC Ćuk converter

The undesirable subharmonics in periodically driven non-linear systems such as switching power converters is a more common problem in power electronic circuits. Such operations are usually avoided by modifying the circuit parameters which necessitates a proper understanding of the system. In the present study, non-linear dynamic behaviour in a zero average dynamics (ZAD) controlled DC–DC Ćuk converter is investigated. The effects of varying the control parameters on the qualitative behaviour of the system are studied in detail. Bifurcation analysis of a ZAD controlled DC–DC Ćuk converter has not been reported so far in the literature as it involves complex modelling and implementation of the overall control system. To reduce the complexity in deriving the map dynamics and computing the ZAD control parameters, a reduced order model is derived. Moment matching technique is used to obtain the reduced order model. It is found that for even small control parameter variations, the system exhibits period-doubling bifurcation. The dynamics of this converter system has been mathematically described and analysed with a simple discrete map. Computer simulations as well as experimental investigations are performed to study the qualitative behaviour of the system under variations of different parameters. The results offer useful information of parameter space for the design and operation of the converter in the desired fundamental stable regime. Finally, a time-delay component is included in the ZAD control strategy and it is shown that the onset of chaos can be delayed.