Stability Analysis of A Third Order DC to DC Converter by Considering Input Current as Output Vector

Luo converters are used in various application because of low ripple, high voltage gain with less number of components. In the literature Luo converter was analysed for voltage gain, output voltage control etc. but the stability of the third order system was not analysed. In this paper the stability was analysed by root locus method. Initially the state space modelling was applied by considering input current as the output vector and the input to output transfer function is obtained. The transfer function reveals that the third order system falls under the category of marginally stable system. In order to bring it in to a stable system a PID controller was designed for the third order system. The performance of the PID system for the third order system was compared with  that of the transfer function when it was split in to first order and second order transfer function. For the marginally stable second order transfer function a PID controller, lead compensator and notch filter was designed. The split transfer function performance of lead, notch filter was compared with the PID of the third order system.