Nonlinear controllability analysis of DC-DC converters using Lie Algebraic method

In the present study, the technique of Lie algebra has been applied to test controllability of nonlinear dynamical system of DC-DC converter. In order to perform this study, nonlinear controllability conditions comprising of Lie Algebra Rank Condition (LARC) and Sussman's theorem on small time local controllability has been applied. The DC-DC converter considered in this work has been found to be controllable, which is inferred from the plots of system states such as, current flowing through inductor and voltage across capacitor with respect to time. The controllability index has also been computed and the results obtained from nonlinear controllability analysis based on Lie Algebra are matched with the findings based on evaluated controllability index. DC-DC converter working in continuous current mode (CCM) has been simulated in MATLAB/SIMULINK and the system states have been found to be controllable for the different values of duty cycle and input voltage applied for this study. It is found that variation in both duty cycle and input voltage does not influence the controllability of DC-DC converter. The findings of this mathematical analysis and computer simulation based work are significant to understand the controllability status of the nonlinear dynamical systems of power electronic converters.