Filtering of Noisy Nonlinear Buck Converter with CPL Using Carleman Linerization

Abstract

The paper includes a novel approach for filtering of nonlinear Buck converter with Constant Power Load in noisy environment based on the Carleman linearization approach. The procedure starts with the modeling of Buck converter with Constant Power Load using Hamiltonian framework resulting in the deterministic model of network i.e., a finite dimensional system of ordinary differential equations. To evaluate the effect of noise on it, a Gaussian noise is embedded in the network through switch, which results in the development of stochastic state model and noise present at measurement terminals is considered for measurement equations. Using Carleman linearization approach, the finite-dimensional nonlinear model is transmuted into a bilinear model of infinite-dimension which can be approximated for any chosen order. As a result, we arrive at the finite-dimensional bilinear model of Buck converter with augmented state vector of higher dimension than the original system. State estimation of stochastic dynamical systems in the presence of noisy measurements is an interesting problem and hence, filtering technique is adopted here. The filtering equations in Itô setting are derived for bilinear systems using probabilistic approach for state estimation. The superiority of the proposed bilinear filtering technique over the benchmark EKF is demonstrated by the numerical simulations.