Analysis of Nonlinear Switched System using Statistical Method

Abstract

Fokker-Planck equations are equations in statistical mechanics which defines the evolution of probability of states under the influence of random perturbations. It has found its application to physical and theoretical systems including stochastically perturbed switched electrical networks. The switched electrical networks contribute significantly in the power sector and day to day life. These converters are greatly subjected to noise-both intrinsic and extrinsic. These perturbations and switching uncertainties affect the performance of the converters which includes instability, chaos, bifurcation and component failure as well. However, noise modeling of power converter has received less attention in literature from system theoretic viewpoint. This paper does that. This paper discusses a novel state estimator for a noise influenced three phase PWM inverter is developed using Fokker-Planck analysis. Since sensors can be costly, may be difficult to mount (in specific cases), and may increase the overall system dimensions and complexity apart from loss of accuracy and reliability. In such cases Fokker Planck based estimators can serve as a full state observer for state measurement hence may lead to optimized system performance.